A novel contour descriptor for 2D shape matching and its application to image retrieval

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Abstract

We suggest a novel shape contour descriptor for shape matching and retrieval. The new descriptor is called contour points distribution histogram (CPDH) which is based on the distribution of points on object contour under polar coordinates. CPDH not only conforms to the human visual perception but also the computational complexity of it is low. Invariant to scale and translation are the intrinsic properties of CPDH and the problem of the invariant to rotation can be partially resolved in the matching process. After the CPDHs of images are generated, the similarity value of the images is obtained by EMD (Earth Mover's Distance) metric. In order to make the EMD method used effectively for the matching of CPDHs, we also develop a new approach to the ground distance used in the EMD metric under polar coordinates. Experimental results of image retrieval demonstrate that the novel descriptor has a strong capability in handling a variety of shapes.

Introduction

The ever growing number of images generated everyday by electronic devices has motivated researchers to develop sophisticated algorithms for the retrieval of images from large databases based on their content rather than their textual annotations alone. Among other generic image features that are used to achieve this objective, like color and texture, shape is considered a very important visual feature in object recognition and retrieval [1], [2]. Using the shape of an object for object recognition and image retrieval is an important topic of computer vision and multimedia processing. Finding good shape descriptors and similarity measures are the central issues in these applications [3]. However, shape representation and description is still a difficult task. According to Kim [4], a good shape representation should be compact and retains the essential characteristics of the shape. Meanwhile, invariant to rotation, scale, and translation are also required since such invariance is consistent with the human vision system. Besides, a good method should deal with the challenges like noise, distortion and occlusion since they change a shape in a more complex way.

Many shape representation and analysis methods have been proposed during the past decades [5]. The existing shape representation and description techniques can be generally classified into two categories: contour-based methods and region-based methods. The contour-based methods, such as the curvature scale space [6], which is based on the computation of a similarity measure on the best possible correspondence between maximal convex/concave arcs are contained in simplified versions of the boundary contours. Fourier descriptors [7], [8], which are easy to be implemented are based on the well-developed theory of Fourier analysis. Contour flexibility [3], which represents the deformable potential at each point along a contour, and shape context [9], is a descriptor developed for finding correspondences between point sets. Contour-based methods also include robust symbolic representation [10], distance sets [11], and elastic matching [12], etc. These methods extract information from the boundary of a shape only and ignore the rich information contained in the shape region. On the other hand, the region-based methods consider the global information of all the pixels within a shape. Some methods in this category are termed moment analysis [13], [14], generic Fourier descriptor [15] etc. There are also hybrid methods that combine both contour-based and region-based methods together, such as rolling penetrate descriptor [16].

We are interested in the first one, i.e. contour-based shape techniques, because an increasing attention has been paid to this topic. But most of approaches in this field need to find the correspondence between contour points from two shapes respectively. This work suffers from not only time-consuming but also missing correspondences, in most cases, because the correspondences are obtained only by local (part) contour information.

In this paper, we propose a new descriptor for closed curves, called contour points distribution histogram (CPDH), which belongs to the contour-based methods and depicts the deformable potential at each point along a curve. Because of the peculiarity of the CPDHs, a novel ground distance calculation technique is developed, in the EMD scheme, for shape matching.

The rest of the paper is organized as follows. In Section 2, the proposed novel shape contour descriptor is discussed in detail. The similarity between CPDHs measured by the EMD approach is discussed in 3 Similarity of the CPDHs, 4 Computational complexity includes computational complexity of the proposed approach. The experimental results are presented in Section 5. Finally, Section 6 concludes the paper.

Section snippets

CPDH descriptor

In this section we describe how to extract the contour point's distribution histogram which is invariant with respect to the scale of the shape. Analyzing the contour of an object is the first and most important step in shape matching. Based on the contour of the object, a variety of shape descriptors and matching methods have been proposed in the literature. The most similar works to ours can be found in Ref. [9]. In the following we will outline the proposed contour descriptor CPDH.

Similarity of the CPDHs

Similarity measure scheme is quite significant to the recognition and retrieval results. Several measures of similarity between histograms have been defined. The commonly used histogram similarity measures that are used for image recognition and retrieval are Minkowski distance [17], histogram intersection distance [17], quadratic distance [18], edit distance [19], χ2 statistics distance and Earth Mover's Distance (EMD) [20]. Minkowski distance and histogram intersection distance belong to

Computational complexity

In this section we analyze the complexity for the CPDH representation extraction stage and its similarity matching stage independently, as they usually perform separately.

The CPDH extraction mainly involves contour extraction, points sampling, counting and calculating the distance between the sampled points and the object centroid. Therefore, the complexity of the extraction stage is O(n), where n denotes the number of points sampled from the contour in the CPDH representation. All of these

Experimental results and analysis

In this section we will demonstrate and compare the performance of our method with some typical methods. Most publicly obtained benchmark shape databases will be considered and used for the comparison.

Conclusion

We have presented a new shape representation CPDH and the matching methods based on the distribution of points on the contour of objects under polar coordinates. CPDH is intrinsically insensitive to scale and translation and the rotation invariance can be partially obtained through the circular shift and mirror matching scheme. The simplicity of the computations of the shape representation along with the flexibility of the EMD similarity measure is another contribution of this paper. We

Acknowledgements

The authors would like to thank the anonymous reviewers for their constructive advices. This work is supported by National Natural Science Foundation of PR China (Grant Nos. 60572034, 60973094) and Natural Science Foundation of Jiangsu Province (Grant No. BK2006081) and Natural Science Foundation of Jiangsu Provincial Universities (Grant No.10KJB520006). The authors thank Dr. Yossi Rubner for making the EMD codes available on the web.

Xin Shu received B.E. and M.E. degrees both in Computer Science and Technology from Jiangsu University of Science and Technology (JUST), P.R. China in 2002 and 2005, respectively. He is currently a Ph.D. candidate of Jiangnan University, Wuxi, P.R. China. His main research interests include computer vision, shape matching and image/video retrieval.

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    Xin Shu received B.E. and M.E. degrees both in Computer Science and Technology from Jiangsu University of Science and Technology (JUST), P.R. China in 2002 and 2005, respectively. He is currently a Ph.D. candidate of Jiangnan University, Wuxi, P.R. China. His main research interests include computer vision, shape matching and image/video retrieval.

    Xiao-Jun Wu received his B.S. degree in mathematics from Nanjing Normal University, Nanjing, P.R. China in 1991 and M.S. degree in 1996, and Ph.D. degree in Pattern Recognition and Intelligent System in 2002, both from Nanjing University of Science and Technology, Nanjing, P.R. China, respectively. He was a fellow of the United Nations University, International Institute for Software Technology (UNU/IIST) from 1999 to 2000. He won the most outstanding postgraduate award by Nanjing University of Science and Technology. From 1996 to 2006, he taught in the School of Electronics and Information, Jiangsu University of Science and Technology where he was an exceptionally promoted professor. He joined the School of Information Engineering, Jiangnan University in 2006 where he is a professor. He has published more than 100 papers. He was a visiting researcher in the Centre for Vision, Speech, and Signal Processing (CVSSP), University of Surrey, UK from 2003 to 2004. His current research interests are pattern recognition, computer vision, and intelligent systems.

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