The research introduces a novel axial representation of two- and three-dimensional shapes that implements Binford's original notion of ribbons and generalized cylinders for generic objects. Unlike current representation schemes based on generalized cylinders, which use much more restrictive parametric models such as straight homogeneous generalized cylinders, and are thus limited to instances of these models, this representation can be constructed for arbitrary objects by computing the one- dimensional valleys of a multi-dimensional height field defined by the area of intersection of the object and a parameterized plane. The main objectives of this research are: (1) to give a data-driven, operational definition of ribbons and generalized cylinders that yields practical algorithms for constructing the description of an arbitrary shape from two- or three-dimensional data; (2) to establish the formal properties of the representation with the aims of assessing its scope and developing rigorous algorithms for detecting generalized cylinder projections in images; and (3) to develop a principled approach to part decomposition and use the constructed part-whole hierarchies to support efficient indexing in object recognition tasks.
