Statistical morphometric analysis is an important and challenging problem in computer vision and medical image analysis. In the medical imaging domain, the goal is to identify morphometric abnormalities in structures of interest that are associated with a particular condition to aid diagnosis and treatment. We present computational techniques for morphometric analysis of 3D surfaces to localize regionally specific shape changes between groups of 3D objects and demonstrate the techniques in several biomedical computing applications. The spherical harmonic (SPHARM) method is employed for surface modeling. We discuss a classical spherical parameterization method designed for voxel surfaces as well as a new approach that works for general triangle meshes. Besides using the first order ellipsoid for establishing surface correspondence and aligning objects, we discuss a new and more general method for establishing surface correspondence that aims to minimize the mean squared distance between two corresponding surfaces. Surface registration issues are addressed for both single object cases and multiple object cases. Two types of techniques are employed for statistical shape analysis: (1) linear classifiers based on a point distribution model, and (2) random fields theory combined with heat kernel smoothing. We show several results in computational neuroscience and cardiology.