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Mathematical Problems in Engineering
Volume 2013, Article ID 817496, 11 pages
Research Article

Approximated Slack Scaling for Structural Support Vector Machines in Scene Depth Analysis

1College of Computer Science & Technology, Zhejiang University of Technology, Hangzhou 310023, China
2Key Laboratory of Visual Media Intelligent Processing Technology of Zhejiang Province, China
3School of Accounting, Zhejiang University of Finance and Economics, Hangzhou, China

Received 31 January 2013; Accepted 31 March 2013

Academic Editor: Carlo Cattani

Copyright © 2013 Sheng Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Based upon the framework of the structural support vector machines, this paper proposes two approaches to the depth restoration towards different scenes, that is, margin rescaling and the slack rescaling. The results show that both approaches achieve high convergence, while the slack approach yields better performance in prediction accuracy. However, due to its nondecomposability nature, the application of the slack approach is limited. This paper therefore introduces a novel approximation slack method to solve this problem, in which we propose a modified way of defining the loss functions to ensure the decomposability of the object function. During the training process, a bundle method is used to improve the computing efficiency. The results on Middlebury datasets show that proposed depth inference method solves the nondecomposability of slack scaling method and achieves relative acceptable accuracy. Our approximation approach can be an alternative for the slack scaling method to ensure efficient computation.