Anisotropic Wavelet-Based Image Nearness Measure

Abstract

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.

Applications of Near Sets

“…The concept of nearness enters as soon as one starts studying digital images (see, e.g., [62,37,52,41,47]). The digital image of a photograph should resemble, as accurately as possible, the original subject, i.e., an image should be globally close to its source.…”

“…Resemblance is determined by considering set descriptions defined by feature vectors (n-dimensional vectors of numerical features that represent characteristics of objects such as digital image pixels). Near sets are useful in solving problems based on human perception [44,76, 49,51,56] that arise in areas such as image analysis [52,14,41, 48,17,18], image processing [41], face recognition [13], ethology [63], as well as engineering and science problems [53,63,44,19,17,18].As an illustration of the degree of nearness between two sets, consider an example of the Henry color model for varying degrees of nearness between sets [17, §4.3].…”

Arthritic Hand‐Finger Movement Similarity Measurements: Tolerance Near Set Approach

“…The hand-finger motion classification method reported in this paper is an outgrowth of earlier work on medical imaging [2, 3] and, in particular, on comparing hand movement image sequences [4]. The term arthritis is derived from the Greek words arthron (referring to joints) and the suffix itis (inflammation of).…”

Measuring Resemblances Between Swarm Behaviours: A Perceptual Tolerance Near Set Approach

“…In contrast, our work considers i) more than one swarm and ii) description-based distance measures. The measures presented in this article are defined in the context of tolerance near sets [30,36,37,35], specialized forms of near sets [28,27,37].…”

“…All of the nearness measures reported in this article originated from studies of image resemblance and the degree of nearness between pairs of disjoint sets representing digital images (see, e.g. [12,17,16,37,24,11,35,26,18]). Prior to this, it was common for us to define nearness measures relative to subimages or pixels in digital images, where an image is viewed as a set of points.…”