Elsevier

Pattern Recognition

Volume 42, Issue 1, January 2009, Pages 54-67
Pattern Recognition

A complex network-based approach for boundary shape analysis

https://doi.org/10.1016/j.patcog.2008.07.006Get rights and content

Abstract

This paper introduces a novel methodology to shape boundary characterization, where a shape is modeled into a small-world complex network. It uses degree and joint degree measurements in a dynamic evolution network to compose a set of shape descriptors. The proposed shape characterization method has an efficient power of shape characterization, it is robust, noise tolerant, scale invariant and rotation invariant. A leaf plant classification experiment is presented on three image databases in order to evaluate the method and compare it with other descriptors in the literature (Fourier descriptors, curvature, Zernike moments and multiscale fractal dimension).

Introduction

In pattern recognition and image analysis, shape is one of the most important visual attributes to characterize objects. It provides the most relevant information about an object in order to identify and classify tasks [1], [2].

In recent years, significant progress has been made in research over shape signatures and recognition [2], [3], [4]. According to Pavlids [5], there are mainly two approaches to shape representation, namely (1) the region-based approach, that use moment descriptors to describe shapes [6], [7], [8] and (2) the boundary-based approach tend to be more efficient for handling shapes that are describable by their object contours [9]. This class of techniques include, among others, Fourier descriptors [10], [11], [12], curvature scale space (CSS) [9], [13], wavelet descriptors [14] and multiscale fractal dimension [2], [15]. There are a very large number of shape signatures schemes in the literature, good surveys can be found in Refs. [16], [17], [5].

This work is related to the approach two, shape boundary-based approach. The literature presents various methods to analyze images and objects using shape boundary, and the basis of most of them considers the shape as a chain of connected points [1]. In this approach, the sequence of the points in the boundary perform an important role, as it is used to extract the shape signature or descriptor that is capable of characterizing the shape boundary.

The method proposed here, has a novel approach to the shape boundary analysis using the complex networks theory [18], [19], [20], [21]. It considers the shape boundary as a set of points and models this set as a graph. The topology of an small-world network model is obtained artificially by transformations on vertices of shape model. The topological features, derived from the dynamics of the network growth, are correlated to physical aspects of the shape. Consequently, these measurements can be used to compose a shape descriptor or signature. These descriptors may be used to identify and distinguish objects.

Traditional shape boundary methods yield the shape descriptors using the contour as continuous closed curves formed by the adjacent sequential pixels. By modeling the shape boundary as complex network, the method proposed here, on the other hand, does not need adjacent and sequential pixels as the graph model only takes the distance between the boundary elements into account.

As will be shown in this paper, the proposed method presents better results in shape characterization. Besides, due to the graph approach, it is more robust as it does not need sequential closed continuous curves of contours. Thus, it can characterize degraded boundary shapes, that have incomplete information such as gaps or holes. It is also noise tolerant and is invariant to scale and rotation.

In order to evaluate the proposed method, a set of shape characterization experiments was done. The main aim of the experiments is to perform plant species classification using the leaf shape boundary. In the experiment, the leaves were intentionally re-shaped in order to evaluate characteristics such as noise tolerance, robustness, scale invariance and rotate invariance. We also did the experiment with other descriptors found in the literature to compare the results and features with the novel method. Additionally, two more traditional shape databases are used to corroborate the efficiency of this novel method.

The data from the experiments were evaluated by the use of the linear discriminant analysis (LDA) [22]. The LDA also enable us to verify the distribution of clusters in the feature space. A descriptor is considered “good” when it creates compact clusters far away from each other for all classes in the corresponding feature space.

This paper starts by presenting an overview of the complex network theory (Section 2). In Section 3, the method is detailed. The following is presented: how to model the shape as a complex network and by using complex network theory to extract different network measures which are related with the object shape. These network measures are used to compose the shape descriptors that characterize the shape of an object. Section 4 presents the results of experiments using the three image databases of shapes contours, where the novel method was compared with other shape descriptors and various aspects are discussed (shape characterization power, rotation invariance, scale invariance, noise tolerance, robustness and the capability to deal with degraded contours). We present the conclusion and our current research on shape descriptors in Section 5.

Section snippets

Complex networks

Complex networks research can be described as the intersection between graph theory and statistical mechanics, which confers a truly multidisciplinary nature to this area, since it integrates computer sciences, mathematics and physics [20].

Due to its great flexibility and generality, the current interest has focused on applying the developed concepts to many real data and situations. Although many topics of computer vision can be modeled using these concepts, this still is an unexplored field,

Complex network shape signature

In this section, the following is proposed: how to model the shape boundary as a complex network and afterwards extract two distinct feature vectors which are the degree descriptors and the joint degree descriptors showing how to use the tools from the complex networks theory to create a feature vector to discriminate a contour shape.

Linear discriminant analysis

In order to analyze the features extracted from the boundary shapes, a statistical analysis was carried out. This analysis was done applying an LDA to the data. LDA is a well-known method to estimate a linear subspace with good discriminative properties. The idea of this method is to find a projection of the data where the variance between the classes is large compared to the variance within the classes. As it is a supervised method, LDA needs class definitions for the estimation process [22],

Conclusion

In this paper, we have proposed a novel pattern recognition method using the complex network theory. It was investigated how the contour of digital images can be effectively represented, characterized and analyzed in terms of the complex network. We showed how measurements such as average and maximum degrees and entropy, energy and average joint degree can be used for the identification of broad classes, thus creating techniques for pattern recognition. The potential of this as a framework has

Acknowledgments

Odemir M. Bruno gratefully acknowledges the financial support of CNPq (National Council for Scientific and Technological Development, Brazil) (Grant #306628/2007-4) and FAPESP (The State of São Paulo Research Foundation) (Proc. #2006/54367-9 and #2006/53972-6). André R. Backes is grateful to FAPESP (Proc. #2006/54367-9) for his doctorate grant. Dalcimar Casanova is indebted to FAPESP (Proc. #2006/53972-6) for his master's grant.

About the Author—ANDRÉ R. BACKES is a Ph.D. student at the Institute of Mathematics and Computer Science at the University of S. Paulo in Brazil. He received his B.Sc. and M.Sc. in Computer Science at the university of S. Paulo. His fields of interest include Computer Vision, Image Analysis and Pattern Recognition.

References (33)

  • O.M. Bruno et al.

    Topological multi-contour decomposition for image analysis and image retrieval

    Pattern Recognition Lett.

    (2008)
  • R. da S. Torres et al.

    A graph-based approach for multiscale shape analysis

    Pattern Recognition

    (2003)
  • Z. Wang et al.

    Shape based leaf image retrieval

    IEEE Proc. Vision Image Signal Process.

    (2003)
  • T.B. Sebastian et al.

    Recognition of shapes by editing their shock graphs

    IEEE Trans. Pattern Anal. Mach. Intell.

    (2004)
  • A. Khotanzad et al.

    Invariant image recognition by Zernike moments

    IEEE Trans. Pattern Anal. Mach. Intell.

    (1990)
  • M.K. Hu

    Visual pattern recognition by moment invariants

    IEEE Trans. Inf. Theory

    (1962)
  • Cited by (0)

    About the Author—ANDRÉ R. BACKES is a Ph.D. student at the Institute of Mathematics and Computer Science at the University of S. Paulo in Brazil. He received his B.Sc. and M.Sc. in Computer Science at the university of S. Paulo. His fields of interest include Computer Vision, Image Analysis and Pattern Recognition.

    About the Author—DALCIMAR CASANOVA received his M.Sc. in Computer Science at the Institute of Mathematics and Computer Science at the University of S. Paulo in Brazil. He is now starting his doctorate at the University of S. Paulo.

    About the Author—ODEMIR M. BRUNO is an associate professor at the Institute of Mathematics and Computer Science at the University of S. Paulo in Brazil. He received his B.Sc. in Computer Science in 1992, from the Piracicaba Engineering College (Brazil), his M.Sc. in Applied physics (1995) and his Ph.D. in Computational Physics (2000) at the University of S. Paulo (Brazil). His fields of interest include Computer Vision, Image Analysis, Computational Physics, Pattern Recognition and Bioinformatics. He is an author of many papers (journal and proceedings) and several book chapters, co-author of a book of Vision Science (Optical and Physiology of Vision: a multidisciplinary approach (Portuguese only)) and an inventor of three patents. His is also a referee of some journals.

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