Existing computational anatomy methodologies for morphometric analysis of medical images are often based solely on the shape transformation, typically being a diffeomorphism, that warps these images to a common template or vice versa. However, anatomical differences as well as changes induced by pathology, prevent the warping transformation from producing an exact correspondence. The residual image captures information that is not reflected by the diffeomorphism, and therefore allows us to maintain the entire morphological profile for analysis. In this paper we present a morphological descriptor which combines the warping transformation with the residual image in an equivalence class formulation, to characterize morphology of anatomical structures. Equivalence classes are formed by pairs of transformation and residual, for different levels of smoothness of the warping transformation. These pairs belong to the same equivalence class, since they jointly reconstruct the exact same morphology. Moreover, pattern classification methods are trained on the entire equivalence class, instead of a single pair, in order to become more robust to a variety of factors that affect the warping transformation, including the anatomy being measured. This joint descriptor is evaluated by statistical testing and estimation of class separation by classification, initially for 2-D synthetic images with simulated atrophy and subsequently for a volumetric dataset consisting of schizophrenia patients and healthy controls. Results of class separation indicate that this joint descriptor produces generally better and more robust class separation than using each of the components separately.