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Convex optimisation for multiclass image labeling
conference contribution
posted on 2007-12-01, 00:00 authored by Z Fu, Antonio Robles-KellyAntonio Robles-KellyIn this paper, we address multiclass pairwise labeling problems by proposing an alternative approach to continuous relaxation techniques which makes use of a quadratic cost function over the class labels. Here, we relax the discrete labeling problem by abstracting the problem of multiclass semi-supervised labeling to a graph regularisation one. By doing this, we can perform multiclass labeling using a cost function which is convex and related to the target function used in discrete Markov Random Field approaches. Moreover, the Hessian of our cost function is given by the graph Laplacian of the adjacency matrix. Therefore, the optimisation of the cost function is governed by the pairwise interactions between pixels in the local neighbourhood. Since the Hessian is sparse in nature, we can find the global minimum of the continuous relaxation problem efficiently by solving a linear equation using Cholesky factorization. In constrast to other segmentation algorithms elsewhere in the literature, the general nature of the cost function we employ is capable of capturing arbitrary pairwise relations. We provide results on synthetic and realworld imagery and demonstrate the efficacy of our method compared to competing approaches. © 2007 IEEE.
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Pagination
438 - 445Publisher DOI
ISBN-13
9780769530673ISBN-10
0769530672Publication classification
E1.1 Full written paper - refereedTitle of proceedings
Proceedings - Digital Image Computing Techniques and Applications: 9th Biennial Conference of the Australian Pattern Recognition Society, DICTA 2007Usage metrics
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