Class of error metrics for gray-scale image comparison

Nial Friel; Ilya S. Molchanov

doi:10.1117/12.323443

24 September 1998 Class of error metrics for gray-scale image comparison

Nial Friel, Ilya S. Molchanov

Proceedings Volume 3457, Mathematical Modeling and Estimation Techniques in Computer Vision; (1998) https://doi.org/10.1117/12.323443
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1998, San Diego, CA, United States

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 F_U 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.

Citation Download Citation

Nial Friel and Ilya S. Molchanov "Class of error metrics for gray-scale image comparison", Proc. SPIE 3457, Mathematical Modeling and Estimation Techniques in Computer Vision, (24 September 1998); https://doi.org/10.1117/12.323443

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