The main contribution of this thesis, is to define similarity measures between two images with the main focus on content-based image retrieval (CBIR). Each image is considered as a set of visual elements that can be described with a set of visual descriptions (features). The similarity between images is then defined as the nearness between sets of elements based on a tolerance and a fuzzy tolerance relation. A tolerance relation is used to describe the approximate nature of the visual perception. A fuzzy tolerance relation is adopted to eliminate the need for a sharp threshold and hence model the gradual changes in perception of similarities. Three real valued similarity measures as well as a fuzzy valued similarity measure are proposed. All of the methods are then used in two CBIR experiments and the results are compared with classical measures of distance (namely, Kantorovich, Hausdorff and Mahalanobis). The results are compared with other published research papers. An important advantage of the proposed methods is shown to be their effectiveness in an unsupervised setting with no prior information. Eighteen different features (based on color, texture and edge) are used in all the experiments. A feature selection algorithm is also used to train the system in choosing a suboptimal set of visual features.

The main contribution of this thesis, is to define similarity measures between two images with the main focus on content-based image retrieval (CBIR). Each image is considered as a set of visual elements that can be described with a set of visual descriptions (features). The similarity between images is then defined as the nearness between sets of elements based on a tolerance and a fuzzy tolerance relation. A tolerance relation is used to describe the approximate nature of the visual perception. A fuzzy tolerance relation is adopted to eliminate the need for a sharp threshold and hence model the gradual changes in perception of similarities. Three real valued similarity measures as well as a fuzzy valued similarity measure are proposed. All of the methods are then used in two CBIR experiments and the results are compared with classical measures of distance (namely, Kantorovich, Hausdorff and Mahalanobis). The results are compared with other published research papers. An important advantage of the proposed methods is shown to be their effectiveness in an unsupervised setting with no prior information. Eighteen different features (based on color, texture and edge) are used in all the experiments. A feature selection algorithm is also used to train the system in choosing a suboptimal set of visual features.