Shape retrieval using hierarchical total Bregman soft clustering.
Shape retrieval using hierarchical total Bregman soft clustering.
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DOI：
10.1109/tpami.2012.44
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发表时间：
2012-12
影响因子：
23.6
通讯作者：
Nielsen F
中科院分区：
文献类型：
--
作者：
Liu M;Vemuri BC;Amari S;Nielsen F
在本文中，我们认为家庭的总Bregman分歧（tBD）作为一个有效的和强大的“距离”的措施来量化形状之间的相异性。我们使用基于tBD的N1范数中心作为一组形状的代表，并称之为t中心。首先，我们简要介绍和分析的tBD和t-中心的性质，我们以前的工作。然后，我们证明了，对于任何tBD，存在一个分布属于提升指数族的统计分布。此外，我们发现，找到提升指数族分布的参数的最大后验估计是等价于最小化的tBD找到的t-中心。这导致了一个新的聚类技术，即总Bregman软聚类算法。我们评估的tBD，t-中心和软聚类算法的形状检索应用。我们的形状检索框架由三个步骤组成：（1）提取形状边界点（2）仿射对齐的形状和高斯混合模型（GMM）的使用，表示对齐的边界，和（3）比较的GMM使用tBD找到最佳匹配给定的查询形状。为了进一步加快形状检索算法，我们使用我们的总Bregman软聚类算法进行层次聚类的形状。这使我们能够将查询与被选择为聚类t中心的形状的小子集进行比较。我们评估我们的方法在各种公共领域的2D和3D数据库，并证明可比或更好的结果比国家的最先进的检索技术。
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. Then, we prove that for any tBD, there exists a distribution which belongs to the lifted exponential family of statistical distributions. Further, we show that finding the maximum a posteriori 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),, 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.