Multivariate orthogonal polynomials to extract singular points

In fluid motion analysis, the extraction of singularity is an important step. This points are crucial for the analysis of physic phenomenas. For instance in meteorology these singularities might represent the center of depression.The objective of this paper is to present an original method for extraction of singularities in a vector field. We study the affine model of the motion to extract potential singularities. The originality of our method reside in the computation of the affine model by projection of the vector field onto multivariate orthogonal polynomials basis. We use a one degree basis so this method is enough computationally efficient to be included in a multiscale scheme. We have tested this method on synthetic and experimental vector field. It provides significant results. Moreover this technique is robust to noise.