Manifold Learning for Compression and Generalization of Euclidean Invariant Signatures of Surface Shapes

摘要

We introduce an approach to the efficient recognition of families of surface shapes in range images. This builds upon earlier work on Tripod Operators (TOs), a method for extracting small sets of N points from 3D surface data in a canonical way such that coordinate independent shape descriptions can be efficiently generated and compared. Using TOs, a specific surface shape generates a signature which is a manifold of dimension ≤ 3 in a feature space of dimension d = N - 3. A runtime application of a TO on surface data generates a d-vector whose distance from the signature manifold is closely related to the likelihood of a match. Ordnance identification is a motivating application.rnIn order to use TOs for recognizing objects from large sets of known shapes, and families of shapes, we introduce the use of manifold learning to represent the signature manifolds with piecewise analytic descriptions instead of discrete point sets. We consider the example of generalizing the signatures of several artillery shells which are qualitatively the same in shape, but metrically different. This can yield a signature that is only slightly more complex than the originals, but enables efficient recognition of a continuous family of shapes.