Fuzzy shell clustering algorithms in image processing: fuzzy C-rectangular and 2-rectangular shells

Objective function-based clustering has been generalized recently to detect contours of circles and ellipses or even hyperbolas in a set of binary data vectors. Although there are special algorithms to discover lines, the detection of rectangles needs further treatment. A simple line-detection algorithm is not sufficient for rectangles since for identifying four lines as one rectangle, additional information such as the length of the lines and whether they are parallel or meet at a right angle is necessary. In this paper, a special fuzzy shell-clustering algorithm for rectangular contours is developed. The principal idea behind it can be generalized for other polygons so we also derive an algorithm that is capable of detecting rectangles and other polygons as well as approximating circles, ellipses, and lines.