Elements of statistical computing: numerical computation
Elements of statistical computing: numerical computation
Image models for 2-D flow visualization and compression
CVGIP: Graphical Models and Image Processing
Dense Estimation of Fluid Flows
IEEE Transactions on Pattern Analysis and Machine Intelligence
Mean Shift: A Robust Approach Toward Feature Space Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Physically based fluid flow recovery from image sequences
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Extraction of Singular Points from Dense Motion Fields: An Analytic Approach
Journal of Mathematical Imaging and Vision
Variational dense motion estimation using the Helmholtz decomposition
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
A Low Dimensional Fluid Motion Estimator
International Journal of Computer Vision
Dynamic Texture Detection Based on Motion Analysis
International Journal of Computer Vision
Detecting regions of dynamic texture
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
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In this paper we propose a new motion estimator for image sequences depicting fluid flows. The proposed estimator is based on the Helmholtz decomposition of vector fields. This decomposition consists in representing the velocity field as a sum of a divergence free component and a curl free component. The objective is to provide a low-dimensional parametric representation of optical flows by depicting them as a flow generated by a small number of vortex and source particles. Both components are approximated using a discretization of the vorticity and divergence maps through regularized Dirac measures. The resulting so called irrotational and solenoidal fields consist then in linear combinations of basis functions obtained through a convolution product of the Green kernel gradient and the vorticity map or the divergence map respectively. The coefficient values and the basis function parameters are obtained by minimization of a functional relying on an integrated version of mass conservation principle of fluid mechanics. Results are provided on real world sequences.