Pierre Dérian

Divergence-free Wavelets and High Order Regularization

Expanding on a wavelet basis the solution of an inverse problem provides several advantages. First of all, wavelet bases yield a natural and efficient multiresolution analysis which allows defining clear optimization strategies on nested subspaces of the solution space. Besides, the continuous representation of the solution with wavelets enables analytical calculation of regularization integrals over the spatial domain. By choosing differentiable wavelets, accurate high-order derivative regularizers can be efficiently designed via the basis’s mass and stiffness matrices. More importantly, differential constraints on vector solutions, such as the divergence-free constraint in physics, can be nicely handled with biorthogonal wavelet bases. This paper illustrates these advantages in the particular case of fluid flow motion estimation. Numerical results on synthetic and real images of incompressible turbulence show that divergence-free wavelets and high-order regularizers are particularly relevant in this context.

Wavelet-Based Optical Flow Estimation of Instant Surface Currents From Shore-Based and UAV Videos

Instant fields of surface current are retrieved from shore-based and unmanned aerial vehicle videos by an optical flow (OF) method named “Typhoon.” This computer vision algorithm estimates dense 2-D 2-component velocity fields from the observable motion of foam patterns in the surf zone. Despite challenging image data resolution and quality, comparison of OF surface current estimates with measurements by an acoustic Doppler velocimeter reveals its ability to capture both wave-to-wave fluctuations and low-frequency variations. The method is also successfully applied to the monitoring of a “flash rip” event. This paper shows clearly the high potential of this method in the nearshore, where the rapid development of webcams and drones offers a large number of applications for swimming and surfing safety, engineering and naval security, and research purpose, by providing quantitative information.

Wavelet-Based Optical Flow for Two-Component Wind Field Estimation from Single Aerosol Lidar Data

AbstractA motion estimation algorithm was applied to image sequences produced by a horizontally scanning elastic backscatter lidar. The algorithm, a wavelet-based optical flow estimator named Typhoon, produces dense two-component vector flow fields that correspond to the apparent motion of microscale aerosol features. To validate the efficacy of this approach for the remote measurement of wind fields in the lower atmosphere, an experiment was conducted in Chico, California, in 2013 and 2014. The flow fields, estimated every 17 s, were compared with measurements from an independent Doppler lidar. Time series of wind speed and direction, statistical assessment of the 10-min averages, and examples of wind fields are presented. The comparison of 10-min averages at 100 m AGL reveals excellent correlations between estimates from the Typhoon algorithm and measurements from the Doppler lidar. Power spectra and spectral transfer functions are computed to estimate the filtering effects of the algorithm in the spati...

Wavelet-Based fluid motion estimation

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.

Optimization of the Cross-Correlation Algorithm for Two-Component Wind Field Estimation from Single Aerosol Lidar Data and Comparison with Doppler Lidar

AbstractNumerical and field experiments were conducted to test an optimized cross-correlation algorithm (CCA) for the remote sensing of two-component wind vectors from horizontally scanning elastic backscatter lidar data. Each vector is the result of applying the algorithm to a square and contiguous subset of pixels (an interrogation window) in the lidar scan area. Synthetic aerosol distributions and flow fields were used to investigate the accuracy and precision of the technique. Results indicate that in neutral static stability, when the mean flow direction over the interrogation window is relatively uniform, the random error of the estimates increases as the mean wind speed and turbulence intensity increases. In convective conditions, larger errors may occur as a result of the cellular nature of convection and the dramatic changes in wind direction that may span the interrogation window. Synthetic fields were also used to determine the significance of various image processing and numerical steps used i...

Comments on “Wind Gust Detection and Impact Prediction for Wind Turbines”

We refute statements in “Zhou, K., et al. Wind gust detection and impact prediction for wind turbines. Remote Sens. 2018, 10, 514.” about the impracticality of motion estimation methods to derive two-component vector wind fields from single scanning aerosol lidar data. Our assertion is supported by recently published results on the performance of two image-based motion estimation methods: cross-correlation (CC) and wavelet-based optical flow (WOF). The characteristics and performances of CC and WOF are compared with those of a two-dimensional variational (2D-VAR) method that was applied to radial velocity fields from a single scanning Doppler lidar. The algorithmic aspects of WOF and 2D-VAR are reviewed and we conclude that these two approaches are in fact similar and practical.

Location Uncertainty Principle: Toward the Definition of Parameter-Free Motion Estimators

In this paper, we propose a novel optical flow approach for estimating two-dimensional velocity fields from an image sequence, which depicts the evolution of a passive scalar transported by a fluid flow. The Eulerian fluid flow velocity field is decomposed into two components: a large-scale motion field and a small-scale uncertainty component. We define the small-scale component as a random field. Then the data term of the optical flow formulation is based on a stochastic transport equation, derived from a location uncertainty principle [17]. In addition, a specific regularization term built from the assumption of constant kinetic energy involves the same diffusion tensor as the one appearing in the data transport term. This enables us to devise an optical flow method dedicated to fluid flows in which the regularization parameter has a clear physical interpretation and can be easily estimated. Experimental evaluations are presented on both synthetic and real images. Results indicate very good performance of the proposed parameter-free formulation for turbulent flow motion estimation.