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MEAN SHIFT Based Covariance Matrices Clustering on Differentiable Manifolds

Author: ZhangYun
Tutor: ZhangXuGuang
School: Yanshan University
Course: Control Theory and Control Engineering
Keywords: Logo images clustering Region Covariance Matrices Singular value decomposition Mean Shift Differentiable manifolds Lie groups
CLC: TP391.41
Type: Master's thesis
Year: 2011
Downloads: 59
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Abstract

Facing continually increasing volumes of documents, it needs a huge time consuming for classification relied on manual. Therefore, in order to facilitate management and access, we need to classify the document image automatically. Logo is a unique marker. It is an effective way for document classification. In this study, the main work focus on the unsupervised clustering of logo images.RCM (Region Covariance Matrices) is an excellent descriptor represented the statistics information of an image which has the advantages of fusing multiple features. This paper use this RCM model describes the features of logo images. Logo images may be polluted by the noise during transmission. Although the traditional covariance matrix can be applied to overcome noise with the same degrees of corruption. However, traditional RCM cannot deal with the noise with different corruption degrees. Meanwhile, traditional covariance matrix contains the features of the gradient which are more sensitive to noise. In order to solve this problem, we use singular value decomposition and reconstruction technique to extract the features of logo images. After singular value decomposition, signal and noise are distributed into different sub-bands. According to this rule, the sub-bands in which the smaller noise is contained should be selected for reconstruction the logo images. Different singular values carry different information of an image. The influences of the noise are higher on the smaller singular values which correspond to the components of the image with lower energy levels. Therefore, the influences of the noise can be reduced by truncating the lower singular values. In this paper, we use the covariance matrix to fuse the spatial information of pixels and the reconstructed images produced by some groups of singular values. Therefore, we propose a novel descriptor called SVRCM (Singular Values Region Covariance Matrices) to represent logo images. Using this feature descriptor, the discriminating ability of the feature model could be enhanced and the influence of noise could be decreased.Mean Shift algorithm is studied for unsupervised clustering in this paper in detail. Fist, Mean Shift algorithm is employed to the vector clustering and image segmentation, and is extended to covariance matrix clustering. However, covariance matrices do not conform to Euclidean geometry. The traditional Mean Shift clustering algorithm can not be used directly for clustering of covariance matrix. The covariance matrix is a symmetric positive definite matrix which has Lie group structure. Therefore, we established the expression of mean shift algorithm on the differentiable manifolds. We run the Mean Shift algorithm on a Lie group by iteratively transforming points between the Lie group and Lie algebra (tangent space) to achieve the unsupervised clustering of covariance matrices. Experimental results demonstrate the clustering rate of the proposed SVRCM model can be achieved as 88.55 percent, Comparing with the traditional covariance matrix and singular value vectors model the clustering rates are increased by 5.39% and 3.94%.

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