Minimum cross-entropy threshold selection

Thresholding is a common and easily implemented form of image segmentation. Many methods of automatic threshold selection based on the optimization of some discriminant function have been proposed. Such functions often take the form of a metric distance or similarity measure between the original image and the segmented result. A non-metric measure, the cross-entropy, is used here to determine the optimum threshold. It is shown that this measure is related to other commonly used measures of distance or similarity under special conditions, although it is in some senses more general. Some typical results using this method are presented, together with results using a metric form of the cross-entropy.