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Group-Valued Regularization for Motion Segmentation of Articulated Shapes

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Innovations for Shape Analysis

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

Motion-based segmentation is an important tool for the analysis of articulated shapes. As such, it plays an important role in mechanical engineering, computer graphics, and computer vision. In this chapter, we study motion-based segmentation of 3D articulated shapes. We formulate motion-based surface segmentation as a piecewise-smooth regularization problem for the transformations between several poses. Using Lie-group representation for the transformation at each surface point, we obtain a simple regularized fitting problem. An Ambrosio-Tortorelli scheme of a generalized Mumford-Shah model gives us the segmentation functional without assuming prior knowledge on the number of parts or even the articulated nature of the object. Experiments on several standard datasets compare the results of the proposed method to state-of-the-art algorithms.

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Authors and Affiliations

  1. Department of Computer Science, Israel Institute of Technology, 32000, Haifa, Israel

    Guy Rosman & Ron Kimmel

  2. Institute of Computational Science, Faculty of Informatics, Universita della Svizzera italiana, Lugano, Switzerland

    Michael M. Bronstein

  3. School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Ramat Aviv, 69978, Israel

    Alexander M. Bronstein

  4. Department of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa, 32000, Israel

    Alon Wolf

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  1. Guy Rosman
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  2. Michael M. Bronstein
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  3. Alexander M. Bronstein
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  4. Alon Wolf
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  5. Ron Kimmel
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Correspondence to Guy Rosman .

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Editors and Affiliations

  1. , Inst. for Appl. Math.&Scient.Comp., Brandenburg Technical University, Platz der Deutschen Einheit 1, Cottbus, 03046, Germany

    Michael Breuß

  2. Department of Computer Science, Technion-Israel Institute of Technology, Haifa, 32000, Israel

    Alfred Bruckstein

  3. School of Electrical &, Computer Engineering, National Technical University of Athens, Athens, 15773, Greece

    Petros Maragos

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Rosman, G., Bronstein, M.M., Bronstein, A.M., Wolf, A., Kimmel, R. (2013). Group-Valued Regularization for Motion Segmentation of Articulated Shapes. In: Breuß, M., Bruckstein, A., Maragos, P. (eds) Innovations for Shape Analysis. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34141-0_12

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