Some applications in remote sensing require estimating a field containing a discontinuity whose exact location is a priori unknown. Such fields of interest include sea surface temperature in oceanography and soil moisture in hydrology. For the former, oceanic fronts form a temperature discontinuity, while in the latter sharp changes exist across the interface between soil types. To complicate the estimation process, remotely sensed measurements often exhibit regions of missing observations due to occlusions such as cloud cover. Similarly, water surface and ground-based sensors usually provide only an incomplete set of measurements. Traditional methods of interpolation and smoothing for estimating the fields from such potentially sparse measurements often blur across the discontinuities in the field.

The approximate Kalman filtering algorithm presented previously (see ibid., vol.3, p.773-88, Nov. 1994) for image sequence processing can introduce unacceptable negative eigenvalues in the information matrix and can have degraded performance in some applications. The improved algorithm presented in this note guarantees a positive definite information matrix, leading to more stable filter performance.

Oceanic temperature fronts observed through composite infrared images from the AVHRR satellite data are fragmented due mostly to cloud occlusion. The sampling frequency of such frontal position observations tends to be insufficiently high to resolve dynamics of the meandering features associated with the frontal contour, so that contour reconstruction using a standard space-time smoothing often leads to introduction of spurious features. Augmenting space-time smoothing with a simple point-feature detection/matching scheme, however, can dramatically improve the reconstruction product. This paper presents such a motion-compensated interpolation algorithm, for reconstruction of open contours evolving in time given fragmented position data. The reconstruction task is formulated as an optimization problem, and a time-sequential solution which adaptively estimates feature motion is provided. The resulting algorithm reliably interpolates position measurements of the surface temperature fronts associated with the highly convoluted portions of strong ocean currents such as the Gulf Stream and Kuroshio.

Large-scale extended Kalman filters for atmospheric and oceanic circulation models can readily be approximated using a wavelet transform or a Markov random field model. For a filtering problem where the unknown field of the state variables is highly correlated and the observations are relatively sparse, the wavelet-approximated filter seems more appropriate. For a problem in which the covariance matrix is non-singular and where a relatively large quantity of independent observations are processed, the MRF-approximated filter seems more appropriate.

In the computation of dense optical flow fields, spatial coherence constraints are commonly used to regularize otherwise ill-posed problem formulations, providing spatial integration of data. We present a temporal, multiframe extension of the dense optical flow estimation formulation proposed by Horn and Schunck (1981) in which we use a temporal coherence constraint to yield the optimal fusing of data from multiple frames of measurements. Conceptually, standard Kalman filtering algorithms are applicable to the resulting multiframe optical flow estimation problem, providing a solution that is sequential and recursive in time. Experiments are presented to demonstrate that the resulting multiframe estimates are more robust to noise than those provided by the original, single-frame formulation. In addition, we demonstrate cases where the aperture problem of motion vision cannot be resolved satisfactorily without the temporal integration of data enabled by the proposed formulation. Practically, the large matrix dimensions involved in the problem prohibit exact implementation of the optimal Kalman filter. To overcome this limitation, we present a computationally efficient, yet near-optimal approximation of the exact filtering algorithm. This approximation has a precise interpretation as the sequential estimation of a reduced-order spatial model for the optical flow estimation error process at each time step and arises from an estimation-theoretic treatment of the filtering problem. Experiments also demonstrate the efficacy of this near-optimal filter.