Geometric Structure and View Invariant Recognition Philosophical

By organizing object recognition as indexing a look-up table of model object fea-tures, it can be made eective in terms of time and memory complexity. However, for general three-dimensional (3D) objects it is not possible to compute non-trivial object-speci c descriptors from a single view that are invariant to general choices of viewpoint. This raises the question of how to eectively organize recognition of 3D objects from single views by making various compromises w.r.t. invariance and eciency of representations. For general shapes we can derive shape constraints, in-variant to viewpoint and other camera parameters, that relate 3D and image struc-ture. These relations can be used for verication of the presence in an image of a speci c 3D object but they do not allow for the computation of view invariant in-dexes. In order to have an indexing system for recognition, there are basically two alternative options: if we want complete view invariance we have to restrict the class of objects. Alternatively, if we want methods that work for general unconstrained object types, we have to restrict the range of viewpoints over which invariant de-scriptors can be computed. We will see how this naturally leads to the introduction of incidence and order structure respectively, as a basis for shape description. The hierarchy of geometric structure descriptions: projective/ane, order and incidence can all be described in a unied way in terms of properties of bracket expressions of image coordinates in arbitrary frames