The Specification of Edge Penalties for Regular and Irregular Pixel Images

Bernard W. Silverman; Christopher Jennison; Julian Stander; Timothy C. Brown

doi:10.1109/34.58874

The Specification of Edge Penalties for Regular and Irregular Pixel Images

Bernard W. Silverman, Christopher Jennison, Julian Stander, Timothy C. Brown

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

One of the ingredients of recent methodology in statistical image reconstruction is the idea of introducing a system of “edges” between pixels in the image. If an edge is present between two contiguous pixels, then they are not considered as neighbors in the reconstruction procedure. In penalized maximum likelihood estimation of the image, the number and configuration of the edges is controlled by a penalty term. In this correspondence, we show how some geometrical insights can be used to provide penalties for the various edge configurations in a way that is roughly independent of the pixel discretization. The penalties obtained are consistent over pixels of different sizes, shapes, and orientations, even if these occur in the same pattern. The cases of square, rectangular, hexagonal, and irregular pixels are considered. In an experiment, our penalties perform substantially better than those previously proposed.

Original language	English
Pages (from-to)	1017-1024
Number of pages	8
Journal	IEEE Transactions on Pattern Analysis and Machine Intelligence
Volume	12
Issue number	10
DOIs	https://doi.org/10.1109/34.58874
Publication status	Published - 1 Oct 1990

Bibliographical note

Funding Information:
Th= edge process idea corresponds to the notion that the image is segmented into regions over each of which its behavior is relatively homogeneous or at least is not subject to abrupt changes; from one region to another, however, large differences in behavior are possible. The changes in behavior may relate either to overall gray level or color, or to more subtle properties such as texture. Of course, the basic motivation for this kind of segmentation of the image is that the true scene is itself segmented into regions, and Manuscript received January 10, 1989; revised March 28, 1990. Recommended for acceptance by A. K. Jain. This work was supported by the U.K. Science and Engineering Research Council, the European Research Office of the U.S. Army, and the National Science Foundation. B. W. Silverman, C. Jennison, and J. Stander are with the School of Mathematical Sciences, University of Bath, Bath BA2 7AY, England. T. C. Brown is with the Department of Mathematics, University of Western Australia, Nedlands, WA 6009, Australia. IEEE Log Number 9037568.

Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

Keywords

Discretization
edge process
Euler-Poincare characteristic
hexagonal pixels
irregular pixels
line length
Markov random field
penalized likelihood
statistical image reconstruction
stochastic geometry
tessellations

ASJC Scopus subject areas

Software
Computer Vision and Pattern Recognition
Computational Theory and Mathematics
Artificial Intelligence
Applied Mathematics

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10.1109/34.58874

Cite this

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title = "The Specification of Edge Penalties for Regular and Irregular Pixel Images",

abstract = "One of the ingredients of recent methodology in statistical image reconstruction is the idea of introducing a system of “edges” between pixels in the image. If an edge is present between two contiguous pixels, then they are not considered as neighbors in the reconstruction procedure. In penalized maximum likelihood estimation of the image, the number and configuration of the edges is controlled by a penalty term. In this correspondence, we show how some geometrical insights can be used to provide penalties for the various edge configurations in a way that is roughly independent of the pixel discretization. The penalties obtained are consistent over pixels of different sizes, shapes, and orientations, even if these occur in the same pattern. The cases of square, rectangular, hexagonal, and irregular pixels are considered. In an experiment, our penalties perform substantially better than those previously proposed.",

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note = "Funding Information: Th= edge process idea corresponds to the notion that the image is segmented into regions over each of which its behavior is relatively homogeneous or at least is not subject to abrupt changes; from one region to another, however, large differences in behavior are possible. The changes in behavior may relate either to overall gray level or color, or to more subtle properties such as texture. Of course, the basic motivation for this kind of segmentation of the image is that the true scene is itself segmented into regions, and Manuscript received January 10, 1989; revised March 28, 1990. Recommended for acceptance by A. K. Jain. This work was supported by the U.K. Science and Engineering Research Council, the European Research Office of the U.S. Army, and the National Science Foundation. B. W. Silverman, C. Jennison, and J. Stander are with the School of Mathematical Sciences, University of Bath, Bath BA2 7AY, England. T. C. Brown is with the Department of Mathematics, University of Western Australia, Nedlands, WA 6009, Australia. IEEE Log Number 9037568. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.",

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The Specification of Edge Penalties for Regular and Irregular Pixel Images

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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