Determination of singular points in 2D deformable flow fields

Digital image analysis appears to be more and more relevant to the study of physical phenomena involving fluid motion, and of their evolution over time. In that context, 2D deformable motion analysis is one of the important issues to be investigated. The interpretation of such deformable 2D flow fields can generally be stated as the characterization of linear models provided that first order approximations are considered in an adequate neighborhood of so-called singular points, where the velocity becomes null. This paper describes an efficient method, based on a statistical approach, which explicitly addresses these problems, and allows us to locate, characterize and track such singular points in an image sequence. It does not require the prior computation of the velocity field. The method has been validated by experiments carried out with synthetic and real examples corresponding to meteorological image sequences. In fact, the described approach can be of interest in different applications dealing with the characterization of vector fields.