Model-based Invariant Functions and Their Use for Recognition

Using three dimensional invariant representations, we address the problem of changes in appearance that result from a change in camera orientation (or change of viewpoint). This approach is based on a Euclidean invariant representation of three dimensional objects, where the metric information is kept using the Gramian of 4 basis points and the affine coordinates of the remaining points, or using the generalized inverse Gramian of all the object points. We describe functions which operate on two dimensional images of three dimensional objects, and which are invariant under changes of viewpoint. These functions can be used to improve and extend various existing recognition approaches, including alignment, linear combination, and indexing. The invariant representation can be computed with a linear algorithm from a sequence of images.

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