Point configuration invariants under simultaneous projective and permutation transformations

摘要

The projective invariants used in computer vision today are permutation-sensitive since their value depends on the order in which the features were considered in the computation. We derive, using tools from representation theory, the projective and permutation (p2) invariants of the four collinear and the five coplanar points configurations. The p2-invariants are insensitive to both projective transformations and changes in the labeling of the points. When used as model database indexing functions in object recognition systems, the p2-invariants yield a significant speedup. Permutation invariants for affine transformations are also discussed.