Invariant Representation and Recognition of 3D Objects using Lie Algebra of Hamiltonian vector field

Abstract

In order to find object representation method which can unify local information, such as tangent vector fields or normal vector fields, and global recognition. The authors have proposed a method which is acle to recognize objects invariantly under Euclidean motion, using linear Lie subalgebra of perceptional vector field of their contours. This subalgebra can represent a very wide class of non algebraic shapes, although they are often non-compact. This paper presents a novel method to represent objects using Lie algebra of Hamiltonian vector field which are has stronger descriptive power and can represent compact shapes. We also show the complete set of invariants of objects under Euclid motion.