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NonLocal via Local–NonLinear via Linear: A New Part-coding Distance Field via Screened Poisson Equation

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Abstract

Interesting phenomena in shape perception is nonlocal and nonlinear. Thus, it is crucial that a shape perception system exhibits a nonlocal and nonlinear behaviour. From the computational point of view, however, neither nonlinearity nor nonlocality is desired. We propose a repeated use of Screened Poisson PDE (leading to a sparse linear system) to compute a part coding and extracting distance field, a mapping from the shape domain \(\varOmega \subset R^n\) to the real line. Despite local and linear computations, the field exhibits highly nonlinear and nonlocal behaviour, leading to efficient and robust coding of both the local and the global structures. The proposed computation scheme is applicable to shapes in arbitrary dimensions as well as shapes implied by fragmented partial contours. The local behaviour is independent of the image context in which the shape resides.

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Acknowledgments

This work is funded by the Turkish National Science Foundation TUBITAK under Grant No. 112E208. We thank three anonymous reviewers for their constructive feedback.

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Authors and Affiliations

  1. Middle East Technical University, 06800, Ankara, Turkey

    Murat Genctav, Asli Genctav & Sibel Tari

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  1. Murat Genctav
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  2. Asli Genctav
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  3. Sibel Tari
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Correspondence to Sibel Tari.

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Genctav, M., Genctav, A. & Tari, S. NonLocal via Local–NonLinear via Linear: A New Part-coding Distance Field via Screened Poisson Equation. J Math Imaging Vis 55, 242–252 (2016). https://doi.org/10.1007/s10851-015-0614-8

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  • DOI: https://doi.org/10.1007/s10851-015-0614-8

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