HBSP: a hybrid bilinear and semidefinite programming approach for aligning partially overlapping point clouds

Area of Science:

• Computer Vision
• Computational Geometry
• Optimization

Background:

• Aligning partially overlapping 3D point clouds is crucial for many applications.
• Existing methods often struggle with invariance to transformations and robustness to noise or deformation.

Purpose of the Study:

• To develop a novel algorithm for robust and invariant alignment of partially overlapping point clouds.
• To address limitations in current point cloud registration techniques.

Main Methods:

• Reformulation of the binary linear assignment-least squares (BLALS) problem.
• Utilizing semidefinite relaxation and convex envelope for problem relaxation.
• Development of a branch-and-bound (BnB) algorithm with focused branching on transformation variables.

Main Results:

• The proposed method demonstrates robustness against non-rigid deformations and separable outliers.
• Performance degrades when outliers are mixed with inlier data.
• The algorithm's runtime is higher due to the iterative solution of semidefinite programs.

Conclusions:

• The presented BLALS minimization approach offers a promising solution for point cloud alignment.
• Further research may focus on improving computational efficiency and outlier handling in mixed scenarios.