Regularised differentiation for image derivatives

Abstract

This study investigates a regularised differentiation method to estimate image derivatives. The scheme minimises an integral functional containing an anti-differentiation data discrepancy term and a smoothness regularisation term. When discretised, the Euler–Lagrange necessary conditions for a minimum of the functional yield a large scale sparse system of linear equations, which can be solved efficiently by Jacobi/Gauss–Seidel iterations. The authors investigate the impact of the method in the context of two important problems in computer vision: optical flow and scene flow estimation. Quantitative results, using the Middlebury dataset and other real and synthetic images, show that the authors’ regularised differentiation scheme outperforms standard derivative definitions by smoothed finite differences, which are commonly used in motion analysis. The method can be readily used in various other image analysis problems.