Note on the equivalence relationship between Renyi-entropy based and Tsallis-entropy based image thresholding

Renyi entropy based image thresholding in [Sahoo, P., Wilkins, C., et al., 1997. Thresholding selection using Renyi's entropy. Pattern Recognition 30 (1), 71-84; Sahoo, P.K., Arora, G., 2004. A thresholding method based on two dimensional Renyi's entropy. Pattern Recognition 37 (6), 1149-1161] and Tsallis entropy based image thresholding in [Albuquerque, M.P., Esquef, I.A., et al., 2004. Image thresholding using Tsallis entropy. Pattern Recognition Letters 25 (9), 1059-1065] are two important global threshold selection approaches in image segmentation. In this correspondence, the equivalence relationship between these two approaches is revealed, that is to say, with the same parameter, these two approaches will obtain the same threshold.