Aligning Partially Overlapping Point Sets: an Inner Approximation Algorithm

TL;DR

This paper introduces an inner approximation algorithm for aligning partially overlapping point sets without prior transformation info, offering robustness, efficiency, and global optimality in computer vision tasks.

Contribution

It presents a novel inner approximation optimization method that handles non-regularized, no-prior-information point set alignment with guaranteed global optimality.

Findings

Demonstrates superior robustness over state-of-the-art algorithms.

Efficiently solves the linear assignment problem as a core step.

Proves the method's $\epsilon$-global optimality and robustness.

Abstract

Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point matching algorithm to a function of a low dimensional variable. The resulting function, however, is only concave over a finite region including the feasible region. To cope with this issue, we employ the inner approximation optimization algorithm which only operates within the region where the objective function is concave. Our algorithm does not need regularization on transformation, and thus can handle the situation where there is no prior information about the values of the transformations. Our method is also $\epsilon-$globally optimal and thus is guaranteed to be robust. Moreover, its most computationally expensive subroutine is a linear assignment problem which can be efficiently solved. Experimental results demonstrate the better robustness of the proposed method over state-of-the-art algorithms. Our method is also efficient when the number of transformation parameters is small.