dc.contributor.authorWu, Chunlin
dc.contributor.authorZhang, Juyong
dc.contributor.authorDuan, Yuping
dc.contributor.authorTai, Xue Cheng
dc.identifier.citationWu, 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.en_US
dc.description.abstractRecently 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.en_US
dc.relation.ispartofseriesJournal of scientific computingen_US
dc.rights© 2011 Springer Science+Business Media, LLC.en_US
dc.subjectDRNTU::Engineering::Computer science and engineering
dc.titleAugmented Lagrangian method for total variation based image restoration and segmentation over triangulated surfacesen_US
dc.typeJournal Article
dc.contributor.schoolSchool of Computer Engineeringen_US

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