Image Quality Indices Based on Fuzzy Discrimination Information Measures IOANNIS K. VLACHOS, GEORGE D. SERGIADIS Aristotle University of Thessaloniki, Faculty of Technology Department of Electrical & Computer Engineering, Telecommunications Laboratory GR–54124, Thessaloniki, GREECE Abstract:–Quality measures play an important role in the field of image processing. Such measures are commonly used to assess the performance of different algorithm that are designed to perform a specific image processing task. In this paper we propose two novel indices for image quality assessment based on the notion of discrimination information between two fuzzy sets. Two different definitions for the discrimination information have been used. In order to calculate the proposed quality indices two approaches were evaluated, one with application of the indices directly to the pixels of the image and the other using the fuzzy set corresponding to the normalized histogram of the image. A comparative study of the proposed indices is performed by investigating their behavior using images with different types of distortions, such as impulsive “salt & pepper” noise, additive white Gaussian noise, multiplicative speckle noise, blurring, gamma distortion, and JPEG compression. Key-words:–Image quality assessment, Discrimination information measures, Fuzzy cross-entropy, Fuzzy sets 1 Introduction Image quality assessment is of great importance in dig- ital image processing. There are two basic categories of quality or distortion measures [1]. The first cate- gory involves mathematically defined measures such as the mean squared error (MSE), the signal-to-noise ration (SNR), the peak signal-to-noise ration (PSNR) and others. The second category contains measure that take into account the properties of the human visual system. Fuzzy sets theory [2] has been successfully applied to several image processing and computer vision prob- lems. The extensive use of fuzzy logic in digital im- age processing is based on the ability of fuzzy sets to model the ambiguity and vagueness often present in digital images. In addition, fuzzy sets theory provides a solid mathematical framework for incorporating ex- pert knowledge into digital image processing systems. In [3] measures that express the similarity between fuzzy sets were used for image comparison in terms of their normalized histograms. In our work we propose two mathematically defined quality indices based on the notion of discrimination information between fuzzy sets. These indices turn out to be efficient for assessing the quality of images, by measuring the degree of discrimination, in terms of informational content, between the reference and the distorted image. Two different approaches for the cal- culation of the indices are presented and a comparison between them is carried out with different types of dis- torted images. 2 Discrimination Information Be- tween Fuzzy Sets 2.1 Fuzzy Cross-Entropy Let us consider two non-empty fuzzy sets A and B de- fined on the same universe X , with membership func- tions µ A and µ B respectively. Using fuzzy sets nota- tion, A and B are defined as follows: A = ( x, µ A (x) )  x ∈ X  , where µ A : X → [0, 1] , (1)