Efficient Deterministic Search With Robust Loss Functions for Geometric Model Fitting

Geometric model fitting is a fundamental task in computer vision, which serves as the pre-requisite of many downstream applications. While the problem has a simple intrinsic structure where the solution can be parameterized within a few degrees of freedom, the ubiquitously existing outliers are the main challenge. In previous studies, random sampling techniques have been established as the practical choice, since optimization-based methods are usually too time-demanding. This prospective study is intended to design efficient algorithms that benefit from a general optimization-based view. In particular, two important types of loss functions are discussed, i.e., truncated and $l_1$ losses, and efficient solvers have been derived for both upon specific approximations. Based on this philosophy, a class of algorithms are introduced to perform deterministic search for the inliers or geometric model. Recommendations are made based on theoretical and experimental analyses. Compared with the existing solutions, the proposed methods are both simple in computation and robust to outliers. Extensive experiments are conducted on publicly available datasets for geometric estimation, which demonstrate the superiority of our methods compared with the state-of-the-art ones. Additionally, we apply our method to the recent benchmark for wide-baseline stereo evaluation, leading to a significant improvement of performance. Our code is publicly available at https://github.com/AoxiangFan/EifficientDeterministicSearch .