Detecting singular patterns in 2D vector fields using weighted Laurent polynomial

In this paper, we propose a method for detecting patterns of interest in vector fields. Our method detects patterns in a scale- and rotation-invariant manner. It works by approximating the vector-field data locally using a Laurent polynomial weighted by radial basis functions. The proposed representation is able to model both analytic and non-analytic flow fields. Invariance to scale and rotation is achieved by combining the linearity properties of the model coefficients and a scale-space parameter of the radial basis functions. Promising detection results are obtained on a variety of fluid-flow sequences.

► A SIFT-like flow-field singular pattern detector.
► Scale- and rotation-invariant descriptor for flow-field patterns.
► Complex-valued representation modeling both analytic and non-analytic flow fields.
► Algebraic handling of flow-field geometric transformations.