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Fluctuating Distance Fields, Parts, Three-Partite Skeletons

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Innovations for Shape Analysis

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

Abstract

Shapes are continuous objects, even when they are drawn on digital media or composed using finite number of elements. As such, they defy analytic approach; explicitization of their parts, hierarchies, skeletons, or even centroids is ill-posed. I describe a novel approach to perceptually organize shapes and explicate their features without being negligent of their continuous nature. The basic construct is an unusual phase field that can be conceived in a number of varying ways using varying mathematical machinery, so highlighting the field itself rather than how it is being computed. Connections among the field, Mumford-Shah and Tari-Shah-Pien models, and reaction-diffusion equation suggest that the field may bridge low-level and high-level visual processing.

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Acknowledgements

The author thanks to the Alexander von Humboldt Foundation for a generous financial support and extends her gratitude to Folkmar Bornemann, Sci. Comp. Dept. of Tech. Universität München for providing a wonderful sabbatical stay during which this work has been completed. She also thanks to anonymous reviewers and the editors, A. Bruckstein, M. Breuß and P. Maragos, for their meticulous editing.

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  1. Middle East Technical University, 06531, Ankara, Turkey

    Sibel Tari

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  1. Sibel Tari
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Correspondence to Sibel Tari .

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  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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Tari, S. (2013). Fluctuating Distance Fields, Parts, Three-Partite Skeletons. 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_20

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