Customized TRS invariants for 2D vector fields via moment normalization

• We extend the theory of moment normalization from real functions to 2D vector fields.
• We calculate the most general TRS normalized moments.
• A customized normalization can be derived from the general results.
• We explicitly show this for the example of pattern recognition for flow fields.

The behavior of vector fields under translation, rotation and scaling differs with respect to the underlying application. Moment invariants that are customized to the specific problem can be constructed by means of normalization.In this paper, we calculate general TRS (translation, rotation, and scaling) moment invariants for two-dimensional vector fields. As an example, we show explicitly how to customize the result for the detection of flow field patterns.