Conditional transport boosts 3d deformable point cloud matching accuracy
BridgeMatch: Conditional Transport Bridges in Matching Matrix Space for 3D Deformable Registration
Computer Vision and Pattern Recognition
Summary
Matching points between two 3D shapes that deform is tricky, especially when the shapes only partially overlap. The authors introduce BridgeMatch, a new two-step method that first finds a rough global match and then refines it carefully without losing any possible correct matches. This approach uses advanced math tools called diffusion models and transport bridges to better guess which points correspond, even in challenging cases. Their experiments show it works better than previous methods and adapts well across different datasets.
What this means in practice
- •For medical imaging teams: Improve anatomical registration accuracy by generating more reliable point correspondences for deformable 3D medical scans.
- •For robotics engineers: Enhance embodied perception systems with more accurate matching of deformable object shapes for manipulation and interaction.
Authors
Qianliang Wu, Haobo Jiang, Guangwei Gao, Shuo Chen, Jin Xie, Jian Yang, Yaqing Ding
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. Stage~I 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. Stage~II 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 Schrödinger 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.