Many types of diseases manifest themselves as observable changes in the shape of the affected organs. Using shape classification, we can look for signs of disease and discover relationships between diseases. We formulate the problem of shape classification in a holistic framework that utilizes a lossless scalar field representation and a non-parametric classification based on sparse recovery. This framework generalizes over certain classes of unseen shapes while using the full information of the shape, bypassing feature extraction. The output of the method is the class whose combination of exemplars most closely approximates the shape, and furthermore, the algorithm returns the most similar exemplars along with their similarity to the shape, which makes the result simple to interpret. Our results show that the method offers accurate classification between three cerebellar diseases and controls in a database of cerebellar ataxia patients. For reproducible comparison, promising results are presented on publicly available 2D datasets, including the ETH-80 dataset where the method achieves 88.4% classification accuracy.