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Screened poisson hyperfields for shape coding

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Güler, Rıza Alp and Tari, Sibel and Ünal, Gözde (2014) Screened poisson hyperfields for shape coding. SIAM Journal on Imaging Sciences, 7 (4). pp. 2558-2590. ISSN 1936-4954 (Online)

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Official URL: http://dx.doi.org/10.1137/140956117

Abstract

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.

Item Type:Article
Uncontrolled Keywords:Screened Poisson equation, Elliptic models for Distance Transforms, conditioned random walker, shape decomposition, Screened Poisson Encoding Maps (SPEM), non-negative sparse coding, non-rigid shape retrieval, level-set models
Subjects:Q Science > Q Science (General)
Q Science > QA Mathematics > QA075 Electronic computers. Computer science
ID Code:25338
Deposited By:Gözde Ünal
Deposited On:09 Dec 2014 11:46
Last Modified:02 Aug 2019 12:20

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