Screened Poisson Hyperfields for Shape Coding

Download

index.pdf

Date

2014-01-01

Author

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

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

82
views

0
downloads

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

Suggestions

OpenMETU
Core

Generalized bent functions with perfect nonlinear functions on arbitrary groups Yılmaz, Emrah Sercan; Özbudak, Ferruh; Department of Cryptography (2012) This thesis depends on the paper ‘Non-Boolean Almost Perfect Nonlinear Functions on Non- Abelian Groups’ by Laurent Poinsot and Alexander Pott and we have no new costructions here. We give an introduction about character theory and the paper of Poinsot and Pott, and we also compare previous definitions of bent functions with the definition of the bent function in the paper. As a conclusion, we give new theoretical definitions of bent, PN, APN ana maximum nonlinearity. Moreover, we show that bent and PN func...
An error analysis of iterated defect correction methods for linear differential-algebraic equations Karasözen, Bülent (1996-01-01) Asymptotic expansions of the global error of iterated defect correction (IDeC) techniques based on the implicit Euler method for linear differential-algebraic equations (dae's) of arbitrary index are analyzed. The dependence of the maximum attainable convergence order on the degree of the interpolating polynomial, number of defect correction steps, and on the index of the differential-algebraic system is given. The efficiency of IDeC method and extrapolation is compared on the basis of numerical experiments...
On the consistency of the solutions of the space fractional Schroumldinger equation (vol 53, 042105, 2012) Bayin, Selcuk S. (2012-08-01) Recently we have reanalyzed the consistency of the solutions of the space fractional Schroumldinger equation found in a piecewise manner, and showed that an exact and a proper treatment of the relevant integrals prove that they are consistent. In this comment, for clarity, we present additional information about the critical integrals and describe how their analytic continuation is accomplished.
A Window-based characterization method for biophysical time series Katırcıoğlu, Deniz; Baykal, Nazife; Department of Medical Informatics (2017) In thesis, we propose a robust similarity score-based time series characterization method, termed as Window-based Time series Characterization (WTC). Specifically, WTC generates domain-interpretable results and involves remarkably low computational complexity thereby rendering itself useful for densely sampled and populated time series datasets. In this study, we apply WTC to a proprietary action potential (AP) time series dataset on human cardiomyocytes and three precordial leads from a publicly available ...
On the Orthogonality of q-Classical Polynomials of the Hahn Class Alvarez-Nodarse, Renato; Adiguzel, Rezan Sevinik; Taşeli, Hasan (2012-01-01) The central idea behind this review article is to discuss in a unified sense the orthogonality of all possible polynomial solutions of the q-hypergeometric difference equation on a q-linear lattice by means of a qualitative analysis of the q-Pearson equation. To be more specific, a geometrical approach has been used by taking into account every possible rational form of the polynomial coefficients in the q-Pearson equation, together with various relative positions of their zeros, to describe a desired q-wei...

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.