Anisotropic Wavelet-Based Image Nearness Measure

The problem considered in this article is how to solve the image correspondence problem in cases where it is important to measure changes in the contour, position, and spatial orientation of bounded regions. This article introduces a computational intelligence approach to the solution of this problem with anisotropic (direction dependent) wavelets and a tolerance near set approach to detecting similarities in pairs of images. Near sets are a recent generalization of rough sets introduced by Z. Pawlak during the early 1980s. Near sets resulted from a study of the perceptual basis for rough sets. Pairs of sets containing objects with similar descriptions are known as near sets. The proposed wavelet-based image nearness measure is compared with F. Hausdorff and P. Mahalanobis image distance measures. The results of three wavelet-based image resemblance measures for several well-known images, are given. A direct benefit of this research is an effective means of grouping together (classifying) images that correspond to each other relative to minuscule similarities in the contour, position, and spatial orientation of bounded regions in the images, especially in videos containing image sequences showing varied object movements. The contribution of this article is the introduction of an anisotropic wavelet-based measure of image resemblance using a near set approach.