BridgeMatch: Conditional Transport Bridges in Matching Matrix Space for 3D Deformable Registration

arXiv:2609.11472v1 Announce Type: new Abstract: Reliable non-rigid point cloud correspondences are important for deformable anatomical registration, embodied perception and manipulation, and dynamic 3D reconstruction. Coarse-to-fine methods reduce computational cost by selecting the top-(K) coarse regions. However, this pruning may remove weak but correct hypotheses and restrict fine matching to an incomplete search space. We present paper, a two-stage generative solver that maintains the complete soft matching matrix at both coarse and high resolutions. StageI uses denoising diffusion to estimate a global matching matrix in the compact coarse-resolution space. We then lift this matrix to high resolution while preserving its hierarchy. The lifted matrix is rank-bounded and block-constant. StageII refines it through a conditional transport bridge. We implement the bridge with two types of dynamics: a deterministic endpoint-parameterized conditional Flow Matching (CFM) ODE and a stochastic Brownian-bridge SDE inspired by Schrodinger bridges. Both variants share the lifted source, a time-conditioned transformer, and a matching-matrix endpoint predictor. Experiments on 4DMatch and 4DLoMatch show that both variants produce more accurate correspondences than the compared methods and improve downstream registration, with larger gains in low-overlap cases. They also improve cross-dataset generalization on CAPE and DeepDeform without target-domain adaptation while using the same deformation solver.

Related

• FUSER: Feed-Forward MUltiview 3D Registration Transformer and SE(3)^N Diffusion Refinement
• UBone3D: Physics-Rectified Conditional Flow Matching for Anatomical 3D Shape Completion from Ultrasound
• Phase-Aligned Finite-Fourier Periodic Deformation for 4D Medical Image Interpolation

Source: arXiv cs.CV | 2026-09-11