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The quantication of cortical surface folding is important in identifying and classifying many neurodegenerative diseases. Much work has been done to identify regional and global brain folding, and in this paper we review some of these methods, as well as propose a new method that has advantages over the existing state of art. Using our novel proposed method, we mapped the local gyrification index on the cortical surface for subjects with mild Alzheimer's dementia (n=20) , very mild dementia (n=23) and age-matched healthy subjects (n=52). In our experiments we find a consistent pattern of gyrification changes in the dementia subjects, with regions generally affected early on in the progression of Alzheimer pathology, including medial temporal lobe, and cingulate gyrus, having decreased gyrification. At the same time we observe increased gyrification in dementia subjects, in frontal, anterior temporal and posteriorly located regions. We speculate that in neurodegenerative diseases including Alzheimer Disease, the folding of the entire cortical mantle undergoes dynamic changes as regional atrophy begins and expands, with both decreases and increases in gyrification.