2.2.1. Morphology-Aware Dynamic Receptive Field Attention
The structural information contained in the underwater echo signal streak image (UESSI) reflects topographical variations within the detection region and changes in the elevation of detection targets. Maintaining consistent structural information in streak images throughout the enhancement process is critical for achieving high-precision detection with LiDAR. However, only a tiny percentage of the streak image is made up of streak information; the majority is made up of black regions that are devoid of echo signals. Neural networks may find it challenging to extract streak features when streak information is not spatially dominating because the backdrop may dampen signals from objects of interest. There is limited chance of recovery during training if the target signal is lost as a result of downsampling. Additionally, the neural network’s capability to extract features from underwater echo signals is diminished since basic neural networks’ fixed-size convolution kernels are unable to extract features from intricate structural transformations, potentially resulting in the loss of image information. Within the same UESSI, regions with dense strong signals require small receptive fields to accurately preserve local details, while regions with weak signals require large receptive fields to infer signal continuity using contextual information. To address these challenges, we propose Morphology-Aware Dynamic Receptive Field Attention (MADRA). The overall architecture of MADRA consists of three submodules connected in series: Morphology-Aware Dynamic Receptive Field Generation Module (MDRF), Frequency-Enhanced Multi-Scale Feature Extraction (FEMFE), and Spatially Adaptive Receptive Field Aggregation (SARFA). The network architecture diagram is shown in
Figure 3.
The core task of MDRF is to dynamically generate optimal receptive field configuration parameters for each spatial location based on the morphological structure of the input feature map. We introduce a learnable Morphological Response Kernel (MRK) and Receptive Field Prediction Network (RFPN) to achieve content-adaptive generation of receptive field parameters. Unlike traditional convolutions that use fixed weights to extract spatial features, MRK consists of a set of differentiable morphological operators. Specifically, for an input feature
, MRK computes a local morphological descriptor at each spatial location:
where
and
represent the gradient magnitudes in the horizontal and vertical directions, respectively, characterizing the local orientation and edge intensity of the streak signals;
is a local curvature estimate, reflecting the degree of curvature of the streak;
is a measure of local information entropy, used to distinguish signal-dense regions from sparse background regions.
This morphological descriptor provides structure-aware prior information for the subsequent dynamic prediction of receptive fields, enabling the model to comprehend the type of image structure at each location and thereby generate matching receptive field parameters.
After obtaining the morphological descriptor
, the RFPN is responsible for predicting the optimal receptive field configuration parameters for each spatial location. The RFPN consists of two layers of 1 × 1 convolutional kernels and nonlinear activation functions, mapping the morphological descriptor to a three-dimensional receptive field configuration vector:
where
is the three-dimensional receptive field configuration vector at position
, corresponding to dilation coefficient
, used to dynamically adjust the equivalent dilation rate of subsequent convolutional kernels, thereby achieving spatial adaptive fine-tuning of the receptive field scale; deformation amplitude coefficient
, which controls the scale of the deformation offset
in snake convolution; frequency modulation coefficient
, used to adjust the gain factors of each frequency band in the frequency enhancement module;
is the Sigmoid activation function, ensuring that the predicted receptive field configuration parameters
are normalized to serve as smooth, continuous modulation factors; ReLU is a rectification function that introduces nonlinear expressive capability as an activation function;
and
are learnable weight matrices in the fully connected layer.
performs linear transformation and nonlinear mapping on the input morphological descriptor
to extract deep features for predicting the receptive field, while
maps the extracted features to the final three-dimensional receptive field configuration parameters
.
In the UESSI streak feature extraction task, the MDRF ensures that tends toward smaller values in signal-dense regions to enable fine-grained local perception, while in signal-sparse regions, tends toward larger values to facilitate context-based inference. Additionally, in regions with high curvature, is set to a larger value to enhance adaptability to serpentine bending. This dynamic generation mechanism enables each neuron to obtain the optimal receptive field configuration based on the morphological characteristics of its location.
The FEMFE module receives the receptive field configuration vector generated by MDRF and performs multiscale feature extraction across three parallel feature extraction branches. FEMFE integrates Parametric Dilated Convolution (PDConv), Morphology-Guided Snake Convolution (MG-SConv), and Frequency Adaptive Modulation (FAM) into each branch.
The base dilation rate for each branch of PDConv is set to 1, 2, and 4, respectively, to cover a multiscale range from local details to global semantics. PDConv receives the dilation rate coefficient
output by MDRF and performs continuous fine-tuning at the spatial position level near the base dilation rate via a learnable mapping function, enabling the receptive field scale to be finely calibrated according to local morphological features. The dilation rate of PDConv is dynamically determined by
; if the branch index is
, then the dilation rate of the kth branch is:
where
represents the base dilation rate, which is initially set to 1, 2, and 4 in this paper;
is the maximum adjustable range;
is the scaling factor, which allows the dilation rate to be continuously fine-tuned around the base value according to the streak structure.
The dilation rate and the dilation rate coefficient output by the MDRF are continuously adjusted around the base value. This design enables the receptive field size at each spatial location to be precisely calibrated according to its morphological features—the receptive field is automatically reduced in signal-dense regions to preserve local details, and automatically expanded in signal-sparse regions to infer structural continuity using contextual information. This approach ensures both the breadth of multiscale coverage and fine-grained calibration at each spatial location.
MG-SConv concatenates the morphological descriptor
generated by MDRF with the input feature map along the channel dimension, then inputs them together into the offset generation convolution. The offset is globally scaled via the deformation amplitude coefficient
:
where
denotes the concatenation operation for channel dimensions;
is the global scaling factor;
represents the convolution kernel weight of the convolution layer that generates deformable convolution offsets.
The introduction of guarantees that the deformation direction is simultaneously constrained by morphological information, such as curvature and edge orientation, rather than being purely determined by local gradients. This maximizes the preservation of signal structure continuity and integrity during downsampling by enabling the snake convolution’s kernel shape to more closely match the true geometric trajectories of the echo signal streak in UESSI and the narrow and curved local structures within the echo signals.
FAM first converts the feature maps of each branch into the frequency domain using the Fast Fourier Transform, obtaining the amplitude spectrum
and the phase spectrum
. The amplitude spectrum is further decomposed into three subbands: low-frequency, mid-frequency, and high-frequency
. Then FAM uses the frequency modulation coefficient
output by the MDRF to generate the adaptive gain for each subband:
where
are learnable frequency band weighting coefficients.
The gain for the mid-frequency subband remains fixed, whereas the low- and high-frequency subbands receive a gain factor relating to . The signal is restored to the spatial domain using the Inverse Fast Fourier Transform after the enhanced amplitude spectrum is combined with the original phase spectrum.
In UESSI-enhanced tasks, the edges and texture information of the streak signal are primarily distributed in the high-frequency subbands, while background noise typically occupies the low-frequency components. FAM is designed as an asymmetric frequency modulation mechanism aimed at maintaining the stability of mid-frequency information and ensuring that the continuity of streak edges is not disrupted by dynamic modulation. Additionally, it provides flexibility for both high-frequency and low-frequency components to be dynamically adjusted. It effectively improves the model’s capacity to capture details in weak echo signals while suppressing the propagation of background interference in the feature space by selectively enhancing high-frequency responses and moderately suppressing low-frequency components.
The SARFA module reconstructs the weight allocation mechanism in the form of spatial attention, enabling each pixel location to independently select the optimal receptive field size based on its morphological features. SARFA first concatenates the feature maps from the three branches with the morphological description operator from MDRF along the channel dimension. It then generates branch selection probabilities for each spatial position across the three branch feature maps output by FEMFE using a 1 × 1 convolutional layer and a Softmax activation function. The final output feature map is obtained by combining the three resulting weight scores with the feature maps using a spatially weighted Hadamard product and element-wise summation. The incorporation of morphological description operators enables the distribution of attention weights to be sensitive to image structure: at signal edges, higher weights are assigned to small-receptive-field branches to preserve details, while within the signal, higher weights are assigned to large-receptive-field branches to infer structural integrity using contextual information. This spatially adaptive aggregation strategy enables MADRA to dynamically configure optimal receptive field combinations for regions of different characteristics in UESSIs—dense signal regions, sparse signal regions, and signal-free background regions. This effectively prevents information loss in complex heterogeneous image content during downsampling caused by a single receptive field, providing high-quality multiscale feature representations for subsequent upsampling reconstruction of the generator.
2.2.2. Spatial-Temporal Decoupled Frequency-Enhanced Global Feature Fusion Block
The deflection electric field direction in ASTIL’s streak tube possesses time resolution capability, while the perpendicular direction to the deflection electric field provides spatial resolution capability [
26]. These two axes are respectively termed the time axis and the spatial axis. Each row parallel to the time axis can be represented as a time resolution channel, and each column parallel to the spatial axis can be represented as a spatial resolution channel. This is manifested in the streak image as the position coordinates of the echo signal pixels. In the streak image generated by the echo signal, the horizontal coordinate of each pixel reflects the target’s distance information, while the vertical coordinate reflects the target’s spatial position information. ASTIL determines the spot position by locating the center of mass within the echo signal streak image [
27,
28], thereby calculating the laser’s time-of-flight and spatial information to compute the precise location of the detected target. During image augmentation, unsupervised neural networks may cause shifts in the position of the center of mass, which could lead to larger errors in both the temporal and spatial resolution of ASTIL as well as a decrease in target detection accuracy. Additionally, the generated streak images from echo signals show great similarity when terrain variations within the same detection area are minor, making it simple for the neural network to ignore these minor variations throughout the learning process. We suggest Spatial-Temporal Decoupled Frequency-Enhanced Global Feature Fusion Block (STDFBlock) as a solution to these problems. STDFBlock consists of three components: Frequency-domain Global Context Encoder (FGCE), Spatial-Temporal Decoupled Channel Attention (STDC), and Content-Aware Gated Fusion (CAGF); the network architecture diagram is shown in
Figure 4. STDFBlock significantly enhances the neural network’s ability to capture global contextual information and multi-view channel relationships. Its parallel-structure design and the introduction of a channel attention mechanism facilitate information exchange and feature fusion across different branches, enabling the effective integration of transformed multi-scale features. The channel attention mechanism enables the model to adaptively learn the importance weights of each channel, enhancing the model’s perception of subtle details by increasing the weights of key channels.
While high-frequency components encode the edges and local texture details of the echo signals, low-frequency components carry the majority of the global structure of streak images. Conventional spatial-domain global pooling compresses high-frequency and low-frequency information indiscriminately, causing the latter to contaminate the former. FGCE transforms the input feature map into the frequency domain via a two-dimensional discrete cosine transform (DCT). UESSI’s primary structure and content information are highly concentrated in the low-frequency coefficients, while high-frequency textures are distributed across coefficients far from the origin. The DCT possesses excellent energy compression properties. Based on this property, FGCE retains only the low-frequency subbands of the DCT coefficients for global context encoding, enhancing the module’s global perception capabilities. It explicitly separates low-frequency structures from high-frequency information, fully preserving high-frequency details for independent processing by subsequent local attention branches, thereby avoiding the irreversible damage to fine-scale structural information caused by global pooling. The global frequency-domain description vector is obtained by applying global average pooling to the truncated low-frequency coefficients obtained by DCT using a preset low-frequency truncation threshold. A global frequency-domain weight vector is then generated by passing this vector through a channel weight generator made up of two fully connected layers. These weights reflect the importance of each channel at the global structural level and can adaptively enhance the ability to extract streak structural features.
STDC completely decouples the temporal and spatial attention calculations for streak images into two independent parallel subbranches: the spatial attention branch and the temporal attention branch. The spatial attention branch compresses the information of each channel in the horizontal dimension into a one-dimensional description in the vertical direction for the input feature map by performing average pooling along the temporal axis to extract channel attention responses regarding the target spatial location in the vertical direction. One-dimensional convolution is then used to aggregate local neighborhood information along the vertical direction, and normalization and a Sigmoid activation function are used to create a spatial attention weight vector. This weight vector reflects the relative importance of each channel at different spatial locations along the vertical direction and can adaptively enhance the channel response to changes in the corresponding target’s spatial position. The temporal attention branch compresses the input feature map along the spatial axis to extract channel attention responses regarding target distance information in the horizontal direction, similarly generating a temporal attention weight vector. This vector encodes the sensitivity of each channel to changes in target distance information in the horizontal direction. Finally, the spatial and temporal attention weights are fused into a complete spatio-temporal attention map through an outer product operation.
In UESSIs, regions with sparse weak echo signals need stronger feature enhancement to compensate for information loss during downsampling, while features in dense strong echo signal regions are easily learned and excessive enhancement may introduce artifacts. CAGF provides a differentiated fusion strategy for different regions. CAGF first calculates the local mean and local standard deviation at each spatial position along the channel dimension for an input feature map . The local mean reflects the overall signal intensity at that spatial location, while the local standard deviation quantifies the texture complexity and the degree of abrupt variation in features within that region. A two-channel statistical feature map is created by concatenating these two components along the channel dimension. The statistical features are then mapped to a spatially adaptive gating factor using a 1 × 1 convolution and a Sigmoid activation function, generating an independent adaptive gating factor for each spatial location that is sensitive to the content features of each local region. The final output feature map uses gated weighted fusion to combine the original features with the enhanced features, which have been modulated by both spatiotemporal attention and global weights in the frequency domain. This mechanism enhances regions with strong signals more significantly to highlight key features, while preserving more original information in regions with weak signals and background areas to maintain stability, thereby achieving pixel-by-pixel differentiated control over the enhancement intensity across different image regions.