Variational Model for Depth Estimation from Images

被引:0
作者
Malyshev, Alexander [1 ]
Tai, Xue-Cheng [1 ]
机构
[1] Univ Bergen, Dept Math, Bergen, Norway
来源
2019 13TH INTERNATIONAL CONFERENCE ON SOFTWARE, KNOWLEDGE, INFORMATION MANAGEMENT AND APPLICATIONS (SKIMA) | 2019年
基金
欧盟地平线“2020”;
关键词
Computer vision; Optimization; Minimization methods;
D O I
10.1109/skima47702.2019.8982425
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
We propose a variant of convex reformulation of the standard variational model with non-convex data terms. The proposed convex relaxation of multilabel problems is a continuous formulation of Ishikawa's method for extension of the graph min-cut to the multilabel problems. Our convex continuous reformulation is based upon functional lifting to a higher-dimensional space using superlevel functions. We solve the resulting convex variational problem by the augmented Lagrangian method. The most time consuming part of this method is the numerical solution of a boundary value problem for the Poisson equation in three-dimensional space, which is implemented by means of a fast Poisson solver. We illustrate the developed theory with several numerical examples for the standard correspondence problem for a rectified stereo image pair.
引用
收藏
页数:8
相关论文
共 22 条
[1]  
[Anonymous], 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition
[2]  
[Anonymous], P MACHINE LEARNING R
[3]  
Bae E, 2014, LECT NOTES COMPUT SC, V8293, P134, DOI 10.1007/978-3-642-54774-4_7
[4]  
Berkels B, 2009, LECT NOTES COMPUT SC, V5567, P26, DOI 10.1007/978-3-642-02256-2_3
[5]   Fast approximate energy minimization via graph cuts [J].
Boykov, Y ;
Veksler, O ;
Zabih, R .
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 2001, 23 (11) :1222-1239
[6]  
Chambolle A, 2001, J CONVEX ANAL, V8, P149
[7]  
Chan TF, 2005, IMAGE PROCESSING AND ANALYSIS, P1, DOI 10.1137/1.9780898717877
[8]  
Federer H., 1969, Die Grundlehren der mathematischen Wissenschaften, V153
[9]   Exact optimization for Markov random fields with convex priors [J].
Ishikawa, H .
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 2003, 25 (10) :1333-1336
[10]  
Ishikawa H., 2012, IMAGE PROCESSING ANA, P25