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1887

access icon free Regularised differentiation for image derivatives

© The Institution of Engineering and Technology
Received 18/05/2016, Accepted 23/01/2017, Revised 10/12/2016, Published 26/01/2017

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.

Inspec keywords: differentiation; iterative methods; computer vision; image sequences

Other keywords: linear equations; smoothness regularisation term; scene flow estimation; motion analysis; optical flow estimation; image derivative estimation; Middlebury dataset; large scale sparse system; Jacobi-Gauss-Seidel iterations; integral functional minimization; Euler-Lagrange necessary conditions; computer vision; image analysis problems; synthetic images; anti-differentiation data discrepancy term; smoothed finite differences; regularised differentiation method

Subjects: Interpolation and function approximation (numerical analysis); Numerical integration and differentiation; Optical, image and video signal processing; Numerical integration and differentiation; Interpolation and function approximation (numerical analysis); Computer vision and image processing techniques

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