The growing clinical importance of Diffusion tensor imaging (DTI) in disease investigation has prompted large population studies that require computational neuroanatomic techniques for tensor processing, as conventional analysis of scalar maps of DTI does not identify the full impact of pathology. In this paper we propose a comprehensive framework called Manifold Based Morphometry (MBM) for the computational and statistical analysis of DTI datasets, consisting of spatial normalization to a template, followed by voxel-based analysis based on embedding the tensors to a linear submanifold using kernel-based manifold learning and applying statistics in this embedded space. Regions of significant difference are identified and compared with those found with conventional voxel-based analysis of scalar maps of anisotropy and diffusivity. MBM has then been applied to the group-based statistical analysis of dataset of schizophrenia patients and controls. The comparison yields that MBM consisting of the full tensor DTI analysis reveals regions of difference that encompass regions identified by the analysis of scalar maps thereby reinforcing the comprehensive nature of the designed framework.