On the Utility of Different Entropy Measures in Image Thresholding

Over last few years, several methods have been proposed for image thresholding based on entropy maximization. Some of these methods use gray level histogram, while others use entropy associated with the two-dimensional histogram or the co-occurrence matrix. Few recent methods use the cross entropy or divergence also. But most of these attempts are based on Shannon’s entropy except a few which use the exponential entropy or quadratic entropy. There are many other measures of information or entropy definitions whose utility in image processing has not been explored. This paper attempts to review some of these non-Shannon entropic measures and investigates their usefulness in image segmentation. Most of these “non-Shannonian” entropy measures have some parameters whose influence on the performance of the thresholding algorithms is investigated. In this regard we consider two types of algorithms, one based on global image information (or histogram) and the other based on local image information (co-occurrence or two dimensional histogram). Our findings are: (i) the co-occurrence based entropy methods perform better than histogram based methods for image thresholding; (ii) some of the entropy measures are not very sensitive to their parameters and a few of them are not at all useful at least for histogram based thresholding; and (iii) maximization of the histogram entropy of a partitioned image, at least the way it is being used in the literature, is not a good principle for image segmentation.