DC4Former: Orientation-Stable UAV Disaster Image Segmentation via Diagonal-Complemented C4 Consistency

Highlights

What are the main findings?

• DC4Former improves UAV disaster segmentation stability by combining $C_4$-consistent operators with a single ${45}^{\circ }$ training augmentation.
• On RescueNet, the three-seed worst-angle foreground mIoU improves from 54.90% to 67.66%, and the eight-angle standard deviation decreases from 4.17 to 0.33.

What are the implications of the main findings?

• Rotation-wise evaluation should complement canonical-orientation mIoU in UAV disaster mapping.
• The method improves reliability under changing image orientation with an associated increase in inference latency.

Abstract

UAV disaster imagery is often acquired under varying flight headings and camera yaw orientations, which can change the in-plane orientation of the observed scene. We propose DC4Former, an orientation-stable segmentation framework built on LRFormer. The architecture-only variant, C4Former, targets four grid-preserving rotations ($0^{\circ }$, ${90}^{\circ }$, ${180}^{\circ }$, and ${270}^{\circ }$) by redesigning three rotation-sensitive operations: stride-1 spatial convolution, strided downsampling, and low-resolution pooling attention. It uses $C_4$-symmetrized kernels, feature-rotation-averaged downsampling, and aligned four-view pooling attention with constrained branch fusion. DC4Former further adds a single ${45}^{\circ }$ rotation augmentation during training to improve empirical robustness at diagonal angles while retaining $C_4$ as the grid-preserving architectural basis. FloodNet and RescueNet experiments use an eight-angle protocol and a 24-angle stress test. Compared with LRFormer, DC4Former increases the three-seed worst-angle foreground mIoU from 70.14% to 76.83% on FloodNet and from 54.90% to 67.66% on RescueNet, while reducing the RescueNet eight-angle standard deviation from 4.17 to 0.33. Relative to LRFormer-RandRot, which adds no inference-time overhead, the observed deployment trade-off is dataset- and protocol-dependent. On FloodNet, LRFormer-RandRot has slightly higher All-8, Worst-8, Mean-24, and Worst-24 values. On RescueNet, it has higher Mean-24 and Worst-24 and a lower Std.-24, whereas DC4Former has higher All-8 and Worst-8 and a lower Std.-8 under the eight-angle protocol at increased inference latency. Taken together, these results show that operator-aware $C_4$ consistency combined with diagonal training exposure provides an architecture-level route to improved reliability across the eight principal orientations relative to the unmodified LRFormer backbone.

1. Introduction

UAVs provide very-high-resolution observations of damaged, inaccessible, and safety-critical areas, revealing roads, buildings, vegetation, water, vehicles, debris, and damaged infrastructure. Semantic segmentation converts these observations into pixel-level thematic maps that support emergency mapping, damage assessment, and recovery planning. Public benchmarks such as FloodNet [1] and RescueNet [2], together with recent aerial flood benchmarks and disaster-oriented segmentation studies [3,4,5], have facilitated the development and evaluation of UAV disaster-scene segmentation methods. These benchmarks and studies primarily report performance in the original image orientation. In deployment, however, UAV flight headings and camera yaw orientations can change across sorties or even within the same mission. The same road, building, vehicle, water boundary, or damaged region may therefore appear at different in-plane orientations while retaining the same semantic meaning. In-plane orientation variation differs from region, season, sensor, and spectral-domain shifts [6], yet it raises the same deployment concern: performance measured under one acquisition condition may not predict map repeatability under another. Canonical-orientation mIoU alone is therefore insufficient to measure the repeatability of UAV disaster maps under changing image orientations.

Two complementary strategies can be used to address orientation-dependent prediction variation. The first is training-time rotation augmentation, which exposes images and dense labels to additional orientations. This approach is straightforward, introduces no architectural inference overhead, and can provide a strong practical baseline. Nevertheless, the resulting robustness is learned implicitly from the sampled training transformations; augmentation does not directly constrain how internal spatial and token operations respond to rotation. The second strategy is architecture-level transformation modeling. Architecture-level approaches encode geometric priors through group-equivariant convolution, steerable filters, rotation-aware detection, and rotation-equivariant segmentation networks [7,8,9,10,11,12,13,14]. These studies show that transformation behavior can be addressed within network operators, although practical segmentation pipelines still face padding, interpolation, and spatial-alignment effects. Rotation augmentation supplies transformation exposure during training, whereas architecture-level consistency changes how the model responds to transformed inputs. The two approaches can be combined, and their usefulness varies with the dataset, reliability target, and inference budget.

This issue is particularly relevant to hierarchical segmentation Transformers. Modern segmentation models combine local convolution, multistage feature reduction, token pooling, and attention-based context aggregation. Representative CNN and Transformer architectures include FCN [15], U-Net [16], PSPNet [17], DeepLabv3+ [18], DenseASPP [19], Swin Transformer [20], SegFormer [21], MaskFormer [22], Mask2Former [23], and LRFormer [24]. LRFormer is especially relevant because it reduces attention cost by computing self-attention in a low-resolution token space. However, its spatial-token pathway contains several operations whose responses may change under image rotation, including convolutional positional encoding, local depthwise convolution, overlapping patch embedding, strided downsampling, adaptive token pooling, and low-resolution attention aggregation. These operations are coupled along the feature hierarchy: a rotated input changes the local sampling pattern seen by spatial convolutions, the altered responses are then subsampled by stride-dependent reductions, and the resulting tokens are pooled and aggregated by attention in a low-resolution coordinate system. Existing rotation-aware methods motivate explicit geometric modeling, but the combined effects of stride-1 convolution, strided sampling, token pooling, and attention within a hierarchical segmentation Transformer remain less systematically addressed. Modifying only a convolutional kernel or only an attention operation may therefore leave other orientation-sensitive stages in the spatial-token pathway unaddressed. Accordingly, we examine whether coordinated treatment of these operation classes can reduce right-angle inconsistency, whether one diagonal training representative can reduce the remaining orthogonal–diagonal gap, and how this design compares with continuous random-rotation augmentation under matched training exposure.

We address this gap using the four grid-preserving rotations of the discrete $C_4$ group: $0^{\circ }$, ${90}^{\circ }$, ${180}^{\circ }$, and ${270}^{\circ }$. These transformations map a regular square-pixel lattice onto itself through exact index permutations and can therefore be applied without interpolation. In contrast, diagonal rotations such as ${45}^{\circ }$, ${135}^{\circ }$, ${225}^{\circ }$, and ${315}^{\circ }$ require interpolation-based resampling and introduce additional boundary and sampling effects. We therefore use $C_4$ for the interpolation-free architectural path and evaluate diagonal rotations as a separate empirical robustness problem. The architecture-only variant, C4Former, redesigns three rotation-sensitive operation classes in LRFormer: stride-1 spatial convolution, strided downsampling, and low-resolution pooling attention. It uses $C_4$-symmetrized kernels, feature-rotation averaged downsampling, and aligned four-view pooling attention with constrained branch fusion.

To complement the grid-preserving $C_4$ construction, DC4Former introduces a single-diagonal augmentation (SDA) based on the discrete eight-angle decomposition

$$C_8=C_4\cup ({45}^{\circ }+C_4).$$

(1)

The ${45}^{\circ }$ transformation provides one training representative of the complementary diagonal set, while composition with the four $C_4$ rotations relates this representative to the remaining diagonal orientations. The diagonal transformation requires interpolation, and the complete segmentation pipeline contains finite boundaries, padding, decoder resizing, and bounded adaptive fusion. Under these practical conditions, C4Former targets approximate consistency over the four grid-preserving rotations, and DC4Former combines this architecture-level constraint with diagonal training exposure to improve empirical orientation stability over the evaluated eight-angle and 24-angle protocols.

We evaluate the proposed design on FloodNet and RescueNet through three complementary questions: whether the operator-aware $C_4$ redesign reduces right-angle inconsistency, whether single-diagonal exposure improves robustness beyond $C_4$, and how the resulting reliability compares with continuous random-rotation augmentation. The evaluation combines multi-seed eight-angle and 24-angle tests, internal feature/logit/prediction consistency diagnostics, complete operator ablations, matched RandRot controls, and inference-cost measurements. These analyses separate the effects of architecture-level consistency, diagonal training exposure, and computational cost.

The main contributions of this paper are summarized as follows:

• We develop an operator-aware $C_4$-consistent LRFormer backbone by separately redesigning three rotation-sensitive operation classes: stride-1 spatial convolution, strided downsampling, and low-resolution pooling attention. The attention pathway aligns four rotated low-resolution branches and applies constrained adaptive fusion as a bounded correction to uniform $C_4$ averaging. Together, these operator-specific designs form the C4Former architecture.
• We extend C4Former with a single ${45}^{\circ }$ diagonal training augmentation motivated by the discrete decomposition $C_8=C_4\cup ({45}^{\circ }+C_4)$. This design combines a grid-preserving $C_4$ architectural basis with training exposure to one representative of the complementary diagonal set, forming DC4Former. Because the augmentation is applied only during training, it introduces no additional inference cost relative to C4Former.
• We conduct a controlled multi-seed evaluation that combines matched RandRot controls, complete operator ablations, internal consistency diagnostics, eight-angle and 24-angle tests, and inference-cost measurements. The results characterize the respective contributions of architecture-level $C_4$ consistency and training-time rotation exposure, together with their dataset-dependent reliability–latency trade-off.

The present implementation is instantiated on LRFormer. Extending the same operator-aware design principle to other hierarchical segmentation Transformers and improving the reliability–latency trade-off remain directions for future work.

2. Related Work

2.1. UAV-Based Disaster Scene Segmentation

UAV disaster segmentation must separate roads, buildings, water, vegetation, vehicles, debris, and damage-related categories from very-high-resolution images acquired under varying flight headings. These scenes contain small structures, ambiguous water–land boundaries, occlusions, damaged regions, and visually similar categories. FloodNet [1] and RescueNet [2] provide representative post-disaster UAV benchmarks for this setting. FloodNet supports post-flood scene understanding with categories such as flooded buildings, flooded roads, water, vehicles, vegetation, and background, whereas RescueNet focuses on natural-disaster damage assessment with building-damage levels, blocked roads, vehicles, water, trees, and related scene classes.

Existing UAV disaster segmentation methods mainly improve canonical-orientation accuracy by strengthening contextual representation, multi-scale feature aggregation, domain adaptation, multimodal fusion, or flood-specific scene modeling. Comprehensive semantic segmentation studies on high-resolution UAV disaster imagery establish baseline comparisons and show that disaster categories such as flooded roads, damaged buildings, and debris-like regions remain challenging because of small object size and ambiguous boundaries [4]. Multitemporal and multisensor fusion methods improve flood segmentation by combining complementary observations [25], while adversarial domain adaptation reduces cross-domain gaps in flood mapping [26]. Recent lightweight Transformer and flood-focused designs further improve aerial disaster or flooded-region segmentation, including CSDNet for context-aware disaster aerial imagery segmentation [5], SwinSegFormer for aerial flood detection [27], and Flood-Eye for flooded-region segmentation and area estimation [28]. Recent aerial flood benchmarks also extend flood-focused segmentation and scene-understanding evaluation [3]. These methods improve segmentation accuracy, efficiency, cross-domain robustness, or flood-area assessment under the standard evaluation setting, but they do not explicitly evaluate whether predictions remain stable when the same UAV scene is observed under different in-plane rotations.

2.2. Semantic Segmentation Backbones

Semantic segmentation now relies on both CNN-based and Transformer-based architectures. Representative CNN methods established dense prediction baselines through encoder–decoder structures, pyramid pooling, and atrous spatial context aggregation, including FCN [15], U-Net [16], PSPNet [17], DeepLab [29], DeepLabv3+ [18], and DenseASPP [19]. Another line of work targets efficient segmentation with compact encoders, bilateral paths, or real-time Transformer blocks, including ENet [30], ERFNet [31], LEDNet [32], BiSeNetV2 [33], and RTFormer [34]. These designs improve accuracy-efficiency trade-offs, but they do not by themselves explicitly enforce stable predictions under rotated UAV inputs.

Transformer-based segmentation models use attention to model global context and multi-scale features. ViT [35] established the pure Transformer image backbone, after which Swin Transformer [20], PVT [36], SegFormer [21], MaskFormer [22], Mask2Former [23], and LRFormer [24] adapted hierarchical attention and mask prediction to dense segmentation. Recent Remote Sensing studies have also explored Mamba-based real-time segmentation, scalable Transformer segmentation for ultra-high-resolution imagery, and global–local context learning for remote sensing scenes [37,38,39]. LRFormer is particularly relevant here because it computes self-attention in a low-resolution space. This design reduces attention cost, but its patch embedding, strided downsampling, convolutional positional encoding, local enhancement, token pooling, and attention aggregation can still introduce orientation-dependent responses. High canonical-orientation mIoU alone may therefore be insufficient to characterize behavior under rotated UAV inputs.

Recent remote-sensing foundation-model studies also show that segmentation performance can degrade substantially under deployment-relevant distribution shifts. For example, SpectralX [6] uses parameter-efficient fine-tuning to adapt optical Remote Sensing Foundation Models to multispectral and hyperspectral semantic segmentation, and evaluates generalization across unseen regions and seasons. Although these shifts differ from in-plane rotation, this work provides broader motivation for evaluating remote-sensing segmentation models under the specific distribution changes expected at deployment, extending evaluation beyond performance measured under a single canonical condition.

2.3. Rotation Augmentation and Learned Invariance

Data augmentation is a widely used route to transformation robustness because it requires no architectural modification [40]. For semantic segmentation, an image and its dense label map can be jointly rotated to preserve spatial correspondence. However, training on rotated samples encourages robustness only implicitly and does not explicitly enforce that predictions commute with rotation. Moreover, the appropriate augmentation range is task-dependent. Augerino learns distributions over transformations jointly with model parameters, showing that the useful invariance range can be data-dependent [41]. Invariance-constrained augmentation further formalizes when and how strongly augmentation should be applied [42]. Dense random rotation expands orientation coverage but also increases interpolation exposure during training; we therefore evaluate it alongside architecture-level consistency instead of using it as the sole robustness mechanism.

2.4. Rotation-Equivariant and Rotation-Robust Networks

In contrast, architecture-level methods encode transformation priors directly into network operators. Group-equivariant convolutional networks [7] provide a foundational framework for convolution over discrete transformation groups such as rotations and reflections. Related studies exploit cyclic symmetry [43], encode rotation-equivariant vector fields [44], and design steerable filters or E(2)-equivariant CNNs [9,10,45]. For dense prediction, rotation-equivariant encoder–decoder networks improve sample efficiency and transformation robustness [12]. These studies make a practical point for segmentation: rotation stability depends on the feature representation and on how downsampling, upsampling, and output mapping handle transformed inputs.

In aerial and remote sensing analysis, rotation-aware representations are especially relevant because absolute object orientation is often arbitrary. RotEqNet has been applied to very-high-resolution land-cover mapping, where explicit rotation equivariance reduces parameter requirements while retaining semantic-labeling accuracy [46]. FRINet further targets rotation-invariant few-shot aerial image semantic segmentation, where support-query matching can be degraded by orientation changes [47]. ReDet [13] combines equivariant features with rotation-invariant RoI alignment for aerial object detection, while FRED extends the objective toward end-to-end rotation-equivariant oriented detection [48]. A recent aerial-detection study directly compares strict and approximate rotation equivariance and highlights conventional downsampling as a key source of equivariance error [49]. Other work revisits strict rotation equivariance under real-world symmetry-breaking conditions and suggests that relaxed formulations can better accommodate imperfectly symmetric visual data [50]. This distinction is relevant to UAV disaster imagery because finite boundaries, occlusions, anisotropic structures, and interpolation effects can break idealized rotational symmetry assumptions in practical image-processing pipelines.

For semantic segmentation, rotation consistency is demanding because the output prediction must remain spatially aligned with the input. PreCM [14] proposes a padding-based rotation-equivariant convolution mode and evaluates prediction disagreement under rotated inputs. The same study formulates strict equivariance over the four right-angle rotations and discusses interpolation as a key obstacle at non-right-angle rotations on discrete image grids. Recent segmentation benchmarks also argue that equivariant designs require direct segmentation evaluation [51]. Existing methods motivate explicit rotation modeling, but the combined effects of mixed convolutional, downsampling, pooling, and attention operations in LRFormer-like segmentation Transformers remain less systematically studied. Since strided subsampling can disrupt equivariance, group-equivariant subsampling has been studied as a dedicated problem [52]. We treat strided downsampling as a separate operation class in LRFormer.

2.5. Rotation-Consistent Transformers

These operator-level issues become more complex in attention-based models. Attentive group-equivariant CNNs show that group-structured features can be combined with adaptive weighting rather than only fixed averaging [53]. Group equivariant self-attention [54] and equivariant Vision Transformers [55] show that attention mechanisms can incorporate symmetry priors. Recent Transformer studies further show that tokenization, positional encoding, self-attention, and patch merging can affect equivariance or consistency [56,57,58]. For segmentation Transformers, rotation consistency must be considered at the tokenization and attention levels, not only at local convolutional layers.

Rotation-consistent segmentation Transformers remain challenging because dense prediction models contain multi-stage feature hierarchies and heterogeneous spatial operations. In LRFormer, rotation sensitivity may arise from convolutional positional encoding, IRB depthwise convolutions, overlapping patch embedding, strided downsampling, adaptive token pooling, and low-resolution attention interactions. Modifying only the attention operation or only the convolutional kernel may be insufficient for stable segmentation under rotated UAV inputs.

Motivated by this gap, our method targets the full spatial-token pathway of LRFormer. C4Former separately handles stride-1 spatial operators, strided downsampling operators, and low-resolution pooling attention. DC4Former then combines this architecture-level C4 consistency with a C4-complementary single-diagonal augmentation strategy. The method separates grid-preserving orthogonal rotations from interpolation-based diagonal rotations and evaluates stability across eight orientations with $C_4$ consistency as the architectural basis.

3. Materials and Methods

3.1. Overview of DC4Former

Throughout this section, scalars are written in italics, vectors in bold lowercase, and images, kernels, feature tensors, or spatial maps in bold uppercase; model and transformation symbols denote operators. Let $\mathbf{I}\in {\mathbb{R}}^{B\times 3\times H_0\times W_0}$ denote a batch of input UAV images, and let F denote a semantic segmentation model that outputs a logit tensor $\mathbf{L}=F\left(\mathbf{I}\right)\in {\mathbb{R}}^{B\times C_{\mathrm{cls}}\times H_0\times W_0}$ after resizing to the input resolution. Let $\mathcal{C}=\{0,\dots ,C_{\mathrm{cls}}-1\}$ denote the semantic class-index set. The corresponding prediction map is ${\widehat{\mathbf{M}}}_{b,h,w}=\arg {\max }_{c\in \mathcal{C}}{\mathbf{L}}_{b,c,h,w}$, with $\widehat{\mathbf{M}}\in {\mathcal{C}}^{B\times H_0\times W_0}$. For a counterclockwise rotation operator $R_k$ with angle $90k^{\circ }$, where $k\in \{0,1,2,3\}$, a $C_4$-consistent segmentation model is expected to approximately satisfy

$$F\left(R_k\mathbf{I}\right)\approx R_{k}F\left(\mathbf{I}\right),k\in \{0,1,2,3\}.$$

(2)

This approximate commutation relation means that rotating an input before inference should yield nearly the same result as rotating the corresponding prediction afterward. Here, the symbol ≈ denotes closeness after spatial alignment rather than exact pixel-wise equality. Small residual discrepancies can arise from image boundaries, padding, decoder interpolation, and bounded adaptive fusion. We use the term C4-consistent to emphasize this approximate implementation-level behavior under $C_4$ transformations. Directional feature learning and transformation consistency describe different properties: a model can learn orientation-dependent filters or features while leaving the relation between $F\left(\mathbf{I}\right)$ and the inverse-aligned response $R_{-k}F\left(R_k\mathbf{I}\right)$ unconstrained. Standard segmentation backbones can violate this relation more strongly because their spatial-token operations are not designed around $C_4$ transformations.

In this paper, C4 consistency denotes the architecture-level behavior targeted by C4Former for the four grid-preserving right-angle rotations. Orientation stability denotes the empirical stability of segmentation accuracy across the evaluated rotation protocols, including both the $C_4$ angles and the diagonal or intermediate angles. C4Former therefore addresses the in-group consistency part of the problem, whereas DC4Former combines C4Former with diagonal training exposure and is evaluated for broader orientation stability.

The method focuses on the four grid-preserving $C_4$ rotations, $0^{\circ }$, ${90}^{\circ }$, ${180}^{\circ }$, and ${270}^{\circ }$, because they map a regular square-pixel lattice onto itself through exact index permutations without interpolation. In contrast, rotations such as ${45}^{\circ }$, ${135}^{\circ }$, ${225}^{\circ }$, and ${315}^{\circ }$ require interpolation-based resampling and introduce boundary and sampling discrepancies. Inspection of LRFormer’s spatial-token pathway identifies three major sources of rotation sensitivity: stride-1 spatial operators, strided downsampling operators, and low-resolution pooling attention. C4Former introduces three corresponding designs:

• C4 weight symmetrization for stride-1 spatial convolutions;
• C4 feature-rotation averaging for strided downsampling layers;
• C4 multi-view formulation for low-resolution pooling attention.

DC4Former separates in-group consistency from out-of-group exposure. At the architecture level, C4Former replaces the rotation-sensitive parts of LRFormer with operator-aware $C_4$-consistent counterparts. At the training level, DC4Former adds a single diagonal representative. The encoder redesign targets interpolation-free $C_4$ rotations, whereas the ${45}^{\circ }$ augmentation exposes the model to a representative diagonal orientation without changing the inference pipeline.

Table 1. Operator-aware design summary of DC4Former.

Rotation-Sensitive Component	Source of Instability	Proposed Treatment
Stride-1 spatial convolution	Orientation-biased local kernels	$C_4$ weight symmetrization
Strided downsampling	Rotation changes the sampling lattice	$C_4$ feature-rotation averaging
Low-resolution pooling attention	Rotation changes the pooled-token layout	Aligned $C_4$ multi-view attention
Attention-branch fusion	Adaptivity limitation of uniform $C_4$ averaging	Constrained adaptive correction
Diagonal rotations	Outside the grid-preserving $C_4$ group	Single ${45}^{\circ }$ training-time augmentation

summarizes how each source of rotation sensitivity is addressed.

Figure 1 shows the DC4Former pipeline. Given an input UAV image, the encoder follows the multi-stage LRFormer-S backbone. Rotation-sensitive operators are replaced or reformulated according to their operator classes. Stride-1 spatial convolutions use C4 weight symmetrization, strided downsampling layers use C4 feature-rotation averaging, and low-resolution pooling attention uses a C4 multi-view formulation. The four encoder outputs are aggregated by a lightweight SegFormerHead MLP decoder, which is kept fixed for all LRFormer-family variants to isolate the effects of the encoder redesign and SDA.

DC4Former combines C4Former with single-diagonal augmentation during training. The augmentation exposes the model to ${45}^{\circ }$, which serves as one representative of the complementary diagonal coset evaluated at ${45}^{\circ }$, ${135}^{\circ }$, ${225}^{\circ }$, and ${315}^{\circ }$. Its main practical advantage is that it introduces no inference overhead relative to C4Former. We use neither a test-time rotation ensemble nor an auxiliary rotation-consistency loss. The design combines operator-level $C_4$ consistency with training-time diagonal exposure.

3.2. Operator-Aware C4-Consistent Encoder

The C4Former encoder applies a different consistency mechanism to each operation class because stride-1 convolution, strided sampling, and pooled-token attention respond differently to rotation. The following subsections describe these three coordinated treatments.

3.2.1. C4 Weight Symmetrization for Stride-1 Spatial Operators

LRFormer contains several stride-1 spatial operators, such as convolutional positional encoding and depthwise local enhancement in the IRB module. These operations preserve the spatial resolution, but their learned kernels may still become orientation-biased. For a stride-1 spatial convolution, let $\mathbf{X}\in {\mathbb{R}}^{B\times C_{\mathrm{in}}\times H\times W}$ denote the input feature tensor, let $\mathbf{K}\in {\mathbb{R}}^{C_{\mathrm{out}}\times C_{\mathrm{in}}/g\times q\times q}$ denote the convolution kernel with group number g and spatial kernel size $q\times q$, and let $\mathbf{Y}\in {\mathbb{R}}^{B\times C_{\mathrm{out}}\times H\times W}$ denote the output feature tensor under resolution-preserving padding. We construct a C4-symmetrized kernel by averaging its four orthogonal rotations:

$$\tilde{\mathbf{K}}={\displaystyle \frac{1}{4}}{\displaystyle \sum _{k=0}^3}{R}_k\left(\mathbf{K}\right).$$

(3)

The symmetrized kernel retains the shape of the learned kernel, $\tilde{\mathbf{K}}\in {\mathbb{R}}^{C_{\mathrm{out}}\times C_{\mathrm{in}}/g\times q\times q}$. Here, $R_k\left(\mathbf{K}\right)$ rotates only the two spatial kernel dimensions and does not permute the input or output channel indices. The output feature is then computed as

$$\mathbf{Y}=\mathbf{X}\ast \tilde{\mathbf{K}},$$

(4)

where $\ast$ denotes convolution.

The symmetrized kernel is invariant to $C_4$ rotation, i.e., $R_j\left(\tilde{\mathbf{K}}\right)=\tilde{\mathbf{K}}$ for any $j\in \{0,1,2,3\}$. Subject to compatible padding and boundary handling, convolution with this kernel commutes with $C_4$ rotation. Because the four kernels are averaged before convolution, the layer adds no learnable parameters and requires only one convolution per forward pass. We apply this operation to non-$1\times 1$ stride-1 spatial convolutions, including convolutional positional encoding and IRB depthwise convolutions.

3.2.2. C4 Feature-Rotation Averaging for Strided Downsampling

Kernel symmetrization is suitable for stride-1 convolutions, but it is insufficient for strided downsampling. The reason is that downsampling changes the spatial sampling grid, and the sampling positions after rotation are not equivalent to simply rotating the convolution kernel. Therefore, the downsampling operator itself must be treated as a rotation-sensitive component.

Let $S(·)$ denote a shared-weight strided downsampling operator that maps $\mathbf{X}\in {\mathbb{R}}^{B\times C_{\mathrm{in}}\times H\times W}$ to $S\left(\mathbf{X}\right)\in {\mathbb{R}}^{B\times C_{\mathrm{out}}\times H^{\prime }\times W^{\prime }}$, where $H^{\prime }$ and $W^{\prime }$ are determined by the stride, padding, and kernel size. Let $R_{-k}=R_k^{-1}$ denote inverse rotation. We define its $C_4$ feature-rotation averaged form as

$$S_{\mathrm{C}4}\left(\mathbf{X}\right)={\displaystyle \frac{1}{4}}{\displaystyle \sum _{k=0}^3}{R}_{-k}\left(S\left(R_k\mathbf{X}\right)\right).$$

(5)

After inverse alignment, each branch and the averaged output satisfy $R_{-k}\left(S\left(R_k\mathbf{X}\right)\right),$$S_{\mathrm{C}4}\left(\mathbf{X}\right)\in {\mathbb{R}}^{B\times C_{\mathrm{out}}\times H^{\prime }\times W^{\prime }}$. Specifically, the input feature is rotated into four orthogonal coordinate systems, processed by the same shared-weight downsampling operator, inversely aligned, and averaged. Re-indexing the summation shows that, under grid-preserving rotations and compatible boundary handling, $S_{\mathrm{C}4}\left(R_j\mathbf{X}\right)=R_j{S}_{\mathrm{C}4}\left(\mathbf{X}\right)$. Unlike kernel symmetrization alone, this formulation explicitly accounts for the rotated sampling lattice.

Compared with stride-1 kernel symmetrization, this operation is more computationally demanding because it evaluates four rotated branches. Therefore, we apply it only to strided spatial embedding layers, including the stem and overlapping patch-embedding layers, where rotation changes the sampling lattice directly. It adds computation but does not introduce additional learnable parameters.

3.2.3. C4 Multi-View Low-Resolution Pooling Attention with Constrained Fusion

The original LRFormer reduces attention cost by computing self-attention over low-resolution pooled tokens. However, token pooling layouts and attention interactions may change when the input feature map is rotated. As a result, low-resolution pooling attention can become another source of rotation sensitivity.

Let $\mathbf{X}\in {\mathbb{R}}^{B\times C\times H\times W}$ denote the input feature map of the attention block. The implementation first applies aspect-ratio-aware adaptive pooling to the query path. Let $(H_q,W_q)$ denote the resulting pooled-query dimensions; the configured base query-pooling size is $s_q=16$ at all four encoder stages, and the pooled dimensions are adjusted according to the input aspect ratio. For the ${90}^{\circ }$ and ${270}^{\circ }$ branches, the query and key/value pooling dimensions are exchanged. Let $A_q(·)$ denote the low-resolution pooling-attention computation before output projection and upsampling. For each $C_4$ orientation, we compute an aligned attention branch:

$${\mathbf{Z}}_k=R_{-k}\left(A_q\left(R_k\mathbf{X}\right)\right),k\in \{0,1,2,3\},$$

(6)

where the native pooled dimensions are $(H_q,W_q)$ for $k\in \{0,2\}$ and $(W_q,H_q)$ for $k\in \{1,3\}$. After inverse alignment, each branch satisfies ${\mathbf{Z}}_k\in {\mathbb{R}}^{B\times C\times H_q\times W_q}$. Each branch first processes the feature map under a rotated coordinate system and then aligns the low-resolution output back to the canonical pooled-query coordinates. The uniform $C_4$ mean-fusion version is defined as

$${\mathbf{Z}}_{\mathrm{mean}}={\displaystyle \frac{1}{4}}{\displaystyle \sum _{k=0}^3}{\mathbf{Z}}_k,{\mathbf{Z}}_{\mathrm{mean}}\in {\mathbb{R}}^{B\times C\times H_q\times W_q}.$$

(7)

This formulation defines the uniform $C_4$ reference path, which is later evaluated as C4Former-Mean.

After inverse alignment, all branch outputs share a common pooled-query coordinate system. Uniform averaging is $C_4$-consistent because rotating the input cyclically permutes the branch index while rotating each aligned output.

Uniform mean fusion assigns equal weights to the four aligned $C_4$ branches and serves as the reference aggregation rule. Its fixed branch contributions may limit input-dependent adaptivity in complex disaster scenes. For example, roads, flooded regions, debris, and damaged structures may exhibit local anisotropic patterns for which equal branch weighting is less flexible. We therefore introduce a constrained lightweight branch fusion module that retains uniform averaging as the reference component while allowing a bounded input-dependent correction.

Given the aligned low-resolution branch features ${\left\{{\mathbf{Z}}_k\right\}}_{k=0}^3$, a shared lightweight spatial scorer predicts branch-score maps

$${\mathbf{S}}_k=G\left({\mathbf{Z}}_k\right),{\mathbf{S}}_k\in {\mathbb{R}}^{B\times 1\times H_q\times W_q}.$$

(8)

The adaptive weights ${\widehat{\mathbf{W}}}_k\in {[0,1]}^{B\times 1\times H_q\times W_q}$ are computed as

$${\widehat{\mathbf{W}}}_k={\displaystyle \frac{\exp ({\mathbf{S}}_k/\tau )}{{\sum }_{j=0}^3\exp ({\mathbf{S}}_j/\tau )}},$$

(9)

where $\tau$ is a learnable temperature. We then interpolate between the adaptive weights and the uniform branch-weight vector $(1/4,1/4,1/4,1/4)$:

$${\mathbf{W}}_k=(1-\alpha ){\displaystyle \frac{1}{4}}+\alpha {\widehat{\mathbf{W}}}_k,\alpha ={\alpha }_{\max }\sigma \left(\gamma \right),$$

(10)

where $\gamma$ is a learnable scalar logit, ${\alpha }_{\max }$ is a fixed upper bound, and ${\mathbf{W}}_k\in {[0,1]}^{B\times 1\times H_q\times W_q}$. The weights are broadcast along the channel dimension when multiplying the branch features. The fused low-resolution feature is

$${\mathbf{Z}}_{\mathrm{fuse}}={\displaystyle \sum _{k=0}^3}{\mathbf{W}}_k\odot {\mathbf{Z}}_k,{\mathbf{Z}}_{\mathrm{fuse}}\in {\mathbb{R}}^{B\times C\times H_q\times W_q},$$

(11)

where ⊙ denotes element-wise multiplication. The fused feature is flattened into $B\times \left(H_q{W}_q\right)\times C$ tokens, processed by the output projection, reshaped to $B\times C\times H_q\times W_q$, and bilinearly resized to $H\times W$. The attention-block output therefore has shape $\mathbf{Y}\in {\mathbb{R}}^{B\times C\times H\times W}$, or equivalently ${\mathbf{Y}}_{\mathrm{tok}}\in {\mathbb{R}}^{B\times \left(HW\right)\times C}$ in the token representation.

Uniform $C_4$ averaging remains the reference component in this fusion. When $\alpha =0$, the module reduces to $C_4$ mean fusion. When $\alpha >0$, the adaptive branch contributes a bounded correction, while the uniform $C_4$ component retains a mixture coefficient of at least $1-{\alpha }_{\max }$. Exact consistency would additionally require the predicted weights to rotate and cyclically permute with the branches. Although the shared scorer and aligned inputs encourage this behavior, we conservatively treat the resulting module as approximately $C_4$-consistent and verify its behavior empirically. Because the final layer of the branch scorer is zero-initialized, all four adaptive softmax weights are exactly $1/4$ at initialization. The final branch weights are therefore also exactly uniform at initialization, independent of the initial gate value. The gate logit $\gamma$ is initialized to $-2.0$, which controls how rapidly the model can depart from uniform fusion during training. This initialization provides a conservative starting point; the effect of different ${\alpha }_{\max }$ values is evaluated empirically in Section 4.7. For ${\alpha }_{\max }=0.25$, the mixture coefficient of the uniform component is at least 0.75, which prevents the adaptive branch from becoming an unconstrained four-branch selector.

The following bounds characterize how ${\alpha }_{\max }$ limits the branch weights and the gate-driven gradient. For notational simplicity, the bound is written for one spatial location after channel broadcasting. Let $\mathbf{u}=(1/4,1/4,1/4,1/4)$ be the uniform branch-weight vector and let $\widehat{\mathbf{w}}$ denote the four adaptive softmax weights at that location. The final branch-weight vector can be written as $\mathbf{w}=(1-\alpha )\mathbf{u}+\alpha \widehat{\mathbf{w}}$. Because $0\le \alpha \le {\alpha }_{\max }$ and $0\le {\widehat{w}}_k\le 1$, each scalar component satisfies

$${\displaystyle \frac{1-{\alpha }_{\max }}{4}}\le w_k\le {\displaystyle \frac{1+3{\alpha }_{\max }}{4}}.$$

(12)

Thus, ${\alpha }_{\max }=0.25$ constrains each branch weight to $[0.1875,0.4375]$ and preserves at least 75% of the uniform $C_4$ component. Compared with ${\alpha }_{\max }=0.1$, which confines each branch weight to $[0.225,0.325]$, ${\alpha }_{\max }=0.25$ provides a wider adaptive range while still preventing any branch from receiving a majority weight. Writing ${\mathbf{Z}}_{\mathrm{adapt}}={\sum }_{k=0}^3{\widehat{\mathbf{W}}}_k\odot {\mathbf{Z}}_k$, the fused feature is ${\mathbf{Z}}_{\mathrm{fuse}}=(1-\alpha ){\mathbf{Z}}_{\mathrm{mean}}+\alpha {\mathbf{Z}}_{\mathrm{adapt}}$, and the scalar-gate gradient is

$${\displaystyle \frac{\partial {\mathbf{Z}}_{\mathrm{fuse}}}{\partial \gamma }}={\alpha }_{\max }\sigma \left(\gamma \right)\left(1-\sigma \left(\gamma \right)\right)\left({\mathbf{Z}}_{\mathrm{adapt}}-{\mathbf{Z}}_{\mathrm{mean}}\right).$$

(13)

Consequently,

$${∥{\displaystyle \frac{\partial {\mathbf{Z}}_{\mathrm{fuse}}}{\partial \gamma }}∥}_2\le {\displaystyle \frac{{\alpha }_{\max }}{4}}{∥{\mathbf{Z}}_{\mathrm{adapt}}-{\mathbf{Z}}_{\mathrm{mean}}∥}_2.$$

(14)

These bounds show that the deviation from mean fusion and the gate-driven gradient scale with ${\alpha }_{\max }$. The gradient bound in Equation (14) is limited to the scalar gate $\gamma$ and describes how ${\alpha }_{\max }$ constrains the sensitivity of the fused feature to this gate. Gradients through the branch scorer, attention module, and other network parameters are outside the scope of this derivation. The effect of ${\alpha }_{\max }$ on rotation stability and training behavior is evaluated empirically in Section 4.7.

3.3. Single-Diagonal Augmentation for Out-of-Group Rotations

C4Former targets the grid-preserving $C_4$ group:

$$C_4=\{0^{\circ },{90}^{\circ },{180}^{\circ },{270}^{\circ }\}.$$

(15)

The four $C_4$ elements correspond to distinct spatial index mappings and are therefore processed as separate transformations. Using zero-based row–column coordinates on an $H\times W$ feature map, and treating $R_{\theta }$ as the mapping from an original feature coordinate to the rotated feature coordinate, the four mappings are $R_0(i,j)=(i,j)$, $R_{180}(i,j)=(H-1-i,W-1-j)$, $R_{90}(i,j)=(W-1-j,i)$, and $R_{270}(i,j)=(j,H-1-i)$. The ${90}^{\circ }$ and ${270}^{\circ }$ transforms exchange the spatial dimensions. Each branch is therefore inverse-aligned separately before fusion. However, diagonal rotations such as ${45}^{\circ }$, ${135}^{\circ }$, ${225}^{\circ }$, and ${315}^{\circ }$ are outside this group and require interpolation. DC4Former addresses this out-of-group component through one diagonal representative:

$${45}^{\circ }+C_4=\{{45}^{\circ },{135}^{\circ },{225}^{\circ },{315}^{\circ }\}.$$

(16)

Thus,

$$C_8=C_4\cup ({45}^{\circ }+C_4).$$

(17)

During training, a fixed ${45}^{\circ }$ rotation is applied independently to each sampled crop with probability $p_{\mathrm{SDA}}=0.3$. The rotation is a replacement transform in the data pipeline: when selected, the rotated image and label replace that sample’s unrotated versions before packing, with no additional training sample appended. SDA preserves the mini-batch size and the number of optimization iterations. In expectation, 30% of sampled crops are presented at ${45}^{\circ }$ and 70% retain their current orientation. This exposes the model to one representative of the complementary diagonal coset. If the architecture behaves consistently under $C_4$, the remaining diagonal orientations are related to this representative by orthogonal rotations. This argument is a structural motivation for the evaluated eight-angle behavior. Diagonal rotations require interpolation, and the complete model is evaluated for empirical orientation stability around an approximately C4-consistent architecture.

In the LRFormer-based implementation, C4Former applies the above operator-aware design to three computational pathways. The stride-1 spatial pathway uses C4 weight-symmetrized convolution for positional encoding and IRB depthwise convolution. The strided pathway applies feature-rotation averaged convolution in the stem and overlapping patch-embedding layers. The attention pathway computes four rotated low-resolution attention branches, inversely aligns them, and applies either mean fusion or constrained lightweight fusion. The stage-level downsampling convolutions inside the attention module remain ordinary shared-weight convolutions; the enclosing four-view rotation, inverse-alignment, and fusion procedure supplies their rotation-consistent treatment.

In the ablation study, the uniform mean-fusion version is used to evaluate the contribution of the C4 multi-view attention pathway without adaptive correction. The architecture-only model with constrained lightweight branch fusion is denoted as C4Former. DC4Former further adds the single-${45}^{\circ }$ augmentation during training. Throughout this work, every LRFormer-family variant uses the same MMSegmentation SegFormerHead decoder. It receives the four encoder outputs with channel dimensions $(64,128,320,512)$, projects and fuses them using 256 decoder channels, and applies dropout with probability 0.1. Keeping this decoder fixed isolates the effects of the C4-consistent encoder and diagonal-complemented training strategy.

3.4. Datasets

We evaluate the proposed method on two public UAV disaster semantic segmentation datasets, FloodNet [1] and RescueNet [2]. FloodNet contains high-resolution post-flood UAV imagery with semantic categories including building-flooded, building-non-flooded, road-flooded, road-non-flooded, water, trees, vehicles, pools, grass, and background. RescueNet contains high-resolution UAV imagery collected after Hurricane Michael, with categories including background, water, building-no-damage, building-medium-damage, building-major-damage, building-total-damage, vehicle, road-clear, road-blocked, tree, and pool.

For all experiments, we use the fixed train/val/test splits provided by the official dataset releases. The evaluation sets contain 448 FloodNet images and 450 RescueNet images. Within each dataset, the same images are used for canonical-orientation and rotation-wise testing, so differences across angles are not confounded by sample composition. FloodNet is evaluated with 10 semantic classes and RescueNet with 11. All classes, including background, are used during training and inference. The training loss ignores only pixels labeled 255, which correspond to invalid or padded semantic regions. Foreground mIoU is an evaluation metric only: it excludes background class 0 and averages 9 FloodNet foreground classes or 10 RescueNet foreground classes.

3.5. Training and Evaluation Protocol

All reported experiments used NVIDIA GeForce RTX 4090 GPUs (NVIDIA Corporation, Santa Clara, CA, USA) and the same software stack, comprising Python 3.10.18, PyTorch 2.1.2, CUDA 11.8, MMCV 2.1.0, MMEngine 0.10.4, MMSegmentation 1.1.0, and OpenCV 4.11.0. Training, checkpoint selection, rotation-wise inference, and FLOP analysis follow this software setup. Runtime measurements follow the input-size and batch-size protocols specified below; the full-image latency measurement uses the stated warm-up protocol. All parameter counts, FLOP values, and FPS values in

Table 2. Model complexity and seed-0 rotation-wise foreground mIoU overview. Complexity and FPS are measured with $512\times 512$ inputs and batch size 1. Bold values indicate the best value in each column.

Method	FLOPs	Params	FPS	FloodNet			RescueNet
				0°	Orth. Mean	All-8 Mean	0°	Orth. Mean	All-8 Mean
PSPNet	179.00G	48.97M	63.86	74.11	71.21	69.34	65.86	56.27	49.48
DeepLabv3+	177.00G	43.58M	58.53	76.18	73.11	70.89	68.65	56.77	49.25
UPerNet	236.00G	59.84M	43.32	76.13	74.77	72.19	68.00	61.98	56.36
SegFormer-B1	15.44G	13.68M	90.02	75.22	73.66	72.07	61.92	54.43	46.76
Mask2Former	69.05G	47.40M	16.33	77.88	75.89	73.42	70.74	62.70	58.56
UNetFormer	11.70G	11.68M	96.97	69.93	67.99	66.53	63.27	56.12	47.28
LRFormer	29.25G	28.39M	65.58	77.76	75.13	72.92	69.35	62.21	58.35
C4Former	40.59G	28.57M	20.17	76.53	76.53	74.81	68.13	68.09	60.37
DC4Former	40.59G	28.57M	20.17	77.22	77.15	77.26	68.10	68.02	68.04

are measured using $512\times 512$ inputs. FPS is measured with inference batch size 1 on a single RTX 4090, without test-time augmentation. The C4Former encoder adopts LRFormer-S with $\mathrm{embed}\text{\_}\mathrm{dims}=(64,128,320,512)$ and depths $(3,3,12,3)$. The low-resolution pooling sizes are set to $(16,16,16,16)$, and the drop-path rate is 0.15. All LRFormer-family models use the same lightweight SegFormerHead decoder with 256 decoder channels and dropout probability 0.1. The input crop size is $512\times 512$.

Because the source UAV images are large, training samples are generated by online random cropping at $512\times 512$ pixels. We characterize the training budget by the total number of processed crops, computed as the training batch size multiplied by the number of optimization iterations; this crop-level count provides a more direct budget measure than epochs over the original full-resolution images. For FloodNet, each run used a batch size of 16 for 75,000 iterations, corresponding to $1.20\times {10}^6$ processed crops; for RescueNet, each run used a batch size of 17 for 125,000 iterations, corresponding to $2.125\times {10}^6$ processed crops. The best checkpoint was selected according to canonical-orientation ($0^{\circ }$) validation mIoU. Within each dataset, all reported models use the same crop-level training exposure. External baselines use the same crop size and rotation-wise evaluation protocol. No method uses a test-time rotation ensemble. Unless otherwise stated, all backbones were initialized from ImageNet-pretrained weights under the same initialization policy.

We optimize with AdamW using an initial learning rate of $2\times {10}^{-4}$, weight decay of 0.05, $\beta =(0.9,0.999)$, and $ϵ={10}^{-8}$. Mixed-precision training uses dynamic loss scaling. The learning rate is linearly warmed up for 1500 iterations and then follows polynomial decay with power 0.9 and a minimum of ${10}^{-6}$. Gradients are clipped to a maximum norm of 1.0. LRFormer-family ablation settings were trained with three random seeds (0, 42, and 3407), and the corresponding results are reported as mean and standard deviation. The corresponding dense-stress summaries also report mean and standard deviation across these seeds. External baseline comparisons are reported as seed-0 reference runs because they provide a common baseline overview. In the rotation-augmentation analysis, the matched LRFormer-RandRot and C4Former-RandRot comparison is reported over three seeds, whereas the additional angular-sampling variants remain seed-0 diagnostic controls. With only three independent runs per setting, formal significance tests would have low statistical power and unstable variance estimates. We therefore do not report p-values or use significance claims to support the comparisons. The configurations set deterministic=False; fixed seeds standardize stochastic initialization and sampling but do not guarantee bitwise-deterministic reproduction.

For the constrained lightweight branch fusion module, we use ${\alpha }_{\max }=0.25$ as a shared structural cap for both datasets. This bound retains at least 75% of the uniform component while allowing a limited adaptive correction. For the single-diagonal augmentation setting, we likewise use $p_{\mathrm{SDA}}=0.3$ as a shared probability for both datasets. Both hyperparameters were held fixed throughout the main comparative experiments and were not tuned separately for FloodNet and RescueNet. The training pipeline first applies shortest-edge random resizing over scales from 0.5 to 2.0 times 512 pixels, with a maximum size of 2048 pixels, followed by a $512\times 512$ random crop with a maximum single-class ratio of 0.75. It then applies a fixed ${45}^{\circ }$ rotation with probability $p_{\mathrm{SDA}}=0.3$, using image padding value 0, semantic-label padding value 255, and auto_bound=False, followed by photometric distortion. The transformed sample replaces the current crop, so the batch cardinality and training iteration count remain unchanged. This augmentation is used only during training and does not introduce additional inference overhead. Thus, LRFormer and LRFormer-SDA share the same model complexity, and C4Former and DC4Former also share the same model complexity.

To separate architecture-level $C_4$ consistency from training-time rotation exposure, we also evaluate rotation-augmentation controls. LRFormer-RandRot and C4Former-RandRot use the same continuous random-rotation rule, sampling one angle from $[0^{\circ },{360}^{\circ })$ with probability 0.3; these two matched RandRot settings are trained with three random seeds. LRFormer-FourDiag samples one diagonal angle from $\{{45}^{\circ },{135}^{\circ },{225}^{\circ },{315}^{\circ }\}$ with probability 0.3, LRFormer-DenseRot samples one angle from a ${15}^{\circ }$ grid with probability 0.3, and C4Former-RandDiag applies the four-diagonal random augmentation to the C4Former architecture. When applied, each augmentation replaces the current crop with no extra sample appended to the mini-batch. None of these controls uses test-time rotation augmentation. These controls assess how much of the rotation-stability improvement can be explained by training-time rotation exposure under matched training and evaluation settings. Except for the matched RandRot comparison, the additional angular-sampling variants are reported as seed-0 diagnostic references.

Unless otherwise specified, the reported mIoU in the rotation-wise experiments denotes foreground mIoU, where the background class is excluded. The metric averages 9 foreground classes on FloodNet and 10 foreground classes on RescueNet. This setting highlights disaster-related semantic categories and avoids background-dominated conclusions. The canonical-orientation comparison and per-class analysis are also reported using foreground mIoU for consistency.

Evaluation Metrics and Rotation-Wise Protocol

We evaluate each model at eight angles:

$$\mathsf{\Theta }=\{0^{\circ },{45}^{\circ },{90}^{\circ },{135}^{\circ },{180}^{\circ },{225}^{\circ },{270}^{\circ },{315}^{\circ }\}.$$

(18)

The grid-preserving orthogonal rotation group is defined as

$${\mathsf{\Theta }}_{\mathrm{orth}}=\{0^{\circ },{90}^{\circ },{180}^{\circ },{270}^{\circ }\},$$

(19)

and the out-of-group diagonal rotation set is defined as

$${\mathsf{\Theta }}_{\mathrm{diag}}=\{{45}^{\circ },{135}^{\circ },{225}^{\circ },{315}^{\circ }\}.$$

(20)

For each angle $\theta$, we report ${\mathrm{mIoU}}_{\theta }$. We further compute the orthogonal mean, diagonal mean, eight-angle mean, worst-angle mIoU, and rotation-wise standard deviation:

$${\mathrm{mIoU}}_{\mathrm{orth}}={\displaystyle \frac{1}{4}}\sum _{\theta \in {\mathsf{\Theta }}_{\mathrm{orth}}}{\mathrm{mIoU}}_{\theta },{\mathrm{mIoU}}_{\mathrm{diag}}={\displaystyle \frac{1}{4}}\sum _{\theta \in {\mathsf{\Theta }}_{\mathrm{diag}}}{\mathrm{mIoU}}_{\theta },$$

(21)

$${\mathrm{mIoU}}_{\mathrm{all}}={\displaystyle \frac{1}{8}}\sum _{\theta \in \mathsf{\Theta }}{\mathrm{mIoU}}_{\theta },{\mathrm{mIoU}}_{\mathrm{worst}}=\underset{\theta \in \mathsf{\Theta }}{\min }{\mathrm{mIoU}}_{\theta }.$$

(22)

$${\mathrm{Std}}_{\mathrm{rot}}=\sqrt{{\displaystyle \frac{1}{8}}\sum _{\theta \in \mathsf{\Theta }}{\left({\mathrm{mIoU}}_{\theta }-{\mathrm{mIoU}}_{\mathrm{all}}\right)}^2}.$$

(23)

To quantify rotation-induced performance degradation, we report the relative mIoU drop (RMD):

$$\mathrm{RMD}={\displaystyle \frac{{\mathrm{mIoU}}_{0^{\circ }}-\frac{1}{7}{\sum }_{\theta \in \mathsf{\Theta }\setminus \left\{0^{\circ }\right\}}{\mathrm{mIoU}}_{\theta }}{{\mathrm{mIoU}}_{0^{\circ }}}}\times 100\%.$$

(24)

A lower RMD indicates better rotation-wise stability. A negative RMD means that the average non-zero-angle mIoU is slightly higher than the canonical $0^{\circ }$ mIoU.

Consolidated quantitative test protocol. The $512\times 512$ setting is used for training crops and the standardized complexity/FPS measurements, but the accuracy-evaluation pipeline does not crop test images to $512\times 512$. For canonical and rotation-wise accuracy evaluation, each test image is resized with preserved aspect ratio using Resize(scale=(2048,512), keep_ratio=True), padded as required to satisfy the model’s size divisor of 32, and processed using whole-image inference (mode=whole); no sliding-window inference or test-time crop is used. At the canonical $0^{\circ }$ orientation, all 450 RescueNet test images are resized to $512\times 683$ and padded to $512\times 704$. Among the 448 FloodNet test images, 383 images are resized to $512\times 683$ and padded to $512\times 704$, while the remaining 65 images are resized to $512\times 765$ and padded to $512\times 768$. The test batch size is 1. For each evaluated angle, the resized full image and its semantic mask are transformed before packing and inference. All methods use the same angle-specific transform and valid-pixel mask. Right-angle rotations are implemented as exact index permutations without interpolation; the ${90}^{\circ }$ and ${270}^{\circ }$ transforms exchange the height and width dimensions. Non-right-angle rotations use a fixed canvas (auto_bound=False); RGB images use bilinear interpolation and invalid regions are filled with 0, whereas semantic masks use nearest-neighbor interpolation and invalid regions are assigned ignore label 255. Predictions and labels are aligned to a common metric grid before confusion-matrix accumulation. Pixels labeled 255 are excluded from the confusion matrix and all reported metrics. Foreground mIoU additionally excludes background class 0 and averages the remaining 9 FloodNet classes or 10 RescueNet classes.

We adopt a fixed-canvas protocol to evaluate every rotation within the same canonical raster extent. This setting is motivated by UAV camera frames and disaster-mapping tiles, which are commonly processed using fixed tensor dimensions rather than angle-dependent expanded canvases. Allowing the canvas to expand at non-right angles would introduce angle-dependent input dimensions and preserve additional spatial support, thereby coupling orientation effects with changes in tensor size and retained scene content. Under the fixed-canvas protocol, the evaluation measures end-to-end orientation reliability within a finite image frame, including the effects of interpolation, boundary truncation, changes in valid support, and model response. For each evaluated angle, all methods use the same rotation center, interpolation and filling rules, and the same corresponding valid-pixel mask, enabling controlled relative comparison under this deployment-motivated setting.

Practical inference-cost protocol. In addition to the standardized $512\times 512$ FPS measurement, we report full-image latency and peak GPU memory under the canonical $0^{\circ }$ whole-image evaluation pipeline. Here, “full-image” refers to the resized whole test image after aspect-ratio-preserving preprocessing, rather than the raw-resolution UAV image. The measurement follows the same Resize(scale=(2048,512), keep_ratio=True), padding, and whole-image inference setting used for quantitative evaluation. For RescueNet, this produces a resized image of $512\times 683$, which is padded by the data preprocessor to $512\times 704$ before whole-image inference. Latency is measured with batch size 1 on a single RTX 4090 after 20 warm-up images, and the remaining 430 test images are used for timing. Rotation preprocessing, test-time augmentation, visualization, result saving, and metric computation are excluded from the latency measurement. Peak GPU memory denotes the maximum allocated GPU memory during the measured inference loop.

Right-angle rotations are grid-preserving and require no interpolation. Nevertheless, the rotation-wise scores under $0^{\circ }$, ${90}^{\circ }$, ${180}^{\circ }$, and ${270}^{\circ }$ are expected to be close but not necessarily bitwise identical. Aspect-ratio-preserving resizing, height–width exchange, size-divisor padding, decoder resizing, valid-pixel masking, and finite image boundaries can introduce small residual differences, even though the right-angle rotation itself is an exact grid permutation. Dataset-dependent differences among the right-angle scores are therefore consistent with finite-canvas and padding effects under the common protocol, rather than indicating an implementation inconsistency. Non-right-angle results necessarily reflect both model sensitivity and interpolation effects; because every method receives the same transformed inputs and valid-pixel masks, the protocol supports controlled relative comparison. We further quantify this distinction with an image-level rotation–inverse-rotation round-trip diagnostic in Supplementary Table S1 over the eight principal angles: $0^{\circ }$, ${90}^{\circ }$, ${180}^{\circ }$, and ${270}^{\circ }$ introduce zero reconstruction error, whereas ${45}^{\circ }$, ${135}^{\circ }$, ${225}^{\circ }$, and ${315}^{\circ }$ produce non-zero normalized MAE and reduced gradient retention. This diagnostic uses an expanded intermediate canvas and valid-region scoring to isolate interpolation-induced resampling from boundary truncation, whereas the segmentation evaluation uses the fixed-canvas protocol described above.

For qualitative visualization, we use a separate visualization protocol to avoid visually misleading cropping artifacts under non-orthogonal rotations. Specifically, non-right-angle inputs are rotated on an enlarged canvas with constant padding, and the predicted masks are then inversely warped back to the original $0^{\circ }$ coordinate system. The RGB disagreement maps are generated only after this alignment step and are used for visual analysis rather than official mIoU computation.

4. Results

4.1. Canonical-Orientation Results and Complexity

We first compare the standard $0^{\circ }$ segmentation performance and model complexity of the proposed method with representative CNN-based, Transformer-based, and UAV/remote-sensing segmentation baselines. The compared methods include PSPNet [17], DeepLabv3+ [18], UPerNet [59], SegFormer-B1 [21], Mask2Former [23], UNetFormer [60], LRFormer [24], C4Former, and DC4Former. Parameter counts and FLOPs are computed with an input size of $512\times 512$, and FPS is measured using $512\times 512$ inputs with batch size 1 on a single NVIDIA RTX 4090 GPU without test-time augmentation.

Mask2Former achieves the highest canonical-orientation mIoU on both datasets, whereas LRFormer and the proposed variants remain in a similar accuracy range. The proposed variants do not consistently improve the $0^{\circ }$ score. C4Former mainly improves the orthogonal-angle mean, whereas DC4Former improves the All-8 mean on both datasets; the corresponding worst-angle results are examined in the rotation-wise evaluation. Relative to LRFormer, C4Former adds only 0.18M parameters, but increases FLOPs from 29.25G to 40.59G and reduces standardized $512\times 512$ throughput from 65.58 to 20.17 FPS. The multi-view operations incur substantial runtime overhead, and weight sharing across branches does not eliminate this cost.

Table 3. Practical inference cost under a canonical $0^{\circ }$ resized whole-image pipeline. Bold values indicate the best value in each column.

Method Group	512 × 512 FPS ↑	Resized Full-Image Latency ↓	Peak Allocated Memory ↓
LRFormer/LRFormer-SDA	65.58	44.13 ms/image	1.51 GB
C4Former/DC4Former	20.17	95.60 ms/image	1.51 GB

relates the standardized throughput to a representative resized whole-image evaluation pipeline. LRFormer processes one resized-and-padded RescueNet test image in 44.13 ms, whereas C4Former/DC4Former require 95.60 ms. The peak allocated GPU memory remains 1.51 GB for both model groups. The additional cost is therefore latency rather than memory footprint.

4.2. Rotation-Wise Evaluation

Table 4. Seed-0 contextual angle-wise foreground mIoU comparison on FloodNet. Bold values indicate the best value in each column.

Method	0°	45°	90°	135°	180°	225°	270°	315°	All-8	Worst	Std.	RMD
PSPNet	74.11	67.61	70.21	67.52	70.56	67.26	69.98	67.45	69.34	67.26	2.22	7.36
DeepLabv3+	76.18	68.79	72.16	68.89	72.31	68.07	71.78	68.93	70.89	68.07	2.57	7.94
UPerNet	76.13	70.42	74.28	69.27	74.61	68.63	74.05	70.16	72.19	68.63	2.68	5.90
SegFormer-B1	75.22	71.48	73.16	69.52	73.62	69.83	72.64	71.09	72.07	69.52	1.83	4.79
Mask2Former	77.88	71.76	73.93	71.43	75.58	70.76	76.17	69.82	73.42	69.82	2.72	6.55
UNetFormer	69.93	65.07	66.58	64.92	69.34	65.13	66.11	65.13	66.53	64.92	1.88	5.57
LRFormer	77.76	71.11	72.64	71.03	76.09	69.89	74.02	70.84	72.92	69.89	2.62	7.10
LRFormer-SDA	77.67	77.40	74.79	75.03	73.93	73.10	75.08	75.77	75.35	73.10	1.47	3.42
C4Former	76.53	73.08	76.53	73.11	76.53	73.19	76.53	72.97	74.81	72.97	1.72	2.57
DC4Former	77.22	76.97	77.09	77.78	77.09	76.98	77.22	77.75	77.26	76.97	0.30	−0.07

and

Table 5. Seed-0 contextual angle-wise foreground mIoU comparison on RescueNet. Bold values indicate the best value in each column.

Method	0°	45°	90°	135°	180°	225°	270°	315°	All-8	Worst	Std.	RMD
PSPNet	65.86	43.92	50.78	42.15	57.36	41.85	51.07	42.83	49.48	41.85	8.07	28.42
DeepLabv3+	68.65	42.89	50.04	41.16	57.78	40.73	50.62	42.10	49.25	40.73	9.23	32.31
UPerNet	68.00	52.19	58.91	50.34	60.96	49.25	60.06	51.18	56.36	49.25	6.20	19.57
SegFormer-B1	61.92	39.21	50.03	39.03	55.95	38.55	49.83	39.54	46.76	38.55	8.45	27.99
Mask2Former	70.74	55.84	59.34	54.23	62.00	52.84	58.71	54.80	58.56	52.84	5.41	19.67
UNetFormer	63.27	38.44	51.99	38.24	57.41	37.78	51.81	39.27	47.28	37.78	9.45	28.89
LRFormer	69.35	56.40	59.25	53.20	61.21	53.50	59.04	54.82	58.35	53.20	4.96	18.14
LRFormer-SDA	68.74	69.19	60.86	61.44	61.03	61.94	62.18	61.98	63.42	60.86	3.23	8.84
C4Former	68.13	52.83	68.05	52.55	68.04	52.53	68.15	52.67	60.37	52.53	7.72	13.02
DC4Former	68.10	67.71	67.93	68.31	67.92	67.66	68.11	68.57	68.04	67.66	0.28	0.10

provide seed-0 contextual comparisons with external baselines, whereas the main LRFormer-family conclusions are based on the multi-seed results reported in

Table 6. Feature-, logit-, and prediction-level C4 consistency diagnostic. Bold values indicate the best value in each column.

Dataset	Model	Stage-1 L2 ↓	Stage-4 L2 ↓	Logit L2 ↓	Pred. Cons. fg mIoU (%) ↑	Pixel Disagree. (%) ↓
FloodNet	LRFormer	1.054 ± 0.009	0.588 ± 0.008	0.274 ± 0.002	81.51 ± 0.32	7.947 ± 0.179
FloodNet	C4Former	0.637 ± 0.005	0.236 ± 0.001	0.151 ± 0.003	96.14 ± 0.05	0.971 ± 0.008
FloodNet	DC4Former	0.638 ± 0.013	0.234 ± 0.006	0.146 ± 0.002	96.26 ± 0.02	0.958 ± 0.047
RescueNet	LRFormer	1.132 ± 0.002	0.587 ± 0.036	0.246 ± 0.012	68.84 ± 1.92	9.227 ± 0.820
RescueNet	C4Former	0.754 ± 0.008	0.237 ± 0.001	0.130 ± 0.003	94.74 ± 0.12	1.227 ± 0.110
RescueNet	DC4Former	0.755 ± 0.004	0.236 ± 0.001	0.127 ± 0.004	94.73 ± 0.39	1.221 ± 0.129

Values are reported as mean ± cross-seed standard deviation over three seeds; each seed-level value averages the non-zero right-angle rotations.

,

Table 7. Three-seed dense rotation stress-test summary over 24 angles. Bold values indicate the best value in each column.

Dataset	Setting	Mean-24	Worst-24	Std.-24
FloodNet	A: LRFormer	72.64 ± 0.50	69.60 ± 0.20	1.99 ± 0.13
FloodNet	B: LRFormer-SDA	75.56 ± 0.17	73.17 ± 0.28	1.47 ± 0.11
FloodNet	J: C4Former	75.12 ± 0.77	73.35 ± 0.34	1.01 ± 0.21
FloodNet	K: DC4Former	77.19 ± 0.25	76.50 ± 0.47	0.39 ± 0.10
RescueNet	A: LRFormer	58.79 ± 1.19	54.90 ± 1.51	3.40 ± 0.59
RescueNet	B: LRFormer-SDA	63.26 ± 0.14	60.46 ± 0.35	2.78 ± 0.13
RescueNet	J: C4Former	57.10 ± 0.71	51.67 ± 1.13	5.42 ± 0.46
RescueNet	K: DC4Former	65.40 ± 0.69	63.04 ± 1.51	1.91 ± 0.50

,

Table 8. Diagnostic rotation-augmentation controls.

Scheme	Method	Arch.	Train Rot.	All-8	Worst-8	Std.-8	Mean-24	Worst-24	Std.-24
FloodNet
1	LRFormer-RandRot	LR	Rand. 0–360°	77.49 ± 0.33	77.06 ± 0.41	0.32 ± 0.08	77.68 ± 0.30	76.98 ± 0.31	0.36 ± 0.02
2	LRFormer-FourDiag	LR	Rand. diag.	77.26	76.56	0.42	77.28	76.36	0.50
3	LRFormer-DenseRot	LR	Rand. 15° grid	77.61	77.28	0.19	77.81	77.28	0.22
4	C4Former-RandDiag	C4	Rand. diag.	77.31	76.97	0.44	77.15	76.48	0.48
5	C4Former-RandRot	C4	Rand. 0–360°	77.05 ± 0.51	76.74 ± 0.65	0.31 ± 0.12	77.17 ± 0.56	76.74 ± 0.65	0.34 ± 0.07
RescueNet
1	LRFormer-RandRot	LR	Rand. 0–360°	66.43 ± 0.22	64.26 ± 0.50	1.30 ± 0.08	66.62 ± 0.19	64.26 ± 0.50	1.10 ± 0.06
2	LRFormer-FourDiag	LR	Rand. diag.	66.58	63.88	1.91	66.28	63.88	1.49
3	LRFormer-DenseRot	LR	Rand. 15° grid	66.15	64.07	1.33	66.40	64.07	1.23
4	C4Former-RandDiag	C4	Rand. diag.	67.40	67.07	0.35	65.20	63.01	1.63
5	C4Former-RandRot	C4	Rand. 0–360°	67.04 ± 0.44	66.62 ± 0.55	0.28 ± 0.10	66.86 ± 0.54	66.16 ± 0.37	0.35 ± 0.02

LR/C4 denote LRFormer/C4Former. Schemes 1 and 5 are three-seed RandRot comparisons; Schemes 2–4 are seed-0 diagnostics. Italicized dataset names indicate dataset blocks. Boldface compares Schemes 1 and 5 within each dataset. Rand. diag. samples from $\{{45}^{\circ },{135}^{\circ },{225}^{\circ },{315}^{\circ }\}$.

,

Table 9. Diagnostic ablation design of C4Former and DC4Former.

Setting	C4 Spatial	C4 Down.	C4 Attn.	Fusion	SDA
A: LRFormer	–	–	–	–	–
B: LRFormer-SDA	–	–	–	–	✓
C: +C4 Spatial	✓	–	–	–	–
D: +C4 Down.	–	✓	–	–	–
E: +C4 Attn.	–	–	✓	Constrained	–
F: C4 Spatial + Down.	✓	✓	–	–	–
G: C4 Spatial + Attn.	✓	–	✓	Constrained	–
H: C4 Down. + Attn.	–	✓	✓	Constrained	–
I: C4Former-Mean	✓	✓	✓	Mean	–
J: C4Former	✓	✓	✓	Constrained	–
K: DC4Former	✓	✓	✓	Constrained	✓

and

Table 10. Three-seed ablation results on FloodNet and RescueNet. Bold values indicate the best value in each column.

Dataset	Setting	0°	Orth.	Diag.	All-8	Std.	Worst	RMD
FloodNet	A: LRFormer	77.38 ± 0.33	75.32 ± 0.22	71.35 ± 0.81	73.34 ± 0.51	2.30 ± 0.32	70.14 ± 0.29	5.96 ± 1.09
FloodNet	B: LRFormer-SDA	77.63 ± 0.16	75.40 ± 0.09	75.54 ± 0.26	75.47 ± 0.12	1.44 ± 0.06	73.33 ± 0.21	3.18 ± 0.36
FloodNet	C: +C4 Spatial	77.45 ± 0.35	76.09 ± 0.42	71.70 ± 0.27	73.90 ± 0.34	2.34 ± 0.09	70.89 ± 0.42	5.25 ± 0.17
FloodNet	D: +C4 Down.	77.61 ± 0.24	75.71 ± 0.30	72.27 ± 0.11	73.99 ± 0.15	2.07 ± 0.05	71.15 ± 0.30	5.32 ± 0.17
FloodNet	E: +C4 Attn.	77.49 ± 0.09	75.76 ± 0.21	72.53 ± 0.50	74.15 ± 0.26	1.95 ± 0.18	71.29 ± 0.67	4.93 ± 0.36
FloodNet	F: C4 Spatial + Down.	76.66 ± 0.26	76.59 ± 0.41	72.46 ± 0.31	74.52 ± 0.31	2.09 ± 0.18	72.10 ± 0.56	3.19 ± 0.21
FloodNet	G: C4 Spatial + Attn.	77.35 ± 0.43	76.27 ± 0.26	72.32 ± 0.52	74.30 ± 0.35	2.08 ± 0.20	71.58 ± 0.51	4.50 ± 0.42
FloodNet	H: C4 Down. + Attn.	77.49 ± 0.25	75.81 ± 0.14	72.57 ± 0.31	74.19 ± 0.18	1.96 ± 0.16	71.35 ± 0.96	4.87 ± 0.21
FloodNet	I: C4Former-Mean	76.95 ± 0.61	76.90 ± 0.57	72.54 ± 0.51	74.72 ± 0.51	2.20 ± 0.18	72.13 ± 0.39	3.31 ± 0.33
FloodNet	J: C4Former	76.64 ± 0.39	76.64 ± 0.36	73.69 ± 0.53	75.16 ± 0.38	1.50 ± 0.25	73.35 ± 0.34	2.20 ± 0.40
FloodNet	K: DC4Former	76.98 ± 0.44	77.00 ± 0.38	77.39 ± 0.02	77.20 ± 0.19	0.34 ± 0.11	76.83 ± 0.30	−0.32 ± 0.38
RescueNet	A: LRFormer	68.71 ± 0.56	62.85 ± 0.58	56.27 ± 1.65	59.56 ± 1.07	4.17 ± 0.72	54.90 ± 1.51	15.20 ± 2.55
RescueNet	B: LRFormer-SDA	68.54 ± 0.17	63.04 ± 0.25	63.60 ± 0.04	63.32 ± 0.14	3.14 ± 0.08	60.57 ± 0.43	8.70 ± 0.21
RescueNet	C: +C4 Spatial	68.47 ± 0.88	63.75 ± 0.17	53.44 ± 1.16	58.60 ± 0.51	5.57 ± 0.68	52.55 ± 1.20	16.46 ± 1.87
RescueNet	D: +C4 Down.	69.99 ± 0.23	63.33 ± 0.55	57.55 ± 0.57	60.44 ± 0.22	4.18 ± 0.23	55.69 ± 0.45	15.60 ± 0.14
RescueNet	E: +C4 Attn.	69.60 ± 0.17	63.47 ± 0.16	57.30 ± 1.05	60.39 ± 0.45	4.18 ± 0.33	55.51 ± 0.71	15.13 ± 0.52
RescueNet	F: C4 Spatial + Down.	67.29 ± 0.55	66.74 ± 0.37	51.11 ± 0.67	58.92 ± 0.43	7.83 ± 0.33	50.64 ± 0.56	14.22 ± 0.73
RescueNet	G: C4 Spatial + Attn.	69.04 ± 0.40	63.86 ± 0.47	54.47 ± 0.58	59.17 ± 0.51	5.27 ± 0.24	53.49 ± 0.73	16.35 ± 0.88
RescueNet	H: C4 Down. + Attn.	69.65 ± 0.33	63.53 ± 0.12	57.72 ± 0.92	60.62 ± 0.40	4.05 ± 0.26	55.65 ± 0.46	14.81 ± 0.44
RescueNet	I: C4Former-Mean	68.00 ± 0.46	68.02 ± 0.42	52.34 ± 0.35	60.18 ± 0.26	7.85 ± 0.28	51.75 ± 0.40	13.14 ± 0.50
RescueNet	J: C4Former	67.80 ± 0.33	67.79 ± 0.33	52.03 ± 1.08	59.91 ± 0.54	7.88 ± 0.58	51.67 ± 1.13	13.29 ± 0.89
RescueNet	K: DC4Former	67.82 ± 0.31	67.81 ± 0.26	68.21 ± 0.18	68.01 ± 0.04	0.33 ± 0.11	67.66 ± 0.18	−0.32 ± 0.46

. External baselines are used as contextual seed-0 references, while conclusions about the proposed LRFormer-family variants are drawn from the corresponding three-seed experiments.

4.2.1. FloodNet

Table 4 reports the angle-wise foreground mIoU on FloodNet. Canonical-orientation performance and rotation stability show different behavior. Mask2Former obtains the highest $0^{\circ }$ mIoU among external baselines, but its worst-angle mIoU is 69.82%. SegFormer-B1 and UNetFormer show relatively small standard deviations on FloodNet, but their overall mIoU remains lower than the stronger baselines. This low variation mainly reflects lower overall performance on FloodNet; on RescueNet, UNetFormer’s standard deviation rises to 9.45.

The seed-0 FloodNet reference suggests that single-diagonal augmentation and the C4-consistent architecture are complementary. Relative to LRFormer, LRFormer-SDA improves diagonal performance but retains visible angle-wise variation, whereas C4Former makes the four orthogonal scores identical to two decimal places while leaving a diagonal gap. These identical rounded right-angle mIoU values reflect metric rounding; the prediction-level diagnostic in Table 6 reports non-zero pixel disagreement after inverse alignment. In this seed-0 reference, DC4Former substantially reduces this gap: it improves All-8 mIoU by 4.34 points and worst-angle mIoU by 7.08 points over LRFormer, while reducing the standard deviation from 2.62 to 0.30. Although its $0^{\circ }$ mIoU is 0.54 points lower than LRFormer, DC4Former improves the rotated-angle and worst-angle scores, indicating reduced rotation-induced variation as the main source of the gain.

4.2.2. RescueNet

Table 5 reports the angle-wise foreground mIoU on RescueNet. Compared with FloodNet, RescueNet exhibits stronger rotation sensitivity for most external baselines. Diagonal rotations are particularly challenging: the worst-angle mIoU of the external baselines ranges from 37.78% to 52.84% under the fixed-canvas protocol.

The seed-0 RescueNet reference shows stronger rotation sensitivity. Mask2Former attains the highest $0^{\circ }$ mIoU, but its worst-angle score is 52.84%, close to LRFormer’s 53.20%. DC4Former raises LRFormer’s All-8 mIoU by 9.69 points and its worst-angle mIoU by 14.46 points, reducing the standard deviation from 4.96 to 0.28. The improvement comes mainly from more stable performance after rotation, especially at the worst angle, while the unrotated $0^{\circ }$ score remains comparable.

4.2.3. Qualitative Visualization of Rotation Consistency

Figure 2 and Figure 3 compare representative seed-0 predictions on FloodNet and RescueNet. Rotated-input predictions are aligned back to the original $0^{\circ }$ coordinate system before visualization. Columns show the original image, ground truth, and model predictions; rows show $0^{\circ }$, ${90}^{\circ }$, ${135}^{\circ }$, ${225}^{\circ }$, and an RGB disagreement map. Red, green, and blue denote prediction changes induced by ${90}^{\circ }$, ${135}^{\circ }$, and ${225}^{\circ }$, respectively, and mixed colors indicate overlapping disagreement.

The qualitative figures include boxed overviews and zoomed regions of interest. The FloodNet zoom focuses on a road-flooded region and its water boundary, where several baselines change labels under diagonal rotations. The RescueNet zoom focuses on building-total-damage and road-blocked regions, two disaster categories for which orientation changes can alter small connected structures. These local views show where the rotation-wise scores in Table 4 and Table 5 arise spatially; they are not used as additional metrics.

In the zoomed panels, rotation-sensitive predictions appear as colored bands around the FloodNet road-flooded boundary and as shifted or missing components in the RescueNet building-total-damage and road-blocked regions. This visual pattern is consistent with the reduced right-angle prediction disagreement of C4Former and DC4Former and with the lower eight-angle standard deviation of DC4Former.

The qualitative examples are generated from the seed-0 checkpoints and serve as representative visual comparisons; the corresponding multi-seed quantitative evidence is reported in Table 6, Table 7, Table 8, Table 9 and Table 10.

4.3. Feature- and Prediction-Level C4 Consistency

We conduct a C4-consistency diagnostic using the LRFormer, C4Former, and DC4Former checkpoints to examine whether the improved rotation-wise behavior is also reflected in internal features and predictions. The diagnostic uses the same test images, aspect-ratio-preserving resize and padding, exact right-angle transforms, whole-image inference, ignore-index handling, and metric-grid alignment as the rotation-wise evaluation protocol. For each test image, the $0^{\circ }$, ${90}^{\circ }$, ${180}^{\circ }$, and ${270}^{\circ }$ versions are passed through the same checkpoint. The rotated feature maps, raw logits, and predictions are then inverse-rotated to the $0^{\circ }$ coordinate system and compared on their common spatial support. Let $\mathbf{X}$ denote the resized input image tensor and let $f_l\left(\mathbf{X}\right)\in {\mathbb{R}}^{B\times C_l\times H_l\times W_l}$ denote the stage-l encoder feature. For encoder stage l, the relative C4 inconsistency at angle $\theta$ is computed as

$$E_l\left(\theta \right)={\displaystyle \frac{{∥R_{-\theta }{f}_l\left(R_{\theta }\mathbf{X}\right)-f_l\left(\mathbf{X}\right)∥}_2}{{∥f_l\left(\mathbf{X}\right)∥}_2+ϵ}},$$

(25)

where $C_l$, $H_l$, and $W_l$ are stage-specific channel and spatial dimensions, and $ϵ$ is a small numerical constant. We also report the relative L2 error of the aligned raw logits, the foreground mIoU between aligned predictions, and the pixel disagreement rate. Table 6 averages the non-zero right angles over three random seeds.

The diagnostic indicates that C4Former and DC4Former reduce inconsistency before the final mIoU is computed. On FloodNet, C4Former reduces the Stage-4 relative L2 error from 0.59 to 0.24, raises prediction-consistency foreground mIoU from 81.51% to 96.14%, and lowers pixel disagreement from 7.95% to 0.97%. On RescueNet, the corresponding prediction-consistency mIoU increases from 68.84% to 94.74%, while pixel disagreement decreases from 9.23% to 1.23%. These results distinguish canonical-orientation feature quality from rotation consistency: after inverse alignment, LRFormer exhibits substantially larger feature and prediction discrepancies between rotated-input and canonical-input responses than C4Former and DC4Former. Full stage-wise and model-wise results are provided in Supplementary Table S4.

4.4. Dense Rotation Stress Test

The main eight-angle protocol evaluates the $C_4$ orientations and their ${45}^{\circ }$ diagonal complements. The 24-angle protocol further evaluates whether stability learned from the $C_4$ rotations and one diagonal representative extends to sampled intermediate orientations. It provides a discrete stress test of sampled intermediate rotations under the same fixed-canvas protocol. The dense rotation stress test covers LRFormer, LRFormer-SDA, C4Former, and DC4Former over the complete $0^{\circ }$–${345}^{\circ }$ range at ${15}^{\circ }$ intervals, including the original eight angles and 16 intermediate angles. All 24 angles use the same fixed-canvas quantitative protocol, interpolation rules, valid-pixel masking, evaluation images, and foreground mIoU definition described above.

Figure 4 visualizes the three-seed mean response of LRFormer, LRFormer-SDA, C4Former, and DC4Former beyond the eight principal orientations. Table 7 reports the corresponding 24-angle summary statistics for the same four settings. The table computes summary metrics per seed before cross-seed averaging, so the minima of the plotted mean curves are visual references and may differ from the reported Worst-24 values. On FloodNet, DC4Former raises the mean 24-angle foreground mIoU from 72.64% to 77.19% over LRFormer and reduces the 24-angle standard deviation from 1.99 to 0.39. On RescueNet, the corresponding mean improves from 58.79% to 65.40%, and the standard deviation falls from 3.40 to 1.91. For DC4Former on RescueNet, Std.-24 is 1.91, compared with Std.-8 of 0.33, indicating greater variation across the full 24-angle protocol than across the eight principal orientations. On FloodNet, C4Former has a higher Mean-24 and Worst-24 and a lower Std.-24 than LRFormer. On RescueNet, C4Former has a lower Mean-24 and Worst-24 and a higher Std.-24 than LRFormer. Interpolation-induced changes to boundaries and small fragmented structures may contribute to this dataset-dependent pattern. The 24-angle protocol therefore functions as a controlled stress test of sampled intermediate rotations.

4.5. Diagnostic Rotation-Augmentation Controls

Table 8 reports rotation-augmentation controls designed to examine the roles of training-time rotation exposure and architecture. The three-seed comparison is assigned to Schemes 1 and 5 because their shared continuous RandRot rule provides the matched control needed to assess the architectural effect under fixed training-time rotation exposure. Schemes 2–4 serve as seed-0 diagnostics of angular-sampling patterns.

Together, these auxiliary controls show that finite diagonal sampling, denser ${15}^{\circ }$ sampling, and the addition of the $C_4$ architecture produce dataset-dependent reliability patterns. Their primary role is to characterize the interaction between angular evaluation or training exposure and architecture.

The matched RandRot comparison shows that rotation augmentation is a strong training-time baseline with no additional inference cost. This behavior is plausible for a high-capacity Transformer-based segmenter: repeated random rotations expose the same training scenes and labels under many sampled orientations, allowing the model to learn orientation-conditioned appearance patterns empirically. On FloodNet, LRFormer-RandRot has slightly higher three-seed mean All-8 and Worst-8 values than C4Former-RandRot, by 0.44 and 0.32 points, respectively. Under this matched protocol, adding the $C_4$ architecture does not increase these two mean metrics on FloodNet.

In contrast, RescueNet shows a reliability advantage from adding the C4 architecture under the same continuous RandRot rule. C4Former-RandRot improves All-8 from 66.43% to 67.04%, raises Worst-8 from 64.26% to 66.62%, and reduces Std.-8 from 1.30 to 0.28. The 24-angle stress metrics follow the same reliability pattern within this matched attribution comparison, with Worst-24 improving from 64.26% to 66.16% and Std.-24 decreasing from 1.10 to 0.35. These results characterize a dataset-dependent trade-off between inference efficiency and worst-orientation reliability under matched rotation exposure. This section uses C4Former-RandRot for attribution under matched rotation exposure; the final deployment comparison between DC4Former and LRFormer-RandRot is discussed in Section 5.

4.6. Ablation Study

The ablation study follows the LRFormer-family design path in Table 9. The configurations separate single-diagonal augmentation, the three individual $C_4$ operator classes, their pairwise combinations, the full mean-fusion $C_4$ architecture, the full constrained-fusion $C_4$ architecture, and the final diagonal-complemented model. Settings C–E isolate $C_4$ spatial kernel symmetrization, $C_4$ feature-rotation averaged downsampling, and $C_4$ multi-view attention. Settings F–H examine the three pairwise combinations. Settings I and J compare mean and constrained fusion when all three $C_4$ operator classes are enabled, and setting K adds SDA to form DC4Former.

SDA alone (B) mainly affects the diagonal angles. The diagonal mean increases from 71.35% to 75.54% on FloodNet and from 56.27% to 63.60% on RescueNet. The orthogonal means change only slightly, from 75.32% to 75.40% on FloodNet and from 62.85% to 63.04% on RescueNet. This behavior matches the role of SDA as training exposure to one diagonal representative, with the LRFormer operators left unchanged.

The single-module rows show different behavior across the three $C_4$ operator classes. On FloodNet, the isolated $C_4$ spatial, downsampling, and attention settings give close All-8 values of 73.90%, 73.99%, and 74.15%. On RescueNet, C4 Downsampling only and C4 Attention only raise All-8 to 60.44% and 60.39%, while C4 Spatial only gives 58.60% and lowers the diagonal mean to 53.44%. The pairwise rows follow the same dataset- and angle-dependent behavior. On RescueNet, C4 Downsampling + Attention gives the strongest pairwise All-8 and Worst scores, 60.62% and 55.65%, whereas the pairwise settings containing C4 Spatial have lower diagonal means.

On RescueNet, C4Former-Mean raises the orthogonal mean from 62.85% to 68.02% relative to LRFormer; its diagonal mean decreases from 56.27% to 52.34%, and its rotation-wise standard deviation increases from 4.17 to 7.85. The expanded RescueNet ablation reveals a consistent pattern in the diagonal results. All configurations containing $C_4$ spatial kernel symmetrization (C, F, G, I, and J) have lower diagonal means than LRFormer, whereas the configurations without this component (D, E, and H) do not exhibit the same decline. The nearly identical diagonal means of C4Former-Mean and C4Former, 52.34% and 52.03%, further show that replacing uniform fusion with constrained fusion is insufficient to recover the lost diagonal performance. The observed degradation is therefore more closely linked to the $C_4$-symmetrized spatial pathway than to the choice of branch-fusion rule.

After diagonal resampling, fine edges and small structures are represented by local patterns that differ from those seen during training without diagonal rotation exposure. The branch rotations inside the network remain exact right-angle index permutations of the resulting discrete feature maps; the resampling change is introduced before these internal $C_4$ transformations. By tying local-filter responses across the four right-angle orientations, $C_4$ spatial symmetrization reduces the degrees of freedom available for orientation-specific adaptation to the altered local statistics. This effect may be more pronounced on RescueNet because discrimination among building-damage grades and blocked-road regions may draw on fragmented structures, irregular boundaries, narrow obstruction cues, and subtle local appearance differences. The interaction between interpolation-altered cues and tied spatial responses is consistent with the stronger right-angle/diagonal trade-off observed on RescueNet. Because the redesigned operators interact throughout the feature hierarchy, the current ablation does not establish a unique causal mechanism.

Adding SDA to the constrained $C_4$ architecture gives the final setting K. On RescueNet, All-8 increases from 59.56% for LRFormer to 68.01%, Worst-8 increases from 54.90% to 67.66%, and Std.-8 decreases from 4.17 to 0.33. Among settings A–K in Table 10, setting K gives the highest All-8 and Worst-8 scores and the lowest rotation-wise standard deviation on both datasets. The component effects are complementary but non-additive: $C_4$ downsampling and $C_4$ attention provide modest standalone gains; the $C_4$-symmetrized spatial pathway improves right-angle consistency but is also the component most closely linked to the RescueNet diagonal decline; constrained fusion provides a bounded adaptive correction without removing this architecture-only trade-off; and SDA supplies the diagonal training exposure needed for the final eight-angle stability.

DC4Former obtains a slightly negative mean RMD ($-\mathrm{0.32\%}$) on both datasets. RMD compares the canonical $0^{\circ }$ result with the average across the other seven orientations, and its sign characterizes this canonical-versus-nonzero comparison. Table 10 directly reports the relative performance of the diagonal and orthogonal subsets. The diagonal mean mIoU exceeds the orthogonal mean by only 0.39 points on FloodNet and 0.40 points on RescueNet. Diagonal rotations introduce sampling changes because they require interpolation on the fixed canvas. After targeted training exposure, the final segmentation scores can approach parity despite this sampling-related challenge. The RescueNet ablation illustrates this distinction: C4Former obtains orthogonal and diagonal means of 67.79% and 52.03%, respectively, whereas DC4Former, which adds SDA, obtains 67.81% and 68.21%. The diagonal-minus-orthogonal difference changes from $-15.76$ points for C4Former to 0.40 points for DC4Former, while the orthogonal mean changes by only 0.02 points. On both datasets, the magnitude of the mean RMD ($\mathrm{0.32\%}$) is smaller than its cross-seed standard deviation ($\mathrm{0.38\%}$ on FloodNet and $\mathrm{0.46\%}$ on RescueNet). The negative mean RMD represents a small model- and protocol-dependent residual comparable in magnitude to the observed cross-seed variability. Taken together, these results show that DC4Former achieves approximately balanced performance across diagonal and orthogonal orientations under the evaluated protocol.

The ablation supports the design choice used in DC4Former. The $C_4$ operators target grid-preserving right-angle rotations, where pixels or feature cells can be permuted without resampling. Diagonal rotations require interpolation and fixed-canvas boundary handling, which change RGB sampling, label boundaries, and small-structure geometry. The full eight-angle round-trip diagnostic in Supplementary Table S1 supports this distinction between interpolation-free $C_4$ transformations and interpolation-based diagonal inputs. Within the LRFormer-family ablation, the best orientation reliability is obtained when the $C_4$ operator path is combined with constrained fusion and diagonal training exposure.

4.7. Sensitivity to the Constrained Fusion Bound

The main comparative experiments use ${\alpha }_{\max }=0.25$ as the shared structural cap for both datasets. We additionally evaluate the sensitivity of the constrained branch fusion using the full C4Former architecture, the same fixed-canvas evaluation protocol, and seed 0, with only ${\alpha }_{\max }$ varied. Detailed rotation-wise results are reported in Supplementary Table S5. To check whether larger bounds cause optimization instability, Supplementary Figure S1 reports the smoothed training-loss and validation-mIoU trajectories for ${\alpha }_{\max }\in \{0.25,0.5,1.0\}$, and Supplementary Table S6 reports the best validation checkpoint iteration and score. The rotation-wise results vary moderately over ${\alpha }_{\max }\in \{0,0.1,0.25,0.5,0.75,1.0\}$, and larger upper bounds lack a monotonic or cross-dataset-consistent improvement.

On FloodNet, larger values improve several seed-0 metrics, with ${\alpha }_{\max }=1.0$ giving the highest All-8 and Worst-8 scores. The same trend is not reproduced on RescueNet, where ${\alpha }_{\max }=0.5$ gives the highest All-8 score, while ${\alpha }_{\max }=0.1$ gives the highest Worst-8 score and lowest Std.-8. The convergence diagnostics show that the ${\alpha }_{\max }=0.25$, 0.5, and 1.0 runs complete the prescribed schedules without NaNs, loss explosion, or numerical divergence. The training-loss curves follow similar decreasing trajectories, whereas the best validation checkpoints occur at different iterations across settings. Relaxing the cap does not cause optimization failure, but it can affect late-stage validation behavior and the selected checkpoint iteration. The main experiments retain the shared conservative setting ${\alpha }_{\max }=0.25$ used throughout the comparative evaluation. Under the branch-weight bounds in Section 3.2.3, this moderate setting preserves a dominant uniform component, prevents any branch from receiving a majority weight, and provides a wider adaptive range than ${\alpha }_{\max }=0.1$. The sensitivity results characterize its stability across the tested range without claiming dataset-specific or universal optimality.

4.8. Sensitivity to the Diagonal Augmentation Probability

The main comparative experiments use $p_{\mathrm{SDA}}=0.3$ for both datasets, with this probability held fixed rather than tuned separately for each dataset. We additionally evaluate $p_{\mathrm{SDA}}\in \{0.1,0.3,0.5\}$ under the same evaluation protocol using seed 0 to characterize the coarse response to stronger diagonal exposure. The seed-0 results for $p_{\mathrm{SDA}}=0.1$ and $p_{\mathrm{SDA}}=0.3$ are closer, so these two settings are additionally evaluated with all three predefined seeds to estimate cross-seed variability. The $p_{\mathrm{SDA}}=0.5$ setting remains a seed-0 diagnostic reference because it reduces the FloodNet metrics and provides no consistent cross-dataset advantage in the coarse comparison. Full results are reported in Supplementary Table S2. The three-seed comparison shows that $p_{\mathrm{SDA}}=0.3$ gives stronger main eight-angle metrics on RescueNet and remains competitive on FloodNet. These results characterize the observed dataset dependence without establishing a universally optimal augmentation probability.

A separate seed-0 C4Former-Mean-SDA diagnostic is provided in Supplementary Table S3. In this diagnostic, SDA reduces the diagonal-orientation gap of the mean-fusion C4 baseline, but DC4Former retains higher All-8 and Worst-8 scores on RescueNet. The residual seed-0 difference is consistent with an effect of the fusion design, but this diagnostic does not establish the stability or magnitude of that effect across training runs.

4.9. Per-Class and Class-Wise Stability Analysis

4.9.1. Per-Class IoU Analysis

We report per-class IoU under the canonical $0^{\circ }$ setting for FloodNet and RescueNet in

Table 11. Seed-0 per-class IoU on FloodNet under the canonical $0^{\circ }$ setting. B-F: building-flooded; B-NF: building-non-flooded; R-F: road-flooded; R-NF: road-non-flooded. Bold values indicate the best value in each column.

Method	B-F	B-NF	R-F	R-NF	Water	Tree	Vehicle	Pool	Grass	mIoU
PSPNet	71.76	78.57	64.38	82.02	77.98	85.06	52.26	64.55	90.42	74.11
DeepLabv3+	72.70	80.65	66.04	84.48	79.66	85.87	59.18	66.01	91.03	76.18
UPerNet	70.94	79.54	67.03	84.41	78.97	86.07	60.26	66.85	91.07	76.13
SegFormer-B1	70.45	78.67	66.35	83.97	78.85	85.59	57.26	65.16	90.71	75.22
Mask2Former	73.04	80.35	67.80	85.97	81.00	84.99	67.36	69.52	90.91	77.88
UNetFormer	71.46	75.71	48.02	80.36	68.38	80.56	60.49	57.82	86.59	69.93
LRFormer	72.04	79.51	70.88	86.16	81.87	86.62	63.23	68.12	91.38	77.76
C4Former	71.22	79.30	68.67	85.50	79.11	86.30	60.98	66.52	91.19	76.53
DC4Former	71.66	79.04	73.22	85.80	81.51	85.69	59.81	67.10	91.14	77.22

and

Table 12. Seed-0 per-class IoU on RescueNet under the canonical $0^{\circ }$ setting. B-ND: building-no-damage; B-MD: building-medium-damage; B-MaD: building-major-damage; B-TD: building-total-damage; R-C: road-clear; R-B: road-blocked. Bold values indicate the best value in each column.

Method	Water	B-ND	B-MD	B-MaD	B-TD	Vehicle	R-C	R-B	Tree	Pool	mIoU
PSPNet	85.04	65.32	56.61	58.60	58.17	55.38	76.06	47.83	82.65	72.90	65.86
DeepLabv3+	84.99	68.20	60.17	60.78	62.58	61.38	76.84	50.25	83.75	77.60	68.65
UPerNet	85.25	67.92	59.54	59.12	61.75	60.32	77.04	51.18	84.22	73.71	68.00
SegFormer-B1	82.73	62.92	53.87	52.71	55.99	47.50	72.73	41.62	83.00	66.16	61.92
Mask2Former	85.81	70.26	61.33	61.48	63.87	67.93	78.03	51.86	83.71	83.08	70.74
UNetFormer	81.27	64.29	53.47	54.31	59.07	57.63	74.14	40.95	81.41	66.17	63.27
LRFormer	85.20	69.08	60.37	58.65	63.91	64.80	78.08	51.23	84.65	77.57	69.35
C4Former	84.41	71.08	62.28	59.93	64.85	61.93	76.46	45.98	83.24	71.16	68.13
DC4Former	83.90	69.51	61.01	59.49	64.83	61.88	76.64	47.90	84.56	71.22	68.10

. The background class is omitted from the averaged foreground mIoU.

At the canonical orientation, DC4Former produces class-level scores that are generally close to those of the stronger baselines, with strengths that vary by dataset. On FloodNet, it gives the highest flooded-road IoU and stays close to the leading values for buildings, water, and vegetation. On RescueNet, Mask2Former and LRFormer obtain higher $0^{\circ }$ scores for several classes. The per-class $0^{\circ }$ tables therefore provide canonical-accuracy context, and the following analysis evaluates rotation stability for selected disaster-relevant categories.

4.9.2. Class-Wise Rotation Stability

Table 13. Three-seed class-wise rotation stability for selected disaster-relevant categories. Bold values indicate the best value in each column.

Dataset	Class	All-8 ↑		Diag. ↑		Worst ↑		Std. ↓
		LR	DC	LR	DC	LR	DC	LR	DC
FloodNet	B-F	71.14	72.06	69.26	72.73	64.77	71.27	2.77	0.80
FloodNet	R-F	60.82	70.41	57.69	70.04	51.05	67.54	5.96	1.92
FloodNet	Water	71.69	81.20	69.01	81.56	63.89	79.96	4.61	0.91
RescueNet	B-MD	48.53	60.91	44.63	61.40	42.28	60.25	5.23	0.57
RescueNet	B-MaD	46.71	60.76	40.99	61.53	37.44	59.93	6.90	0.79
RescueNet	B-TD	56.93	65.33	53.97	65.83	52.13	64.46	3.62	0.65
RescueNet	R-B	30.27	47.08	25.35	47.08	21.92	46.09	8.16	0.66

Values are cross-seed means. B-F: building-flooded; R-F: road-flooded; B-MD/B-MaD/B-TD: building-medium/major/total-damage; R-B: road-blocked. Arrows indicate the preferred direction.

reports three-seed, eight-angle class-wise statistics for categories tied to post-disaster mapping decisions: flooded buildings, flooded roads, water regions, building-damage levels, and blocked roads. These classes are selected because they represent inundation extent, road passability, and structural damage, and because their thin boundaries or fragmented regions can be sensitive to image orientation. All-8 denotes the mean class IoU over the eight principal angles; Diag. denotes the mean over the four diagonal angles, Worst denotes the minimum across the eight angles, and Std. denotes the corresponding rotation-wise standard deviation. The comparison between LRFormer and DC4Former assesses whether the model-level orientation-reliability improvement extends to the selected disaster-relevant semantic categories.

For the selected disaster-relevant categories, the class-wise analysis follows the model-level orientation-stability trend. On FloodNet, DC4Former raises the three-seed mean worst-angle IoU for flooded roads from 51.05% to 67.54% and reduces its rotation-wise standard deviation from 5.96 to 1.92. On RescueNet, building-major-damage and road-blocked classes show large gains. Their mean worst-angle IoUs increase from 37.44% and 21.92% to 59.93% and 46.09%, respectively. Their rotation-wise standard deviations also fall below 1.0. These selected class-level results provide additional evidence of improved orientation reliability for several operationally important categories.

5. Discussion

The results separate two sources of orientation reliability: consistency within $C_4$ and exposure to rotations outside it. C4Former nearly equalizes performance at $0^{\circ }$, ${90}^{\circ }$, ${180}^{\circ }$, and ${270}^{\circ }$. The feature- and prediction-level diagnostic further shows that the improvement extends beyond the final segmentation metrics: the C4-modified encoders exhibit lower stage-wise feature discrepancy, raw-logit discrepancy, and aligned-prediction disagreement under right-angle rotations. By symmetrizing stride-1 kernels, averaging rotated downsampling responses, and aligning four low-resolution attention branches, the encoder reduces the orientation-specific responses introduced by LRFormer’s spatial-token operations. These operations act on grid-preserving right-angle rotations, where pixels or feature cells can be permuted without resampling. Diagonal rotations introduce interpolation and boundary changes on the fixed canvas. In the evaluated models, diagonal training exposure complements the encoder’s $C_4$ architectural consistency and improves robustness to these changes. DC4Former does not reconstruct high-frequency information removed during diagonal resampling; its measured effect is improved segmentation stability when the network receives interpolation-affected inputs.

The four branches represent the $C_4$ action on the sampled image lattice. Changes in UAV flight heading and camera yaw orientation can rotate the same scene relative to this lattice, so the model should preserve spatial correspondence across transformed inputs. On a regular square-pixel grid, $0^{\circ }$, ${90}^{\circ }$, ${180}^{\circ }$, and ${270}^{\circ }$ are exact index permutations and form the complete grid-preserving $C_4$ set targeted by the encoder. A ${45}^{\circ }$ step requires interpolation and changes the sampled values and boundary support. The RescueNet ablation illustrates this boundary: C4Former reaches an orthogonal-angle mean of 67.79% and a diagonal-angle mean of 52.03%, with a rotation-wise standard deviation of 7.88. After adding the single ${45}^{\circ }$ training complement, DC4Former raises the diagonal mean to 68.21% and reduces the standard deviation to 0.33. Single-diagonal augmentation provides this exposure in a structured way. Applied to standard LRFormer, it improves diagonal accuracy while leaving the backbone operators unchanged. Applied to C4Former, it introduces one representative of ${45}^{\circ }+C_4$ while the architecture handles the grid-preserving $C_4$ rotations. The three-seed ablation supports complementary roles for the two components: $C_4$-consistent operators reduce right-angle variation, while diagonal exposure reduces the remaining orthogonal–diagonal gap. The 24-angle stress test further evaluates sampled intermediate rotations, with dataset- and protocol-dependent behavior relative to augmentation. The experiments evaluate $C_4$ as a grid-preserving architectural basis and examine whether diagonal training exposure extends its stability beyond the four right-angle rotations.

Diagonal training exposure therefore mitigates the diagonal decline associated with the architecture-only C4Former. Future architectural mitigation can follow three directions. First, a bounded unsymmetrized residual kernel path could give the model a limited local-adaptation route after diagonal resampling. Second, applying $C_4$ spatial symmetrization only at selected stages or channels could avoid tying responses where interpolation-altered local cues require more flexibility. Third, resampling-aware anti-aliasing before local filtering could reduce interpolation artifacts in fine edges, narrow obstructions, and fragmented damage cues. Dedicated experiments are needed to test whether these alternatives preserve right-angle consistency while improving adaptation to interpolation-altered inputs.

The matched RandRot comparison indicates that rotation exposure is a strong training-time baseline with no additional inference cost and a dataset-dependent interaction with the C4 architecture. On FloodNet, LRFormer-RandRot remains slightly stronger than C4Former-RandRot, so continuous random rotation is already highly effective. On RescueNet, however, adding the C4 architecture under the same RandRot exposure improves worst-orientation reliability and reduces rotation-wise variation. This matched experiment serves as an attribution analysis by holding training-time rotation exposure fixed while changing the architecture. The final deployment comparison with DC4Former is addressed separately below. DC4Former takes a different route from dense random exposure: it changes how rotation-sensitive operators process features and uses one diagonal representative to complement the $C_4$ path. These routes can also be combined when deployment constraints allow.

The final comparison leads to different deployment choices for DC4Former and LRFormer-RandRot. On FloodNet, LRFormer-RandRot remains slightly higher than DC4Former in All-8, Worst-8, Mean-24, and Worst-24. On RescueNet, DC4Former provides a clearer advantage over the eight principal orientations, increasing All-8 from 66.43% to 68.01%, increasing Worst-8 from 64.26% to 67.66%, and reducing Std.-8 from 1.30 to 0.33. LRFormer-RandRot remains stronger in the RescueNet 24-angle stress test, with higher Mean-24 and Worst-24 and a lower Std.-24. The deployment choice depends on the primary requirement. DC4Former should be selected when reliability across the eight principal orientations is prioritized, particularly for rotation-sensitive data such as RescueNet. LRFormer-RandRot should be selected when inference efficiency or robustness across densely sampled angles is more important. Because only three seeds are used, these comparisons are reported descriptively, with no formal significance claims.

The main gain lies in lower orientation-induced variation, with canonical accuracy remaining comparable. For disaster mapping, reduced sensitivity to flight heading or image orientation is desirable because it improves the repeatability of the resulting semantic maps. Across three seeds on RescueNet, LRFormer loses 13.81 mIoU points between its canonical and worst orientations, compared with 0.16 points for DC4Former. The canonical per-class results show comparable class-level accuracy, while the class-wise rotation analysis is consistent with improved stability for disaster-relevant classes. Orientation reliability is therefore a separate model property and should be evaluated alongside canonical mIoU.

The principal cost is inference latency, with limited parameter growth and unchanged measured peak memory footprint. C4 feature-rotation averaged downsampling and multi-view attention increase FLOPs and require repeated feature transformations, reducing standardized $512\times 512$ throughput from 65.58 to 20.17 FPS relative to LRFormer. Under the canonical $0^{\circ }$ resized whole-image evaluation pipeline on RescueNet, latency increases from 44.13 ms/image for LRFormer to 95.60 ms/image for C4Former/DC4Former. The measured peak allocated GPU memory remains 1.51 GB for both model groups. At 95.60 ms/image, processing the 450-image RescueNet test set would require approximately 43 s of model inference. This calculation excludes data loading, metric computation, visualization, and result saving. Such throughput is compatible with reliability-oriented server-side or near-offline workflows, including post-flood road-passability mapping, inundation-boundary extraction, affected-building or vehicle inventories, and batch map production after UAV flights. It is less suitable for low-power onboard real-time deployment.

The latency difference between LRFormer and DC4Former is 51.47 ms/image. We use this measured increment for a first-order estimate of possible savings from future selective $C_4$ processing. A future stage- or channel-selective implementation could activate a smaller fraction of the current $C_4$ computation. For illustration, under a simple linear-cost assumption for the incremental $C_4$ computation, active fractions of 25%, 50%, and 75% give estimated total latencies of 57.00, 69.87, and 82.73 ms/image, respectively. These values correspond to latency reductions of 40.38%, 26.91%, and 13.46% relative to the full DC4Former latency. Actual latency would also depend on selection overhead, memory access, and hardware scheduling. Knowledge distillation and lightweight multi-view attention provide complementary directions for reducing inference cost.

The present evaluation uses FloodNet and RescueNet, fixed-canvas rotations, and the specified discrete eight- and 24-orientation protocols. Evaluation on additional UAV disaster datasets would further assess the generality of the observed reliability–latency trade-off.

The proposed operator-aware $C_4$ principle may also be transferable to other remote-sensing perception tasks, including object detection, change detection, and instance-level damage assessment, because many backbones contain similar rotation-sensitive spatial, downsampling, and attention or pooling operations. However, extending the design beyond semantic segmentation requires additional task-specific components. Detection heads, for example, introduce geometric factors such as anchor assignment, bounding-box regression, RoI alignment, or angle-aware box parameterization in oriented detection. Extending DC4Former beyond segmentation would therefore require task-specific head design and evaluation, which we leave for future work.

6. Conclusions

We presented DC4Former for rotation-stable UAV disaster segmentation. The method redesigns three rotation-sensitive operations in the LRFormer encoder: stride-1 spatial convolution, strided downsampling, and low-resolution pooling attention. C4Former improves consistency for grid-preserving right-angle rotations, while DC4Former adds a single ${45}^{\circ }$ training augmentation to expose the model to a representative diagonal orientation.

Across FloodNet and RescueNet, the three-seed ablation indicates that DC4Former improves worst-angle foreground mIoU and reduces rotation-wise variability while keeping canonical-orientation accuracy comparable. The feature- and prediction-level consistency diagnostic shows smaller right-angle discrepancies in the internal representations and aligned predictions. The 24-angle stress test also shows smoother sampled intermediate-angle behavior for DC4Former than for LRFormer on both datasets. The matched RandRot comparison shows that training-time rotation exposure is a strong baseline, while the C4 architecture provides additional worst-orientation reliability on RescueNet under the principal eight-angle protocol, where the baseline models exhibit larger rotation-wise variation. These results support reporting rotation-wise evaluation alongside canonical mIoU for UAV disaster maps acquired under varying flight headings and camera yaw orientations.

Future work will evaluate the method on additional UAV disaster datasets and investigate transfer to other remote-sensing perception tasks, such as object detection, change detection, and instance-level damage assessment. More efficient group-aware operators will also be explored to improve the trade-off between orientation reliability and inference speed.