Article ID Journal Published Year Pages File Type
766527 Communications in Nonlinear Science and Numerical Simulation 2016 21 Pages PDF
Abstract

•The Blake–Zisserman functional is a second-order model for image segmentation.•A variational approximation of the functional given by Ambrosio, Faina and March, is discretized.•We propose an efficient block-coordinate descent method for the numerical minimization.•Numerical experiments involve very different types of datasets, including digital surface models.•Results show that, with the proposed method, the second order segmentation can be addressed in competitive time.

In this paper we address the numerical minimization of a variational approximation of the Blake–Zisserman functional given by Ambrosio, Faina and March. Our approach exploits a compact matricial formulation of the objective functional and its decomposition into quadratic sparse convex sub-problems. This structure is well suited for using a block-coordinate descent method that cyclically determines a descent direction with respect to a block of variables by few iterations of a preconditioned conjugate gradient algorithm. We prove that the computed search directions are gradient related and, with convenient step-sizes, we obtain that any limit point of the generated sequence is a stationary point of the objective functional. An extensive experimentation on different datasets including real and synthetic images and digital surface models, enables us to conclude that: (1) the numerical method has satisfying performance in terms of accuracy and computational time; (2) a minimizer of the proposed discrete functional preserves the expected good geometrical properties of the Blake–Zisserman functional, i.e., it is able to detect first and second order edge-boundaries in images and (3) the method allows the segmentation of large images.

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