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Unformatted text preview: IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 18, NO. 10, OCTOBER 2009 2153 A Theory of Phase Singularities for Image Representation and its Applications to Object Tracking and Image Matching Yu Qiao , Member, IEEE , Wei Wang, Nobuaki Minematsu , Member, IEEE , Jianzhuang Liu , Senior Member, IEEE , Mitsuo Takeda, and Xiaoou Tang , Fellow, IEEE Abstract This paper studies phase singularities (PSs) for image representation. We show that PSs calculated with Laguerre-Gauss filters contain important information and provide a useful tool for image analysis. PSs are invariant to image translation and rotation. We introduce several invariant features to characterize the core structures around PSs and analyze the stability of PSs to noise addition and scale change. We also study the characteristics of PSs in a scale space, which lead to a method to select key scales along phase singularity curves. We demonstrate two applications of PSs: object tracking and image matching. In object tracking, we use the iterative closest point algorithm to determine the cor- respondences of PSs between two adjacent frames. The use of PSs allows us to precisely determine the motions of tracked objects. In image matching, we combine PSs and scale-invariant feature transform (SIFT) descriptor to deal with the variations between two images and examine the proposed method on a benchmark database. The results indicate that our method can find more correct matching pairs with higher repeatability rates than some well-known methods. Index Terms Image matching, image representation, object tracking, phase singularity, scale space, transformation invariance. I. INTRODUCTION O NE of the fundamental problems in image processing and computer vision is image representation. A good repre- sentation should be compact and stable to noise addition, trans- formations, and image deformations, while providing rich and distinctive information for image processing and understanding Manuscript received June 19, 2008; revised April 13, 2009. First published July 06, 2009; current version published September 10, 2009.Y. Qiao was supported in part by the Japan Society for the Promotion of Science (JSPS) (P07078). W. Wang and M. Takeda were supported by JSPS B(2) No.18360034. J. Liu and X. Tang were partly supported by a grant from the Research Grants Council of the Hong Kong SAR, China (Project No. CUHK 415408). The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Minh N. Do. Y. Qiao and N. Minematsu are with the Graduate School of Informa- tion Science and Technology, University of Tokyo, Tokyo, Japan (e-mail: qiao@gavo.t.u-tokyo.ac.jp; mine@gavo.t.u-tokyo.ac.jp)....
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