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Proceedings Paper

Class of error metrics for gray-scale image comparison
Author(s): Nial Friel; Ilya S. Molchanov
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Paper Abstract

We suggest a new approach to assess discrepancies between grey- scale images. Such numerical discrepancy measures are usually called error metrics, since they provide a numerical assessment of the dissimilarity between two images. The suggested approach is based on the idea that each upper semicontinuous grey-scale image f corresponds to a random closed set FU equals {x: f(x) >= U} which appear if the image is thresholded as a randomly chosen level U. Then distance between distributions of random sets (which generalize the concept of probability metric distances for random variables) serve as error metrics for grey- scale images. These metrics generalize the famous constructs like uniform distance between distributions of random variables and Monge-Kantorovich metric for distribution functions. However, instead of distribution functions of random variables, their definitions refer to capacity functionals of the corresponding random closed sets. Several general mathematical constructions for such metrics are presented, compared and examined from both theoretical and practical viewpoints. Among wide range of applications of error metrics in image processing we concentrate on their use to assess performance of image restoration algorithms and in Bayesian image reconstruction. In the latter case we focus on one particular error metric and show how it can be used in the context of Bayesian image restoration, where the `true' image is unknown, but is assumed to have a certain prior distribution.

Paper Details

Date Published: 24 September 1998
PDF: 8 pages
Proc. SPIE 3457, Mathematical Modeling and Estimation Techniques in Computer Vision, (24 September 1998); doi: 10.1117/12.323443
Show Author Affiliations
Nial Friel, Univ. of Glasgow (United Kingdom)
Ilya S. Molchanov, Univ. of Glasgow (United Kingdom)

Published in SPIE Proceedings Vol. 3457:
Mathematical Modeling and Estimation Techniques in Computer Vision
Francoise J. Preteux; Jennifer L. Davidson; Edward R. Dougherty, Editor(s)

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