Maximum Entropy Segmentation Based on the Autocorrelation Function of the Image Histogram

Abstract

Most threshold selection schemes using the principle of maximum entropy regard the image or its histogram as a probability distribution. While such models can to a great extent be justified, a common assumption is that the discrete samples in these distributions (pixels or greylevels) are independent. It is intuitively clear that this is not the case. The proposed method uses the histogram autocorrelation function as a measure of grey-level interdependence. The Shannon entropy of this distribution is then viewed as a measure of image grey-level entropy, where grey-level inter- dependence has implicitly been taken into account. The thresholding process splits the histogram into sub-histograms, ideally corresponding to distinct regions within the image. The entropies of the autocorrelation functions of these subranges are determined and maximized to find the optimum threshold. Two methods of maximizing the class entropies are implemented and some typical results are presented.