Moment Invariants for 2D Flow Fields Using Normalization

Abstract

The analysis of 2D flow data is often guided by the search for char- acteristic structures with semantic meaning. One way to approach this question is to identify structures of interest by a human ob- server. The challenge then, is to find similar structures in the same or other datasets on different scales and orientations. In this paper, we propose to use moment invariants as pattern de- scriptors for flow fields. Moment invariants are one of the most pop- ular techniques for the description of objects in the field of image recognition. They have recently also been applied to identify 2D vector patterns limited to the directional properties of flow fields. In contrast to previous work, we follow the intuitive approach of moment normalization, which results in a complete and inde- pendent set of translation, rotation, and scaling invariant flow field descriptors. They also allow to distinguish flow features with differ- ent velocity profiles. We apply the moment invariants in a pattern recognition algorithm to a real world dataset and show that the the- oretic results can be extended to discrete functions in a robust way.