A powerful framework for the representation, characterization and analysis of two-dimensional shapes, with special attention given to neurons, is presented. This framework is based on a recently reported approach to scale space skeletonization and respective reconstructions by using label propagation and the exact distance transform. This methodology allows a series of remarkable properties, including the obtention of high quality skeletons, scale space representation of the shapes under analysis without border shifting, selection of suitable spatial scales, and the logical hierarchical decomposition of the shapes in terms of basic components. The proposed approach is illustrated with respect to neuromorphometry, including a novel and fully automated approach to automated dendrogram extraction and the characterization of the main properties of the dendritic arborization which, if necessary, can be done in terms of the branching hierarchy. The reported results fully corroborate the simplicity and potential of the proposed concepts and framework for shape characterization and analysis.