4.4.2. Effectiveness of the Proposed Module
As shown in
Table 3, the baseline model contains 4.1 M parameters and requires 9.9 GFLOPs, achieving an overall mAP@0.5 of 81.4% and an mAP@0.5:0.95 of 68.6%. After introducing the DKCF module, the number of parameters increases to 4.3 M and the computational cost increases to 10.6 GFLOPs. Meanwhile, the overall mAP@0.5 improves to 83.1%, and the mAP@0.5:0.95 increases to 70.9%. This indicates that with only an additional 0.2 M parameters and approximately 0.7 GFLOPs of computational overhead, the proposed DKCF module achieves improvements of 1.7 and 2.3 percentage points in mAP@0.5 and mAP@0.5:0.95, respectively.
It is worth noting that the DKCF module provides more significant improvements for challenging object categories. As shown in
Table 4, the AP of the Van category increases by 4.05 percentage points in
and 4.02 percentage points in
. Moreover, the Truck category achieves a 2.44 percentage-point improvement in
, while the Freight car category improves by 2.66 percentage points. In the DroneVehicle dataset, these categories generally exhibit larger scale variations, similar appearances, and severe occlusion problems. These results indicate that the DKCF module provides relatively larger improvements for several challenging and less frequent categories, particularly Van, Freight car, and Truck.
From the perspective of metric improvements, the gain in mAP@0.5:0.95 is generally higher than that in mAP@0.5. This indicates that the DKCF module not only improves the capability of object classification and localization but also contributes to more accurate localization under stricter IoU thresholds.
To intuitively demonstrate the effectiveness of the DKCF module, three representative complex scenarios from the DroneVehicle dataset are selected for visualization analysis. As shown in
Figure 6,
Figure 7 and
Figure 8, the feature visualization results of the
,
, and
levels before and after introducing the DKCF module are presented under extremely dark, nighttime, and foggy conditions.
Overall, after incorporating the DKCF module, the model is able to focus more effectively on informative complementary features within the target regions while suppressing background noise and redundant modal information. The visualization results under different scenarios indicate that, in challenging environments such as extremely dark conditions, nighttime scenes, and heavy fog, the originally scattered activation responses gradually concentrate on the regions containing vehicle targets. This demonstrates that the DKCF module enhances the model’s ability to capture discriminative target features and produces more concentrated target-region activations in the selected examples.
To further determine whether the improvement of DKCF originates from explicit discrepancy modeling, channel calibration, or simply from introducing an additional fusion structure, we conduct a controlled component-level ablation. The No-Difference variant removes cross-modal discrepancy modeling while retaining the corresponding fusion scaffold. The Raw-Difference variant directly introduces the processed signed discrepancy without channel calibration. The ECA-only variant retains pooled channel interaction but removes RBF-KAN, whereas the Multilayer Perceptron (MLP) variant replaces RBF-KAN with a conventional nonlinear mapping. The insertion positions and the remaining network structure are kept unchanged.
As shown in
Table 5a, the No-Difference, Raw-Difference, ECA-only, and MLP variants achieve 80.9%, 81.2%, 81.5%, and 81.3% mAP@0.5, respectively, with corresponding mAP@0.5:0.95 values of 68.5%, 68.6%, 68.8%, and 68.7%. In contrast, the complete DDEF-Net achieves 84.9% mAP@0.5 and 72.6% mAP@0.5:0.95. In particular, compared with ECA-only and MLP calibration, the complete model improves mAP@0.5:0.95 by 3.8 and 3.9 percentage points, respectively, while introducing only a modest increase in model complexity. These results indicate that the performance gain cannot be attributed solely to an additional fusion scaffold, direct discrepancy injection, or conventional channel calibration. Under the present architecture, RBF-KAN-based nonlinear calibration provides additional benefit in selectively exploiting cross-modal discrepancy information.
We further investigate whether the benefit of DKCF originates merely from the magnitude of cross-modal discrepancy or from its directional representation. For this purpose, the default signed discrepancy is compared with the absolute discrepancy and the reverse-signed discrepancy . All other components, including nonlinear calibration, residual fusion, insertion positions, and training settings, remain unchanged.
As shown in
Table 5b, the absolute-difference variant achieves 81.7% mAP@0.5 and 69.1% mAP@0.5:0.95, while the reverse-signed variant obtains 81.4% and 68.8%, respectively. In comparison, the default RGB–IR signed formulation reaches 84.9% and 72.6%. Since the three variants have identical parameter counts and computational costs, the results indicate that retaining modality-order-dependent discrepancy information is more effective than using discrepancy magnitude alone under the current fusion architecture.
The influence of the discrepancy gain
in Equation (
28) is further evaluated by setting
to 0.5, 1, 2, and 3 while keeping all other configurations unchanged. As shown in
Table 5c, increasing
from 0.5 to 2 progressively improves mAP@0.5 from 81.3% to 84.9% and mAP@0.5:0.95 from 68.6% to 72.6%. However, further increasing
to 3 reduces the two metrics to 80.9% and 68.3%, respectively. This non-monotonic trend suggests that the discrepancy term should maintain an appropriate balance with the original visible and infrared features. An insufficient gain may limit the contribution of the calibrated complementary information, whereas excessive amplification may disturb the original bimodal representation. Therefore,
, which provides the best performance among the evaluated settings, is retained as the default value.
As shown in
Table 3, the introduction of the SFDE module improves the detection performance of the model. Specifically, the overall mAP@0.5 increases from 81.4% to 83.1%, representing an improvement of 1.7 percentage points. Meanwhile, the mAP@0.5:0.95 increases from 68.6% to 70.8%, with a gain of 2.2 percentage points. Compared with mAP@0.5, the improvement in mAP@0.5:0.95 is more significant, indicating that the SFDE module not only enhances the object detection capability but also contributes to more accurate localization under stricter IoU thresholds. However, this overall improvement does not imply that the two internal branches are independently beneficial. We therefore further disentangle the contributions of the Scharr and Fourier branches through branch-wise ablation experiments, as reported in
Table 6.
To further investigate the individual roles of the two branches within SFDE, we conducted branch-wise ablation experiments by constructing Scharr-only and Fourier-only variants while keeping the insertion position, training settings, and the remaining network architecture unchanged. The results are presented in
Table 6. The Scharr-only variant achieves 80.5% mAP@0.5 and 67.5% mAP@0.5:0.95, while the Fourier-only variant achieves 80.3% and 67.6%, respectively. Both single-branch variants remain close to but below the RGB + IR baseline, indicating that neither branch alone provides a net performance improvement under the current architecture.
In contrast, jointly incorporating the Scharr and Fourier branches increases mAP@0.5 and mAP@0.5:0.95 to 83.1% and 70.8%, respectively, corresponding to improvements of 1.7 and 2.2 percentage points over the baseline. These results suggest that the effectiveness of SFDE primarily arises from the complementary interaction between spatial gradient priors and frequency-domain representations rather than from either branch independently. The Scharr branch emphasizes local edge and contour structures, whereas the Fourier branch provides complementary frequency-domain structural information. Their joint modeling therefore provides a more comprehensive representation of low-level object details, particularly under stricter localization criteria.
To directly examine whether the potential cancellation between signed horizontal and vertical Scharr responses adversely affects SFDE, we further compare the original signed averaging strategy with absolute-response averaging and gradient-magnitude fusion. Except for the directional fusion formulation, all network structures and training settings are kept unchanged.
As shown in
Table 7, the absolute-average variant achieves 79.3% mAP@0.5 and 68.9% mAP@0.5:0.95, while the gradient-magnitude variant achieves 79.6% mAP@0.5 and 69.2% mAP@0.5:0.95. In comparison, the original signed-average formulation achieves 83.1% mAP@0.5 and 70.8% mAP@0.5:0.95. All three variants have the same parameter count of 4.2 M and computational cost of 11.8 GFLOPs.
Although signed averaging may theoretically attenuate responses when the horizontal and vertical gradients have opposite signs, explicitly avoiding such cancellation does not improve detection performance. Instead, the results suggest that preserving signed directional information is more beneficial under the current SFDE architecture, whereas absolute and magnitude formulations discard gradient polarity and alter the original response distribution. Therefore, the signed averaging formulation is retained in the final model.
To further examine the scale-specific effects of SFDE,
,
, and
were evaluated using the COCO area definitions. As shown in
Table 8, the baseline achieves 26.30%, 65.89%, and 47.83%
,
, and
, respectively. Introducing SFDE alone results in 24.40%
, 67.12%
, and 57.03%
. Thus, although SFDE improves
and
by 1.23 and 9.20 percentage points, respectively,
decreases by 1.90 percentage points. The complete model achieves 25.76%
, 68.61%
, and 57.62%
. These results indicate that the performance gains of the current SFDE design are not concentrated in the COCO-defined small-object subset, but are more evident for medium- and large-scale objects.
As shown in
Table 9, from the perspective of individual categories, the improvements introduced by the SFDE module are mainly concentrated in the Van, Freight car, and Truck categories. Among them, the Van category achieves the most significant improvement, with increases of 3.95 and 3.75 percentage points in
and
, respectively. These results indicate that the SFDE module can effectively enhance the representation capability of objects with large intra-class variations and complex visual characteristics.
The feature activation maps in
Figure 9 provide a qualitative illustration of the effect of SFDE in densely distributed vehicle scenes. By introducing Scharr-based edge priors and Fourier-domain feature modeling, SFDE produces more structured target-region responses and clearer contour-related activations in the selected examples.