Rotation invariants of vector fields from orthogonal moments

Vector field images are a type of new multidimensional data that appear in many engineering areas. Although the vector fields can be visualized as images, they differ from graylevel and color images in several aspects. To analyze them, special methods and algorithms must be originally developed or substantially adapted from the traditional image processing area. In this paper, we propose a method for the description and matching of vector field patterns under an unknown rotation of the field. Rotation of a vector field is so-called total rotation, where the action is applied not only on the spatial coordinates but also on the field values. Invariants of vector fields with respect to total rotation constructed from orthogonal Gaussian-Hermite moments and Zernike moments are introduced. Their numerical stability is shown to be better than that of the invariants published so far. We demonstrate their usefulness in a real world template matching application of rotated vector fields.