Aligning Partially Overlapping Point Sets: an Inner Approximation Algorithm
This addresses a challenging computer vision problem for applications like image registration, but it appears incremental as it builds on existing robust point matching techniques.
The paper tackles the problem of aligning partially overlapping point sets without prior transformation information by reducing the robust point matching objective to a low-dimensional function and using an inner approximation algorithm that operates within a concave region. The method achieves ε-global optimality, is robust, and experimental results show better robustness over state-of-the-art algorithms.
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 $ε-$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.