Most of current computer-based facial expression analysis methods focus on the recognition of perfectly posed expressions, and hence are incapable of handling the individuals with expression impairments. In particular, patients with schizophrenia usually have impaired expressions in the form of "flat" or "inappropriate" affects, which make the quantification of their facial expressions a challenging problem. This paper presents methods to quantify the group differences between patients with schizophrenia and healthy controls, by extracting specialized features and analyzing group differences on a feature manifold. The features include 2D and 3D geometric features, and the moment invariants combining both 3D geometry and 2D textures. Facial expression recognition experiments on actors demonstrate that our combined features can better characterize facial expressions than either 2D geometric or texture features. The features are then embedded into an ISOMAP manifold to quantify the group differences between controls and patients. Experiments show that our results are strongly supported by the human rating results and clinical findings, thus providing a framework that is able to quantify the abnormality in patients with schizophrenia.