Optimizing random patterns for invariants-based identification

Pseudo-random point configurations can be used for many vision tasks, both active and passive. Examples are the projection of a pseudo-random light pattern to perform stereo matching or depth estimation by triangulation or robot navigation. The use of the local arrangement of the random features is attractive in some situations because labelling can be performed more robustly than by proliferating the feature types with other coding means. In this context the use of projective invariants provides either a classification measure or an indexing tool which is insensitive to surface position and camera geometry, which have proven invaluable to curb the complexity of the search by order of magnitudes. So far no work has been done on analysing how these pseudo-random patterns should be like to make the use of invariants more effective, in particular with respect to discrimination and noise sensitivity. This paper addresses this problem for the common case of Ei-point projective invariants. ii stochastic approximation strategy is employed that iteratively adjusts the position of the points in the pattern while trying to maximise a spacing measure between the invariants. The results clearly illustrate the benefits of the approach which makes optimised pseudo random patterns of identical features a valid alternative to other forms of pattern coding for three-dimensional capture.