Point Clouds Matching Based on Discrete Optimal Transport.

Area of Science:

• Computer Vision
• Geometric Computing
• Machine Learning

Background:

• Point cloud registration relies on accurate matching, which is challenged by large-scale transformations and noise.
• Existing discrete optimal transport (DOT) methods lack robustness for complex point cloud matching tasks.
• Prior probability plays a crucial role in accurate point cloud matching.

Purpose of the Study:

• To improve the robustness and accuracy of discrete optimal transport (DOT) for point cloud matching.
• To address limitations of classical DOT in handling large-scale affine/nonlinear transformations, noise, and outliers.
• To develop novel DOT models and algorithms for challenging point cloud registration problems.

Main Methods:

• Proposed an improved DOT model incorporating an orthogonal matrix and a diagonal matrix.
• Introduced a relaxed and regularized DOT model to handle outliers effectively.
• Developed two algorithms to solve the proposed DOT models.

Main Results:

• The proposed DOT models demonstrate enhanced capability in handling complex deformations, noise, and outliers.
• Extensive experiments show superior performance compared to state-of-the-art methods (CPD, APM, RANSAC, TPS-ICP, TPS-RPM, RPMNet) on real datasets.
• Numerical results confirm improved robustness and accuracy under various degradation levels, including reflection, rotation, stretch, and noise.

Conclusions:

• The novel DOT models and algorithms offer a more robust and accurate solution for point cloud matching.
• The enhanced DOT approach effectively addresses limitations of previous methods in complex and noisy environments.
• This work advances the state-of-the-art in point cloud registration through improved discrete optimal transport.