Rough Sets and Near Sets in Medical Imaging: A Review

Abstract

Abstract-This paper presents a review of the current literature on rough set and near set-based approaches to solving various problems in medical imaging such as medical image segmentation, object extraction and image classification. Rough set frameworks hybridized with other computational intelligence technologies that include neural networks, particle swarm optimization, support vector machines and fuzzy sets are also presented. In addition, a brief introduction to near sets and near images with an application to MRI images is given. Near sets offer a generalization of traditional rough set theory and a new approach to classifying perceptual objects by means of features in solving medical imaging problems. Challenges to be addressed and future directions of research are identified and an extensive bibliography is also included.

Anisotropic Wavelet-Based Image Nearness Measure

“…A. Sossinsky [55] observes that main idea underlying tolerance theory comes from H. Poincaré [45]. Physical continua (e.g., measurable magnitudes in the physical world of medical imaging [13]) are contrasted with the mathematical continua (real numbers) where almost solutions are common and a given equation have no exact solutions. An almost solution of an equation (or a system of equations) is an object which, when substituted into the equation, transforms it into a numerical 'almost identity', i.e., a relation between numbers which is true only approximately (within a prescribed tolerance) [55].…”

“…Hence, the basic idea in a tolerance space view of images, for example, is to replace the indiscerniblity relation in rough sets [31] with a tolerance relation in partitioning images into homologous regions where there is a high likelihood of overlaps, i.e., non-empty intersections between image tolerance classes. The use of image tolerance spaces in this work is directly linked to recent work on tolerance spaces [9,11,13,38,39,43,[52][53][54]59]. The contribution of this article is the introduction of two new tolerance space-based image resemblance measures and a comparison of the new measures with the original Henry-Peters nearness measure.…”

“…The relation B,0 is useful, since it defines a partition (segmentation) of an image (this was pointed out in [13,18]). Example 1 Grey-Level Tolerance Classes Let I1, I2 denote the pair of images in Fig.…”

“…2 can be used to define a Nearness Measure (NM) between two sets X and Y [13,16]. Let Z = X ∪Y and let the notation…”

“…The proposed approach to measuring image similarity stems from recent work on anisotropic wavelets [46][47][48], image correspondence [13,16,18,37,39] and near sets [16, 26, 34-37, 39, 44]. Similarities between images can be measured by taking into account image features such as contour, spatial orientation and position of line segments along bounded regions contained in sample images.…”