TY - JOUR
T1 - The Specification of Edge Penalties for Regular and Irregular Pixel Images
AU - Silverman, Bernard W.
AU - Jennison, Christopher
AU - Stander, Julian
AU - Brown, Timothy C.
N1 - 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.
PY - 1990/10/1
Y1 - 1990/10/1
N2 - 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.
AB - 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.
KW - Discretization
KW - edge process
KW - Euler-Poincare characteristic
KW - hexagonal pixels
KW - irregular pixels
KW - line length
KW - Markov random field
KW - penalized likelihood
KW - statistical image reconstruction
KW - stochastic geometry
KW - tessellations
UR - http://www.scopus.com/inward/record.url?scp=0025507861&partnerID=8YFLogxK
U2 - 10.1109/34.58874
DO - 10.1109/34.58874
M3 - Article
AN - SCOPUS:0025507861
SN - 0162-8828
VL - 12
SP - 1017
EP - 1024
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
JF - IEEE Transactions on Pattern Analysis and Machine Intelligence
IS - 10
ER -