Rotation moment invariants of vector fields

Vector field images are a type of multidimensional data arising from many engineering areas. This type of images differs significantly from standard graylevel and color images in several aspects. Hence, there is a need for automatic processing of vector fields from application areas, developing special methods and algorithms for vector fields is of great importance. A common task in vector field analysis is the detection of various patterns of interest, such as sinks, vortices, saddle points, and others. The detection of these features is typically accomplished by template matching. The search algorithms must be primarily invariant to total rotation, where the action is applied not only on the spatial coordinates but also on the field values. Moment invariants of vector fields will be introduced. The superiority of orthogonal polynomials for construction of moments will be demonstrated. Their numerical stability will be shown to be higher than of the invariants published so far. The usefulness of invariants constructed from orthogonal moments will be demonstrated in a real world template matching application.