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.
"Locally uniform flow, which is associated with nonsingular flow, sometimes called laminar flow , is represented with the two coefficients A 0,1 and A 0,2 . Singular points in vector fields are locations where the flow field vanishes, i.e., F (z) = 0, which implies that A 0,1 = A 0,2 = 0. "
[Show abstract][Hide abstract] ABSTRACT: Straightforward quantification of variations of flow patterns within aneurysms fails to accurately describe flow patterns of interest. We applied a multiscale decomposition of the flow in well-defined patterns to detect and quantify flow patterns in an aneurysm phantom that was studied with three different modalities: MRI, computational fluid dynamics, and particle image velocimetry. The method intuitively visualizes main patterns such as locally uniform flow, in- and outflow, and vortices. It is shown that this method is a valuable tool to quantitatively compare scale-dependent complex flow patterns in aneurysms.
"Finally, we define both the deformation field and moments using the same family of basis polynomials, leading to a simplified computation procedure. Polynomials are effective in modeling nonrigid motion fields  , but to our knowledge, this is the first work studying the interaction between polynomial models and image moments. "
[Show abstract][Hide abstract] ABSTRACT: Image moments have been widely used for designing robust shape descriptors that are invariant to rigid transformations. In this work, we address the problem of estimating non-rigid deformation fields based on image moment variations. By using a single family of polynomials to both parameterize the deformation field and to define image moments, we can represent image moments variation as a system of quadratic functions, and solve for the deformation parameters. As a result, we can recover the deformation field between two images without solving the correspondence problem. Additionally, our method is highly robust to image noise. The method was tested on both synthetically deformed MPEG-7 shapes and cardiac MRI sequences.
20th International Conference on Pattern Recognition, ICPR 2010, Istanbul, Turkey, 23-26 August 2010; 09/2010
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