DocumentCode :
1424975
Title :
Minimum-Distortion Isometric Shape Correspondence Using EM Algorithm
Author :
Sahillioglu, Y. ; Yemez, Y.
Author_Institution :
Dept. of Comput. Eng., Koc Univ., Istanbul, Turkey
Volume :
34
Issue :
11
fYear :
2012
Firstpage :
2203
Lastpage :
2215
Abstract :
We present a purely isometric method that establishes 3D correspondence between two (nearly) isometric shapes. Our method evenly samples high-curvature vertices from the given mesh representations, and then seeks an injective mapping from one vertex set to the other that minimizes the isometric distortion. We formulate the problem of shape correspondence as combinatorial optimization over the domain of all possible mappings, which then reduces in a probabilistic setting to a log-likelihood maximization problem that we solve via the Expectation-Maximization (EM) algorithm. The EM algorithm is initialized in the spectral domain by transforming the sampled vertices via classical Multidimensional Scaling (MDS). Minimization of the isometric distortion, and hence maximization of the log-likelihood function, is then achieved in the original 3D euclidean space, for each iteration of the EM algorithm, in two steps: by first using bipartite perfect matching, and then a greedy optimization algorithm. The optimal mapping obtained at convergence can be one-to-one or many-to-one upon choice. We demonstrate the performance of our method on various isometric (or nearly isometric) pairs of shapes for some of which the ground-truth correspondence is available.
Keywords :
combinatorial mathematics; computational geometry; expectation-maximisation algorithm; iterative methods; mesh generation; optimisation; 3D Euclidean space; 3D correspondence; EM algorithm iteration; MDS; bipartite perfect matching; combinatorial optimization; expectation-maximization algorithm; greedy optimization algorithm; ground-truth correspondence; high-curvature vertices; injective mapping; isometric method; log-likelihood maximization problem; mesh representations; minimum-distortion isometric shape correspondence; multidimensional scaling; optimal mapping; Approximation methods; Minimization; Optimization; Probabilistic logic; Shape; Spectral analysis; Three dimensional displays; 3D isometric shape correspondence; EM algorithm; bipartite perfect matching; greedy optimization; isometric distortion; multidimensional scaling; spectral embedding; Algorithms; Artifacts; Artificial Intelligence; Image Enhancement; Image Interpretation, Computer-Assisted; Imaging, Three-Dimensional; Information Storage and Retrieval; Pattern Recognition, Automated; Reproducibility of Results; Sensitivity and Specificity; Subtraction Technique;
fLanguage :
English
Journal_Title :
Pattern Analysis and Machine Intelligence, IEEE Transactions on
Publisher :
ieee
ISSN :
0162-8828
Type :
jour
DOI :
10.1109/TPAMI.2012.26
Filename :
6133289
Link To Document :
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