Conference Paper

Wavelet-Based Fluid Motion Estimation.

DOI: 10.1007/978-3-642-24785-9_62 Conference: Scale Space and Variational Methods in Computer Vision - Third International Conference, SSVM 2011, Ein-Gedi, Israel, May 29 - June 2, 2011, Revised Selected Papers
Source: DBLP

ABSTRACT Based on a wavelet expansion of the velocity field, we present a novel optical flow algorithm dedicated to the estimation of continuous motion fields such as fluid flows. This scale-space representation, associated to a simple gradient-based optimization algorithm, naturally sets up a well-defined multi-resolution analysis framework for the optical flow estimation problem, thus avoiding the common drawbacks of standard multi-resolution schemes. Moreover, wavelet properties enable the design of simple yet efficient high-order regularizers or polynomial approximations associated to a low computational complexity. Accuracy of proposed methods is assessed on challenging sequences of turbulent fluids flows.

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    ABSTRACT: This paper addresses the problems of disparity and optical flow partitioning based on the brightness invariance assumption. We investigate new variational approaches to these problems with Potts priors and possibly box constraints. For the optical flow partitioning, our model includes vector-valued data and an adapted Potts regularizer. Using the notation of asymptotically level stable functions we prove the existence of global minimizers of our functionals. We propose a modified alternating direction method of minimizers. This iterative algorithm requires the computation of global minimizers of classical univariate Potts problems which can be done efficiently by dynamic programming. We prove that the algorithm converges both for the constrained and unconstrained problems. Numerical examples demonstrate the very good performance of our partitioning method.
    05/2014; DOI:10.1093/imaiai/iau010
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    ABSTRACT: This paper presents a method for regularization of inverse problems. The vectorial bi-dimensional unknown is assumed to be the realization of an isotropic divergence-free fractional Brownian Motion (fBm). The method is based on fractional Laplacian and divergence-free wavelet bases. The main advantage of these bases is to enable an easy formalization in a Bayesian framework of fBm priors, by simply sampling wavelet coefficients according to Gaussian white noise. Fractional Laplacians and the divergence-free projector can naturally be implemented in the Fourier domain. An interesting alternative is to remain in the spatial domain. This is achieved by the analytical computation of the connection coefficients of divergence-free fractional Laplacian wavelets, which en-ables to easily rotate this simple prior in any sufficiently "regular" wavelet basis. Taking advantage of the tensorial structure of a separable fractional wavelet basis approximation, isotropic regulariza-tion is then computed in the spatial domain by low-dimensional matrix products. The method is successfully applied to fractal image restoration and turbulent optic-flow estimation.
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    ABSTRACT: Optical flow estimation is one of the oldest and still most active research domains in computer vision. In 35 years, many methodological concepts have been introduced and have progressively improved performances, while opening the way to new challenges. In the last decade, the growing interest in evaluation benchmarks has stimulated a great amount of work. In this paper, we propose a survey of optical flow estimation classifying the main principles elaborated during this evolution, with a particular concern given to recent developments. It is conceived as a tutorial organizing in a comprehensive framework current approaches and practices. We give insights on the motivations, interests and limitations of modeling and optimization techniques, and we highlight similarities between methods to allow for a clear understanding of their behavior.
    Computer Vision and Image Understanding 02/2015; DOI:10.1016/j.cviu.2015.02.008 · 1.36 Impact Factor

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