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Shape Retrieval Using Hierarchical Total Bregman Soft Clustering
Dec. 2012 (vol. 34 no. 12)
pp. 2407-2419
Meizhu Liu, Dept. of CISE, Univ. of Florida, Gainesville, FL, USA
B. C. Vemuri, Dept. of CISE, Univ. of Florida, Gainesville, FL, USA
Shun-Ichi Amari, Math. Neurosci. Lab., RIKEN Brain Sci. Inst., Wako, Japan
F. Nielsen, Ecole Polytech., Palaiseau, France
In this paper, we consider the family of total Bregman divergences (tBDs) as an efficient and robust “distance” measure to quantify the dissimilarity between shapes. We use the tBD-based l1-norm center as the representative of a set of shapes, and call it the t-center. First, we briefly present and analyze the properties of the tBDs and t-centers following our previous work in [1]. Then, we prove that for any tBD, there exists a distribution which belongs to the lifted exponential family (lEF) of statistical distributions. Further, we show that finding the maximum a posteriori (MAP) estimate of the parameters of the lifted exponential family distribution is equivalent to minimizing the tBD to find the t-centers. This leads to a new clustering technique, namely, the total Bregman soft clustering algorithm. We evaluate the tBD, t-center, and the soft clustering algorithm on shape retrieval applications. Our shape retrieval framework is composed of three steps: 1) extraction of the shape boundary points, 2) affine alignment of the shapes and use of a Gaussian mixture model (GMM) [2], [3], [4] to represent the aligned boundaries, and 3) comparison of the GMMs using tBD to find the best matches given a query shape. To further speed up the shape retrieval algorithm, we perform hierarchical clustering of the shapes using our total Bregman soft clustering algorithm. This enables us to compare the query with a small subset of shapes which are chosen to be the cluster t-centers. We evaluate our method on various public domain 2D and 3D databases, and demonstrate comparable or better results than state-of-the-art retrieval techniques.
Index Terms:
statistical distributions,image retrieval,maximum likelihood estimation,pattern clustering,shape recognition,GMM,hierarchical total Bregman soft clustering,total Bregman divergences,tBD-based l<sub>1</sub>-norm center,lifted exponential family,lEF,statistical distributions,maximum a posteriori estimate,MAP,exponential family distribution,clustering technique,shape retrieval framework,Gaussian mixture model,Shape analysis,Databases,Clustering algorithms,Robustness,Convex functions,Harmonic analysis,Three dimensional displays,3D shape retrieval,Total Bregman divergence,t-center,lifted exponential families,hard clustering,soft clustering,Gaussian mixture model
Citation:
Meizhu Liu, B. C. Vemuri, Shun-Ichi Amari, F. Nielsen, "Shape Retrieval Using Hierarchical Total Bregman Soft Clustering," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 34, no. 12, pp. 2407-2419, Dec. 2012, doi:10.1109/TPAMI.2012.44
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