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Modeling Shapes with Higher-Order Graphs: Methodology and Applications

  • Chapter
Shape Perception in Human and Computer Vision

Part of the book series: Advances in Computer Vision and Pattern Recognition ((ACVPR))

Abstract

Extrinsic factors such as object pose and camera parameters are a main source of shape variability and pose an obstacle to efficiently solving shape matching and inference. Most existing methods address the influence of extrinsic factors by decomposing the transformation of the source shape (model) into two parts: one corresponding to the extrinsic factors and the other accounting for intra-class variability and noise, which are solved in a successive or alternating manner. In this chapter, we consider a methodology to circumvent the influence of extrinsic factors by exploiting shape properties that are invariant to them. Based on higher-order graph-based models, we implement such a methodology to address various important vision problems, such as non-rigid 3D surface matching and knowledge-based 3D segmentation, in a one-shot optimization scheme. Experimental results demonstrate the superior performance and potential of this type of approach.

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Notes

  1. 1.

    The shape can also be associated with a texture model if photometric information is available.

  2. 2.

    When a bijective mapping between S 1⊂R 3 and S 2⊂R 3 is required, the feasible solution can be defined as all diffeomorphisms that map S 1 to S 2.

  3. 3.

    Photometric variation can be caused by the change of illumination. We mostly focus on the geometric aspect here but the extension to the photometric aspect can be done analogously.

  4. 4.

    The definition of the intrinsically equivalence depends on the problem to be addressed. For instance, when dealing with nonrigid 3D surface matching, we often assume that two surfaces differing by an isometric transformation (with geodesic metrics) are intrinsically equivalent.

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Author information

Authors and Affiliations

  1. Vision Lab, University of California, Los Angeles, USA

    Chaohui Wang

  2. Dept. of Computer Science, Stony Brook University, Stony Brook, USA

    Yun Zeng & Dimitris Samaras

  3. Center for Visual Computing, Ecole Centrale Paris, Châtenay-Malabry Cedex, France

    Nikos Paragios

  4. LIGM Laboratory, University Paris-East & Ecole des Ponts Paris-Tech, Marne-la-Vallée, France

    Nikos Paragios

  5. GALEN Group, INRIA Saclay - Île-de-France, Rocquencourt, France

    Nikos Paragios

Authors
  1. Chaohui Wang
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  2. Yun Zeng
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  3. Dimitris Samaras
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  4. Nikos Paragios
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Corresponding author

Correspondence to Chaohui Wang .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Toronto, King's College Road 6, Toronto, M5S 3G4, Ontario, Canada

    Sven J. Dickinson

  2. Department of Psychological Sciences, Purdue University, Third Street 703, West Lafayette, 47907, Indiana, USA

    Zygmunt Pizlo

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Wang, C., Zeng, Y., Samaras, D., Paragios, N. (2013). Modeling Shapes with Higher-Order Graphs: Methodology and Applications. In: Dickinson, S., Pizlo, Z. (eds) Shape Perception in Human and Computer Vision. Advances in Computer Vision and Pattern Recognition. Springer, London. https://doi.org/10.1007/978-1-4471-5195-1_31

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  • DOI: https://doi.org/10.1007/978-1-4471-5195-1_31

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5194-4

  • Online ISBN: 978-1-4471-5195-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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