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Title: Augmented Lagrangian method for total variation based image restoration and segmentation over triangulated surfaces
Authors: Tai, Xue Cheng
Wu, Chunlin
Zhang, Juyong
Duan, Yuping
Keywords: DRNTU::Engineering::Computer science and engineering
Issue Date: 2011
Source: Wu, C., Zhang, J., Duan, Y., & Tai, X.-C. (2012). Augmented Lagrangian Method for Total Variation Based Image Restoration and Segmentation Over Triangulated Surfaces. Journal of Scientific Computing, 50(1), 145-166.
Series/Report no.: Journal of scientific computing
Abstract: Recently total variation (TV) regularization has been proven very successful in image restoration and segmentation. In image restoration, TV based models offer a good edge preservation property. In image segmentation, TV (or vectorial TV) helps to obtain convex formulations of the problems and thus provides global minimizations. Due to these advantages, TV based models have been extended to image restoration and data segmentation on manifolds. However, TV based restoration and segmentation models are difficult to solve, due to the nonlinearity and non-differentiability of the TV term. Inspired by the success of operator splitting and the augmented Lagrangian method (ALM) in 2D planar image processing, we extend the method to TV and vectorial TV based image restoration and segmentation on triangulated surfaces, which are widely used in computer graphics and computer vision. In particular, we will focus on the following problems. First, several Hilbert spaces will be given to describe TV and vectorial TV based variational models in the discrete setting. Second, we present ALM applied to TV and vectorial TV image restoration on mesh surfaces, leading to efficient algorithms for both gray and color image restoration. Third, we discuss ALM for vectorial TV based multi-region image segmentation, which also works for both gray and color images. The proposed method benefits from fast solvers for sparse linear systems and closed form solutions to subproblems. Experiments on both gray and color images demonstrate the efficiency of our algorithms.
ISSN: 1573-7691
DOI: 10.1007/s10915-011-9477-3
Rights: © 2011 Springer Science+Business Media, LLC.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SCSE Journal Articles

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