Using similarity measures and homogeneity for the comparison of images

Fuzzy techniques can be applied in several domains of image processing. In this paper, we will show how notions of fuzzy set theory are used in establishing measures for image comparison. Objective quality measures or measures of comparison are of great importance in the field of image processing. These measures serve as a tool to evaluate and to compare different algorithms designed to solve problems, such as noise reduction, deblurring, compression, etc. Consequently these measures serve as a basis on which one algorithm is preferred to another. It is well known that classical quality measures, such as the MSE (mean square error) or the PSNR (peak-signal-to-noise-ratio), do not always correspond to visual observations. Therefore, several researchers are-and have been-looking for new quality measures, better adapted to human perception. Van der Weken et al. [Proceedings of ICASSP'2002, Orlando, 2002] gave an overview of similarity measures, originally introduced to express the degree of comparison between two fuzzy sets, which can be applied to images. These similarity measures are all pixel-based, and have therefore not always satisfactory results. To cope with this drawback, we propose similarity measures based on neighbourhoods, so that the relevant structures of the images are observed better. In this way, 13 new similarity measures were found to be appropriate for the comparison of images. (C) 2004 Elsevier B.V. All rights reserved.