Representing Generalized Cylinders

In an influential paper Binford 1971 [1] proposed generalized cylinders as a model for representing visual shape. With reference to Blum ́s medial axis transform he argued that objects, or at least their parts, often can be considered as generated by sweeping a planar curve, the cross section, along an axis or a spine. For instance, both manufactured objects and objects that accrue from natural growth or wearing tend to have such shapes. Extensive work on representation and understanding of shape in computer vision has since been based on this notion, and it has also been used to form theories for object recognition by humans [2]. Despite these vast efforts on applying the generalized cylinders to problems on shape, the general representation that Binford suggested does not necessarily define non-singular surfaces, i.e. surfaces that are boundaries of physical objects. This problem has largely been addressed by only considering very special cases, the main one being that of straight homogeneous generalized cylinders (SHGC:s). Moreover, as pointed out by Koenderink ([3], p. 593) the GC notion is so general that it contains almost everything. Of course, one can argue that it is more natural to consider volumetric representations than surface representations for physical objects. Nevertheless, it is undisputable that surfaces can be observed visually. It is also true that the intuition behind Binford ́s suggested model is quite natural. The attempts to either restrict the model to oversimplified cases, or to only consider local properties is no doubt critical for solving certain recognition problems, but they neither fully exploit the global aspect, nor the intuitiveness of Binford ́s definition. Therefore, it must be of interest to ask if there is any more precise definition of generalized cylinders that specifies the notion better.