Moment Invariants for 3D Flow Fields

Moment invariants are popular descriptors for real valued functions. Their independence from certain transformations makes them a powerful tool for the recognition of patterns and shapes. It has recently been demonstrated that the basic ideas can also be transferred to vector valued functions. Vector moment invariants can be used to define and search for interesting flow structures. A generalization to three-dimensional vector valued functions so far has not been investigated at all. In this paper, we approach that problem. We introduce a definition of moments for three-dimensional vector fields and present how flow field invariants can be constructed from the normalization of the first order vector moment tensor