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Viewpoint Invariant Texture Description Using Fractal Analysis

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Abstract

Image texture provides a rich visual description of the surfaces in the scene. Many texture signatures based on various statistical descriptions and various local measurements have been developed. Existing signatures, in general, are not invariant to 3D geometric transformations, which is a serious limitation for many applications. In this paper we introduce a new texture signature, called the multifractal spectrum (MFS). The MFS is invariant under the bi-Lipschitz map, which includes view-point changes and non-rigid deformations of the texture surface, as well as local affine illumination changes. It provides an efficient framework combining global spatial invariance and local robust measurements. Intuitively, the MFS could be viewed as a “better histogram” with greater robustness to various environmental changes and the advantage of capturing some geometrical distribution information encoded in the texture. Experiments demonstrate that the MFS codes the essential structure of textures with very low dimension, and thus represents an useful tool for texture classification.

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Authors and Affiliations

  1. School of Computer Science and Engineering, South China University of Technology, Guangzhou, 510006, China

    Yong Xu

  2. Department of Mathematics, National University of Singapore, Singapore, 117643, Republic of Singapore

    Hui Ji

  3. Center for Automation Research, University of Maryland, College Park, MD, 20742-3275, USA

    Cornelia Fermüller

Authors
  1. Yong Xu
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  2. Hui Ji
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  3. Cornelia Fermüller
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Corresponding author

Correspondence to Cornelia Fermüller.

Additional information

This research was supported in part by the National Science Foundation, under a grant on NETS-NOSS: Sensory grammars for sensor networks, and a grant on Biologically Inspired Computing: SEER: A gigascale neuromorphic vision system, by the European Commission under the 7th Framework Program on Cognitive Systems (project POETICON), and by the National Nature Science Foundation of China (No. 60603022), National 973 Program of China (No. 2009CB320505). Part of the work was conducted while Yong Xu was visiting the Computer Vision Lab at UMD supported by the China Scholarship Council (No. [2003]3006).

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Xu, Y., Ji, H. & Fermüller, C. Viewpoint Invariant Texture Description Using Fractal Analysis. Int J Comput Vis 83, 85–100 (2009). https://doi.org/10.1007/s11263-009-0220-6

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  • DOI: https://doi.org/10.1007/s11263-009-0220-6

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