Screened Poisson Hyperfields for Shape Coding


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Guler R. A. , TARI Z. S. , ÜNAL G.

SIAM JOURNAL ON IMAGING SCIENCES, cilt.7, ss.2558-2590, 2014 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 7 Konu: 4
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1137/140956117
  • Dergi Adı: SIAM JOURNAL ON IMAGING SCIENCES
  • Sayfa Sayıları: ss.2558-2590

Özet

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.