BRIDGE:Boosting Representation Fidelity via Shape-Informed Distance-field Geometric Encoding for Multimodal Object Detection

Multimodal object detection seeks to exploit complementary information across heterogeneous sensing modalities for robust object perception. Different modalities reveal distinct structural and geometric cues of the same object through different imaging principles. However, heterogeneous imaging mechanisms complicate cross-modal geometric interaction, while complex object geometries remain difficult to capture with shapes parameterized by only a few parameters. In this paper, we introduce BRIDGE, a novel geometric representation framework for object detection that moves beyond predefined shapes toward continuous geometry modeling. Specifically, we observe that Signed Distance Fields (SDF) map heterogeneous modalities into a shared continuous space while preserving fine-grained geometry. We therefore introduce Continuous Geometry Encoding (CGE) to represent objects beyond predefined parametric shapes. We further propose Fourier-Conditioned Geometry Fusion (FCGF) to preserve informative geometric cues while exploiting cross-modal complementarity through frequency-conditioned residual refinement. Finally, we dive into SDF optimization during training and introduce Gradient-Modulated Loss (GML). GML suppresses gradients from well-fit regions while strengthening corrections for severe geometric deviations. Mathematical analysis and experiments show that SDF provides bounded and spatially distributed optimization signals for stable multimodal geometric learning. BRIDGE achieves 85.0% mAP${}_{50}$ on DroneVehicle, outperforming existing multimodal detectors and demonstrating the effectiveness of continuous geometry modeling. The code and models will be available on GitHub: xxxxx to facilitate future work.