We propose a unified framework based on a general definition of geometric transform (GeT) for modeling appearance. GeT represents the appearance by applying designed functionals over certain geometric sets. We show that image warping, Radon transform, trace transform, etc. are special cases of our definition. Moreover, three different types of GeTs are designed to handle deformation, articulation and occlusion and applied to fingerprinting the appearance inside a contour. They include the contour-driven GeT, the feature curve based GeT and selecting functionals to model the appearance inside the convex hull of the contour. A multi-resolution representation that combines both shape and appearance information is also proposed. We apply our approach to image synthesis and object recognition. The proposed approach produces promising results when applied to fingerprinting the appearance of human and body parts despite the challenges due to articulated motion and deformations.