Fast Rigid Alignment of Heterogeneous Images in Sliced Wasserstein Distance

Abstract. Many applications of computer vision rely on the alignment of similar but nonidentical images. We present a fast algorithm for aligning heterogeneous images based on optimal transport. Our approach combines the speed of fast Fourier methods with the robustness of sliced probability metrics and allows us to efficiently compute the alignment between two [Formula: see text] images using the sliced 2-Wasserstein distance in [Formula: see text] operations. We show that our method is robust to translations, rotations, and deformations in the images.