Multivariate orthogonal polynomials to extract singular points

Olivier Kihl (1) , Benoit Tremblais (1) , Bertrand Augereau (1)

1 SIC

In fluid motion analysis, the extraction of singularity is an important step. This points are crucial for the analysis of physics phenomena. For instance in meteorology these singularities 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 in a multivariate orthogonal polynomials basis. We use only a one degree basis so this method is enough computationnaly efficient to be included in a multiscale scheme. We have tested this method on synthetic and experimental vector field and provides significant results. Moreover this technique is robust to noise.

Mots clés: Image processing; feature extraction and analysis; orthogonal polynomials; flow field analysis; phase portrait; singular point extraction; orthogonal polynomials.

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Olivier Kihl, Benoit Tremblais, Bertrand Augereau. Multivariate orthogonal polynomials to extract singular points. IEEE International Conference on Image Processing 2008. ICIP 2008., Oct 2008, San Diego, CA, United States. ⟨hal-00340382⟩