A Robust Graph-Based Method for The General Correspondence Problem Demonstrated on Image Stitching

Abstract

We pose robust matching with parametric and non-parametric constraints as the problem of finding a stable independent set (SIS) in an oriented graph whose vertices are all possible correspondences, whose edges capture the structure of the constraints and whose edge orientation represents pairwise comparison 'is better' based on correspondence quality, including the uncertainty of this comparison. We show SIS possess properties of both robustness and weak optimality. The main contribution of this paper is algorithmic speedup that results from exploiting the dependence between the standard uniqueness constraint and the parametric constraint. The general theory is demonstrated on the example of image stitching using homography model. The algorithm needs at most 𝜅N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> calls of a procedure testing if two ellipse correspondences are consistent with a general homography. The previous known SIS algorithm needed O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> ) tests. Experiments show the method gives good results and is fast in practice with 𝜅≈0.3.