In this work, an attempt has been made to analyze atrophy of MR brain images using Minkowski Functionals (MFs) of the entropy based skull stripped whole brain image. The normal and Alzheimer images considered in this work are obtained from MIRIAD database. The proposed algorithm uses Shannon entropy and Tsallis entropy methods to calculate the global and local threshold values for the edge detection. The obtained edges map are further processed using morphological operation. The mask generated from the edge map is used to extract the brain tissues. The performance of skull stripping is validated by correlating the total brain area and ground truth. The accuracy of entropy based skull stripping is compared with Otsu thresholding method. The structural changes in skull stripped brain images are analysed using Minkowski functionals such as area, perimeter and Euler number. Results show that the entropy based method is able to extract the total brain. The correlation of total brain area with ground truth is high (R = 0.93). It is also observed that the Minkowski functional, Euler number gives significant discrimination (p<0.001) of normal and Alzheimer subjects. Hence, the entropy based method along with Minkowski functionals could be used for diagnosis of Alzheimer conditions in the brain. © 2014 IEEE.