Surface-based morphometry (SBM) is widely used in biomedical imaging and other domains to localize shape changes related to different conditions. This paper presents a computational framework that integrates a set of effective surface registration and analysis methods to form a unified SBM processing pipeline. Surface registration includes two parts: surface alignment in the object space by employing the iterative closest point (ICP) method, and surface alignment in the parameter space by using conformal mapping and landmark-based thin-plate spline methods. Statistical group analysis of registered surface data is then conducted by surface-based general linear model and random field theory addressing multiple testing issues. The effectiveness of the proposed framework is demonstrated by applying it to a fetal alcohol syndrome (FAS) study for identifying facial dysmorphology in FAS patients.