Well-behaved, tunable 3D-affine invariants

Abstract

We derive and discuss a set of parametric equations which, when given a convex 3D feature domain, K, will generate affine invariants with the property that the invariants' values are uniformly distributed in the region [0,1]×[0,1]×[0,1]. Once the shape of the feature domain K is determined and fixed it is straightforward to compute the values of the parameters and thus the proposed scheme can be tuned to a specific feature domain. The features of all recognizable objects (models) are assumed to be three-dimensional points and uniformly distributed over K. The scheme leads to improved discrimination power, improved computational-load and storage-load balancing and can also be used to determine and identify biases in the database of recognizable models (over-represented constructs of object points). Obvious enhancements produce rigid-transformation and similarity-transformation invariants with the same good distribution properties, making this approach generally applicable.