Space efficient connectivity test for n-dimensional images

Abstract

An image is a discrete array whose elements, called points, represent some property. Images are broadly used in computer graphics. In 2D graphics applications, color, depth and other image properties are frequently used. In 3D graphics, a solid may be represented by a 3D binary image whose elements have value 0 or 1 indicating absence or presence of solid. Similarly, many volume applications use non-binary 3D images to represent some spatial function. Here we propose an algorithm to solve the connectivity problem, which can be stated as follows: given an n-dimensional image I, an m-adjacency A and a predicate P which segments the property values into black and white points, check if the black points of I are m-connected, that is, if I has a single m-connected black component.