Estimating the thickness of cerebral cortex is a key step in many MR brain imaging studies, revealing valuable information on development or disease progression. In this work we present a new approach to measure the cortical thickness, based on minimizing line integrals over the probability map of the gray matter in the MRI volume. Previous methods often perform a binary-valued segmentation of the gray matter before measuring the thickness. Because of image noise and partial voluming, such a hard classification ignores the underlying tissue class probabilities assigned to each voxel, discarding potentially useful information. We describe our proposed method and demonstrate its performance on both artificial volumes and real 3D brain MRI data from subjects with Alzheimer's disease and healthy individuals.