Tsallis entropy and the long-range correlation in image thresholding
Signal Processing
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Thresholding techniques for image segmentation is one of the most popular approaches in Computational Vision systems. Recently, M. Albuquerque has proposed a thresholding method (Albuquerque et al. in Pattern Recognit Lett 25:1059–1065, 2004) based on the Tsallis entropy, which is a generalization of the traditional Shannon entropy through the introduction of an entropic parameter q. However, the solution may be very dependent on the q value and the development of an automatic approach to compute a suitable value for q remains also an open problem. In this paper, we propose a generalization of the Tsallis theory in order to improve the non-extensive segmentation method. Specifically, we work out over a suitable property of Tsallis theory, named the pseudo-additive property, which states the formalism to compute the whole entropy from two probability distributions given an unique q value. Our idea is to use the original M. Albuquerque’s algorithm to compute an initial threshold and then update the q value using the ratio of the areas observed in the image histogram for the background and foreground. The proposed technique is less sensitive to the q value and overcomes the M. Albuquerque and k-means algorithms, as we will demonstrate for both ultrasound breast cancer images and synthetic data.