Nonlinear inverse model for velocity estimation from an image sequence

Abstract

[1] Velocity estimation from an image sequence is one of the most challenging inverse problems in computer vision, geosciences, and remote sensing applications. In this paper a nonlinear model has been created for estimating motion field under the constraint of conservation of intensity. A linear differential form of heat or optical flow equation is replaced by a nonlinear temporal integral form of the intensity conservation constraint equation. Iterative equations with Gauss-Newton and Levenberg-Marguardt algorithms are formulated based on the nonlinear equations, velocity field modeling, and a nonlinear least squares model. An algorithm with progressive relaxation of the overconstraint to improve the performance of the velocity estimation is also proposed. The new estimator is benchmarked using a numerical simulation model. Both angular and magnitude error measurements based on the synthetic surface heat flow from the numerical model demonstrate that the performance of the new approach with the nonlinear model is much better than the results of using a linear model of heat or optical flow equation. Four sequences of NOAA Advanced Very High Resolution Radiometer (AVHRR) images taken in the New York Bight fields is also used to demonstrate the performance of the nonlinear inverse model, and the estimated velocity fields are compared with those measured with the Coastal Ocean Dynamics Radar array. The experimental results indicate that the nonlinear inverse model provides significant improvement over the linear inverse model for real AVHRR data sets.

River velocities from sequential multispectral remote sensing images

“…The tracer conservation equation [ Chen , ], where T ( r , t ) is the temperature or tracer intensity with regard to the x and y coordinates, and time t . The velocity is defined by v = v ( x, y, t ) = ( u , v ) T .…”

“…In fact, such nonlinear solutions have been derived for tracers from a numerical model and from SST image sequences in the New York Bight [ Chen , ], and their validity is established by comparing the resulting velocity vectors with those from a numerical model and the velocity maps from the Rutgers CODAR array [ Chen , ]. Moreover, the errors for the retrieved velocity magnitude and angle are only half of the values for the linear GOS [ Chen , ].…”

Bathymetrically controlled velocity‐shear front at a tidal river confluence

“…Later, the approach was expanded to encompass the use of multiple tracers [ Chen et al ., ]. In this work, we use the latest development, which is based on the nonlinear tracer conservation equation and the use of multiple tracers [ Chen , ; Chen and Mied , ]. The method produces a velocity field valid across the entire image by minimizing a cost function derived from the conservation constraint equations for multiple tracers.…”

Reconstructing Large- and Mesoscale Dynamics in the Black Sea Region from Satellite Imagery and Altimetry Data—A Comparison of Two Methods

“…In Section 3.7 we use satellite imagery with 250 m resolution to obtain basin-scale surface currents in the small and enclosed Marmara Sea, where mapped altimetry measurements are unavailable. The Marmara Sea is the first connecting link between the Black Sea and the Atlantic Ocean and its circulation is of importance for the interbasin exchange through the Bosphorus strait [8,14,[59][60][61][62][63][64]. Observation-based data on the surface currents obtained using 4D-Var assimilation of satellite imagery give the possibility of reconstructing complex mesoscale and sub-mesoscale dynamics in the Marmara Sea.…”