SC Seminar: Max Langbein

Dr. Max Langbein, RHRK

Pattern-matching methods in flow fields


Pattern recognition in vector fields helps to understand and visualize complex three-dimensional vector fields which are used e.g. to describe wind in weather simulations, wind/water channel experiments for vehicles, ocean flows, or electromagnetic fields.

Reasonable efficient methods of Pattern recognition in vector fields should use invariants to transformations under which the physical laws are preserved, i.e. Galilei- resp. Lorenz-Transformations.

The most important ones can be expressed as invariants of higher-order tensors which are calculated from the field. The kernel for collecting the pattern tensors has to be invariant (in case of higher-order moment tensors) or the filter kernels applied to achieve a robust derivative (in case of higher order derivative tensors).

Invariance under coordinate transformations is then easily achieved using total contractions of (tensor-products of) the calculated derivative or moment-tensors. A framework has been created to get a set of independent invariants calculated by the method mentioned beforehand. It will be shown how the invariants including topological ones can be classified and expressed with this method.

Bookmark the permalink.