A Generalization of Moment Invariants on 2D Vector Fields to Tensor Fields of Arbitrary Order and Dimension

摘要

For object recognition in tensorfields and in pointclouds, the recognition of features in the object irrespective of their rotation is an important task. Rotationally invariant features exist for 2d scalar fields and for 3d scalar fields as moments of a second order structure tensor. For higher order structure tensors iterative algorithms for computing something similar to an eigenvector-decomposition exist. In this paper, we introduce a method to compute a basis for analytical rotationally invariant moments of tensorfields of - in principle - any order and dimension and give an example using up to 4th-order structure tensors in 3d.