A gray-level threshold selection method based on maximum entropy principle

Ab..tract-The gray-level threshold selection method for im2 e segmen-tation presented here is based on the maximum entropy pri ciple. The optimal threshold value is determined by maximizing the , posteriori entropy subject to certain inequality constraints which are ,Ierived by means of special measures characterizing uniformity and the s 'ape of tbe Manu"cripl rcceivcd Novcmber 3. function h(x, y) at gray level/is a binary image J-inction h,(x, f). The explicit representation of h,(x, y) is expres,ed as { ai' ifh(x,.y)~/ h,(x,y)-. where No is the total number of pixels in the image and I is the total number of gray levels. Dunn et al. [5] proposed a uniform error threshold selection method which equalizes the probflbility of misclassification between the object and the background pixels in an image. The optimal threshold value in uniform error method is obtained by finding a threshold t E Z,+ such thit b(t)(b(t) +1)-(a2(t) + c(t»)-0 where a(t) = Pr {a pixel has gray value> t} b(t) = Pr { two adjacent pixels have gray values> t} c(t) = Pr {four neighboring pixels have gray values> t. The probabilities a(t), b(t), and c(t) are estimated by exanllning 2x2 neighborhoods in the image for fixed t. The uniform '~rror method is a global region-dependent thresholding method. ,\viad and Lozinskii [1] proposed a thresholding method base,:! on minimizing the ambiguity which results from the different contexts in which gray levels are classified as object or backgrl ,undo Pavlidis and Wolberg [22] have given an algorithm based ()n a model of the image distortion. Forte and Sahoo [7] introdu. ~d a measure for the loss of information due to reduction on the J ,LOge of a real random variable and proposed a thresholding mt !hod based on the loss of information criterion. Their method be ()ngs to the class of point-dependent global techniques. Another i,tlor-mation theoretic method that recently appeared in the liter;.llure is due to Beattie [2]. Other recent publications related to ;'11to-matic threshold selection include [10], [13], and [17]. III. MAXIMUM ENTROPY THRESHOLDING The success of the maximum entropy method for sol \1ng problems in image reconstruction [32], [33] and other areas :13] has encouraged us to apply this method to threshold selectior As is well-known, the maximum entropy principle serves as a criterion to select a priori probability distributions when very litt;<: or nothing is known. It states that, for a given amount of info! …