Non Uniform Multiresolution Method for Optical Flow and Phase Portrait Models: Environmental Applications

Projet AIRIn this paper we define a complete framework for processing large image sequences for a global monitoring of short range oceanographic and atmospheric processes. This framework is based on the use of a non quadratic regularization technique in optical flow computation that preserves flow discontinuities. We also show that using an appropriate tessellation of the image according to an estimate of the motion field can improve optical flow accuracy and yields more reliable flows. This method defines a non uniform multiresolution approach for coarse to fine grid generation. It allows to locally increase the resolution of the grid according to the studied problem. Each added node refines the grid in a region of interest and increases the numerical accuracy of the solution in this region. We make use of such a method for solving the optical flow equation with a non quadratic regularization scheme allowing the computation of optical flow field while preserving its discontinuities. The second part of the paper deals with the interpretation of the obtained displacement field. We make use of a phase portrait model with a new formulation of the approximation of an oriented flow field allowing to consider arbitrary polynomial phase portrait models for characterizing salient flow features. This new framework is used for processing oceanographic and atmospheric image sequences and presents an alternative to complex physical modeling techniques

Image Understanding and Robotics Research at Columbia University

The research investigations of the Vision/Robotics Laboratory at Columbia University reflect the diversity of interests of its four faculty members, two staff programmers and 15 Ph.D. students. Several of the projects involve either a visiting computer science post-doc, other faculty members in the department or the university, or researchers at AT&T Bell Laboratories or Philips laboratories. We list below a summary of our interest and results, together with the principal researchers associated with them. Since it is difficult to separate those aspects of robotic research that are purely visual from those that are vision-like (for example, tactile sensing) or vision-related (for example, integrated vision-robotic systems), we have listed all robotic research that is not purely manipulative

Solving ill-posed Image Processing problems using Data Assimilation

International audienceData Assimilation is a mathematical framework used in environmental sciences to improve forecasts performed by meteorological, oceanographic or air quality simulation models. It aims to solve an evolution equation, describing the temporal dynamics, and an observation equation, linking the state vector and observations. In this article we use this framework to study a class of ill-posed Image Processing problems, usually solved by spatial and temporal regularization techniques. An approach is proposed to convert an ill-posed Image Processing problem in terms of a data Assimilation system, solved by a 4D-Var method. This is illustrated by the estimation of optical ow from a noisy image sequence, with the dynamic model ensuring the temporal regularity of the result. The innovation of the paper concerns first, the extensive description of the tasks to be achieved for going from an image processing problem to a data assimilation description; second, the theoretical analysis of the covariance matrices involved in the algorithm; and third a specic discretisation scheme ensuring the stability of computation for the application on optical flow estimation

Hierarchical Estimation of Oceanic Surface Velocity Fields From Satellite Imagery.

Oceanic surface velocity fields are objectively estimated from time-sequential satellite images of sea-surface temperature from the Advanced Very High Resolution Radiometey on board the National Oceanic and Atmospheric Administration\u27s polar orbiters. The hierarchical technique uses the concept of image pyramids and multi-resolution grids for increased computational efficiency. Images are Gaussian filtered and sub-sampled from fine to coarse grid scales. The number of pyramid levels is selected such that the maximum expected velocity in the image results in a displacement of less than one pixel at the coarsest spatial scale. Maximum Cross-Correlation at the sub-pixel level with orthogonal polynomial approximation is used to compute a velocity field at each level of the pyramid which is then iterated assuming a locally linear velocity field. The first image at the next finer level of the pyramid is warped towards the second image by the calculated velocity field. At each succeeding finer grid scale, the velocity field is updated and the process repeated. The final result is an estimated velocity at each pixel at the finest resolution of the imagery. There are no free parameters as used in some gradient-based approaches and the only assumption is that the velocity field is locally linear. Test cases are shown using both simulated and real images with numerically simulated velocity fields which demonstrate the accuracy of the technique. Results are compared to gradient-based techniques using concepts of optical flow and projection onto convex sets and to the standard Maximum Cross-Correlation technique. The hierarchical computations for a real satellite image numerically advected by a rotational sheared flow recover the original field with a rms speed error of 12.6% and direction error of 4.9\sp\circ. Hierarchically-estimated velocity fields from real image pairs are compared to ground-truth estimates of the velocity from satellite-tracked drifters in the eastern Gulf of Mexico. Results indicate the technique underestimates daily mean buoy vector speeds, but with reasonably good direction. The problems of ground truth relations to hierarchically computed flows are discussed with regard to mismatches of time and space scales of measurement

Earth Observatory Satellite system definition study. Report 5: System design and specifications. Volume 2: EOS-A system specification

The objectives of the Earth Observatory Satellite (EOS) program are defined. The system specifications for the satellite payload are examined. The broad objectives of the EOS-A program are as follows: (1) to develop space-borne sensors for the measurement of land resources, (2) to evolve spacecraft systems and subsystems which will permit earth observation with greater accuracy, coverage, spatial resolution, and continuity than existing systems, (3) to develop improved information processing, extraction, display, and distribution systems, and (4) to use space transportation systems for resupply and retrieval of the EOS

Simultaneous inversion of mantle properties and initial conditions using an adjoint of mantle convection

Through the assimilation of present-day mantle seismic structure, adjoint methods can be used to constrain the structure of the mantle at earlier times, i.e., mantle initial conditions. However, the application to geophysical problems is restricted through both the high computational expense from repeated iteration between forward and adjoint models and the need to know mantle properties (such as viscosity and the absolute magnitude of temperature or density) a priori. We propose that an optimal first guess to the initial condition can be obtained through a simple backward integration (SBI) of the governing equations, thus lessening the computational expense. Given a model with known mantle properties, we show that a solution based on an SBI-generated first guess has smaller residuals than arbitrary guesses. Mantle viscosity and the effective Rayleigh number are crucial for mantle convection models, neither of which is exactly known. We place additional constraints on these basic mantle properties when the convection-induced dynamic topography on Earth's surface is considered within an adjoint inverse method. Besides assimilating present-day seismic structure as a constraint, we use dynamic topography and its rate of change in an inverse method that allows simultaneous inversion of the absolute upper and lower mantle viscosities, scaling between seismic velocity and thermal anomalies, and initial condition. The theory is derived from the governing equations of mantle convection and validated by synthetic experiments for both one-layer viscosity and two-layer viscosity regionally bounded spherical shells. For the one-layer model, at any instant of time, the magnitude of dynamic topography is controlled by the temperature scaling while the rate of change of topography is controlled by the absolute value of viscosity. For the two-layer case, the rate of change of topography constrains upper mantle viscosity while the magnitude of dynamic topography determines the temperature scaling (lower mantle viscosity) when upper-mantle (lower-mantle) density anomaly dominates the flow field; this two-stage scheme minimizes the tradeoff between temperature and lower mantle viscosity. For both cases, we show that the theory can constrain mantle properties with errors arising through the adjoint recovery of the initial condition; for the two-layer model, this error is manifest as a tradeoff between the temperature scaling and lower mantle viscosity

Dynamic sea surface topography, gravity and improved orbit accuracies from the direct evaluation of SEASAT altimeter data

A method for the simultaneous solution of dynamic ocean topography, gravity and orbits using satellite altimeter data is described. A GEM-T1 based gravitational model called PGS-3337 that incorporates Seasat altimetry, surface gravimetry and satellite tracking data has been determined complete to degree and order 50. The altimeter data is utilized as a dynamic observation of the satellite's height above the sea surface with a degree 10 model of dynamic topography being recovered simultaneously with the orbit parameters, gravity and tidal terms in this model. PGS-3337 has a geoid uncertainty of 60 cm root-mean-square (RMS) globally, with the uncertainty over the altimeter tracked ocean being in the 25 cm range. Doppler determined orbits for Seasat, show large improvements, with the sub-30 cm radial accuracies being achieved. When altimeter data is used in orbit determination, radial orbital accuracies of 20 cm are achieved. The RMS of fit to the altimeter data directly gives 30 cm fits for Seasat when using PGS-3337 and its geoid and dynamic topography model. This performance level is two to three times better than that achieved with earlier Goddard earth models (GEM) using the dynamic topography from long-term oceanographic averages. The recovered dynamic topography reveals the global long wavelength circulation of the oceans with a resolution of 1500 km. The power in the dynamic topography recovery is now found to be closer to that of oceanographic studies than for previous satellite solutions. This is attributed primarily to the improved modeling of the geoid which has occurred. Study of the altimeter residuals reveals regions where tidal models are poor and sea state effects are major limitations

Current Status of Forecasting Toxic Harmful Algae for the North-East Atlantic Shellfish Aquaculture Industry

Across the European Atlantic Arc (Scotland, Ireland, England, France, Spain, and Portugal) the shellfish aquaculture industry is dominated by the production of mussels, followed by oysters and clams. A range of spatially and temporally variable harmful algal bloom species (HABs) impact the industry through their production of biotoxins that accumulate and concentrate in shellfish flesh, which negatively impact the health of consumers through consumption. Regulatory monitoring of harmful cells in the water column and toxin concentrations within shellfish flesh are currently the main means of warning of elevated toxin events in bivalves, with harvesting being suspended when toxicity is elevated above EU regulatory limits. However, while such an approach is generally successful in safeguarding human health, it does not provide the early warning that is needed to support business planning and harvesting by the aquaculture industry. To address this issue, a proliferation of web portals have been developed to make monitoring data widely accessible. These systems are now transitioning from “nowcasts” to operational Early Warning Systems (EWS) to better mitigate against HAB-generated harmful effects. To achieve this, EWS are incorporating a range of environmental data parameters and developing varied forecasting approaches. For example, EWS are increasingly utilizing satellite data and the results of oceanographic modeling to identify and predict the behavior of HABs. Modeling demonstrates that some HABs can be advected significant distances before impacting aquaculture sites. Traffic light indices are being developed to provide users with an easily interpreted assessment of HAB and biotoxin risk, and expert interpretation of these multiple data streams is being used to assess risk into the future. Proof-of-concept EWS are being developed to combine model information with in situ data, in some cases using machine learning-based approaches. This article: (1) reviews HAB and biotoxin issues relevant to shellfish aquaculture in the European Atlantic Arc (Scotland, Ireland, England, France, Spain, and Portugal; (2) evaluates the current status of HAB events and EWS in the region; and (3) evaluates the potential of further improving these EWS though multi-disciplinary approaches combining heterogeneous sources of information.Versión del edito