Multivariate orthogonal polynomials to extract singular points.
ABSTRACT 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.
- SourceAvailable from: Eraldo Ribeiro[Show abstract] [Hide abstract]
ABSTRACT: This paper presents a survey of the state-of-the-art in motion estimation of continuum objects such as elastic solids (e.g., human organs, skin, and biomedical tissues) and fluids (e.g., clouds, ocean flows, and air flows). The survey is focused on the estimation methodologies, rather than on specific applications. We begin by summarizing the main components and challenges of continuum-motion estimation, and structure our review around these components. We provide a classification of the related work according to their solutions to these challenges. A discussion on the methodologies for quantitative evaluation of methods is also provided. Finally, we conclude the survey by pointing out some open problems in continuum-motion estimation.Image Vision Comput. 01/2011; 29:509-523.
Conference Paper: Estimating Nonrigid Shape Deformation Using 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; 01/2010
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ABSTRACT: We present a method for detecting and describing features in vector ow elds. Our method models ow elds locally using a linear combination of complex monomials. These monomials form an orthog- onal basis for analytic ows with respect to a correlation-based inner- product. We investigate the invariance properties of the coecients of the approximation polynomials under both rotation and scaling opera- tors. We then propose a descriptor for local ow patterns, and developed a method for comparing them invariantly against rigid transformations. Additionally, we propose a SIFT-like detector that can automatically de- tect singular ow patterns at dierent scales and orientations. Promising detection results are obtained on dierent uid ow data.Structural, Syntactic, and Statistical Pattern Recognition, Joint IAPR International Workshop, SSPR&SPR 2010, Cesme, Izmir, Turkey, August 18-20, 2010. Proceedings; 01/2010