Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Dense Estimation of Fluid Flows
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Wavelet transforms for vector fields using omnidirectionally balanced multiwavelets
IEEE Transactions on Signal Processing
Complex motion models for simple optical flow estimation
Proceedings of the 32nd DAGM conference on Pattern recognition
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Imaging plays an important role in experimental fluid dynamics. It is equally important both for scientific research and a range of industrial applications. It is known, however, that estimated velocity fields of fluids often suffer from various types of corruptions like missing data, for instance, that make their physical interpretation questionable. We present an algorithm that accepts a wide variety of corrupted 2-D vector fields as input data and allows to recover missing data fragments and to remove noise in a physically plausible way. Our approach essentially exploits the physical properties of incompressible fluid flows and does not rely upon any particular model of noise. As a result, the developed algorithm performs well and robust for different types of noise and estimation errors. The computational algorithm is sufficiently simple to scale up to large 3-D problems.