Entropy-Based Image Segmentation by Boundary Detection

An entropy-based image segmentation method using template matching and boundary detection is described. A template is postulated to approximate the true scene that gives rise to the gray-scale image to be segmented. The degree of approximation is measured by an index called Gray-scale Image Entropy (GIE); which is defined to measure the amount of information contained in a gray-scale image. It is shown that when the object in the template is located over the boundary of the object in the true scene, the GIE value would have be zero. By moving the template object to different locations, a GIE map is plotted and the zero values correspond to the true scene object boundary points. By linking the detected boundary points, the object boundary can be found and then the object segmented out. We consider that there is a true scene that contains several objects in a background. An image capturing process captures a gray-scale image about the true scene. An image segmentation process operates on the gray-scale image to classify each pixel into either one of the objects or the background. The result of classification is produced in a segmented image. Without loss of generality, we will assume that the true scene is made of J-I objects and a background, i.e. there are totally J different classes into which the pixels are to be classified by image segmentation. There are N picture elements (pixels) in the gray-scale image with each pixel being characterized by a discrete gray-level value ge {O, 1, ..., L-l}. The gray-level values of the pixels belonging to the loth class are random variables following a probability density function (pdt) fj, where fj(g) denotes the probability that a pixel randomly chosen from the loth class has a gray-level value of g. The size of the l"h class is a j of the total image size, i.e. a j N pixels. Hence we have ao +a( +...+aJ-1 = 1. The pdf of the entire image is then given by f(g)=ao.fo(g)+~J;(g)+...+aJ-JJ-I(g) (1) When there is no problem of ambiguity, we will use the symbol f j to denote the function f j (g) . J-I GIE = 8[f]La )8[f)] (3) )=0