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.
Numerical minimization of a second-order functional for image segmentation / Zanetti, Massimo; Ruggiero, Valeria; Miranda Jr, Michele. - In: COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION. - ISSN 1007-5704. - 36:(2016), pp. 528-548. [10.1016/j.cnsns.2015.12.018]
Numerical minimization of a second-order functional for image segmentation
Zanetti, Massimo;
2016-01-01
Abstract
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.File | Dimensione | Formato | |
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