Open AccessRegularised differentiation for image derivatives
Author(s) -
Mathlouthi Yosra,
Mitiche Amar,
Ben Ayed Ismail
Publication year - 2017
Publication title -
iet image processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.401
H-Index - 45
eISSN - 1751-9667
pISSN - 1751-9659
DOI - 10.1049/iet-ipr.2016.0369
Subject(s) - context (archaeology) , smoothness , optical flow , term (time) , mathematics , computer science , gauss , image (mathematics) , automatic differentiation , mathematical optimization , scheme (mathematics) , algorithm , artificial intelligence , mathematical analysis , computation , biology , paleontology , physics , quantum mechanics
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.