Screened Poisson Hyperfields for Shape Coding

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2014-01-01

Author

Guler, R. A.
Tarı, Zehra Sibel
ÜNAL, GÖZDE

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We present a novel perspective on shape characterization using the screened Poisson equation. We discuss that the effect of the screening parameter is a change of measure of the underlying metric space. Screening also indicates a conditioned random walker biased by the choice of measure. A continuum of shape fields is created by varying the screening parameter or, equivalently, the bias of the random walker. In addition to creating a regional encoding of the diffusion with a different bias, we further break down the influence of boundary interactions by considering a number of independent random walks, each emanating from a certain boundary point, whose superposition yields the screened Poisson field. Probing the screened Poisson equation from these two complementary perspectives leads to a high-dimensional hyperfield: a rich characterization of the shape that encodes global, local, interior, and boundary interactions. To extract particular shape information as needed in a compact way from the hyperfield, we apply various decompositions either to unveil parts of a shape or parts of a boundary or to create consistent mappings. The latter technique involves lower-dimensional embeddings, which we call screened Poisson encoding maps (SPEM). The expressive power of the SPEM is demonstrated via illustrative experiments as well as a quantitative shape retrieval experiment over a public benchmark database on which the SPEM method shows a high-ranking performance among the existing state-of-the-art shape retrieval methods.

Subject Keywords

Screened Poisson equation, Elliptic models for distance transforms, Conditioned random walker, Shape decomposition, Screened Poisson encoding maps (SPEM), Nonnegative sparse coding, Nonrigid shape retrieval, Level-set models

URI

https://hdl.handle.net/11511/32694

Journal

SIAM JOURNAL ON IMAGING SCIENCES

DOI

https://doi.org/10.1137/140956117

Collections

Department of Computer Engineering, Article

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Citation Formats

R. A. Guler, Z. S. Tarı, and G. ÜNAL, “Screened Poisson Hyperfields for Shape Coding,” SIAM JOURNAL ON IMAGING SCIENCES, pp. 2558–2590, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32694.