A hierarchical shape decomposition method called Convex-Hull Carving, derived from Sklansky's Concavity Tree and designed to accommodate the incorporation of human flexible resolution visual perception strategies in machine recognition, is proposed. The method characterizes an arbitrary complex shape at multiple hierarchical levels starting from a gross perspective of the entire shape itself, and progressing to decomposed and quantified convex sub-shapes, etc. Calculation complexity and the amount of data to be processed for object recognition applications are reduced. Sklansky's Concavity Tree is a hierarchical arrangement for describing nonconvex shapes. The concavity tree of a shape is defined as a tree describing the hierarchical arrangement of concavities; i.e., concavities within concavities. In the proposed Convex-Hull Carving method, the concavity tree structure is converted to a structure analogous to a chemical molecule. Tree components represent the `atoms' of the molecule and are characterized by their geometric position and a recently defined quantitative shape attribute called the shape quantifier. In addition, the number of hierarchical levels of shape description employed during recognition is driven by: (1) meeting `need to discriminate' criteria; or (2) the determination that all components (`atoms') are convex within predefined acceptance criteria (i.e., no further reduction is possible). The method was implemented to classify a set of two-dimensional aircraft shapes. Results showed that the method is stable with variation of rotation, scaling, and image resolution factors, as well as small viewing angle projection changes.