Toshio Mike Chin

Probabilistic and sequential computation of optical flow using temporal coherence

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.

A distributed and iterative method for square root filtering in space-time estimation

Abstract We describe a distributed and iterative approach to perform the unitary transformations in the square root information filter implementation of the Kalman filter, providing an alternative to the common QR factorization-based approaches. The new approach is useful in approximate computation of filtered estimates for temporally evolving random fields defined by local interactions and observations. Using several examples motivated by computer vision applications, we demonstrate that near-optimal estimates can be computed for problems of practical importance using only a small number of iterations, which can be performed in a finely parallel manner over the spatial domain of the random field.

Space-time interpolation of oceanic fronts

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.

Stochastic Petri net modeling of wave sequences in cardiac arrhythmias

We describe a methodology for modeling heart rhythms observed in electrocardiograms. In particular, we present a procedure to derive simple dynamic models that capture the cardiac mechanisms which control the particular timing sequences of P and R waves characteristic of different arrhythmias. By treating the cardiac electrophysiology at an aggregate level, simple network models of the wave generating system under a variety of diseased conditions can be developed. These network models are then systematically converted to stochastic Petri nets which offer a compact mathematical framework to express the dynamics and statistical variability of the wave generating mechanisms. Models of several arrhythmias are included in order to illustrate the methodology.

Variational approaches on discontinuity localization and field estimation in sea surface temperature and soil moisture

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.

Kalman filtering of large-scale geophysical flows by approximations based on Markov random field and wavelet

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.

Modeling of cardiac rhythms: A signal-processing perspective

The authors describe their perspective on the modeling of cardiac rhythms as a component of cardiac arrhythmia signal-processing algorithms. They emphasize that these models are for a specific end purpose and that the aspects of cardiac behavior that are captured by the models are only those relevant for the development of the signal-processing algorithms. The approach is to use statistics to describe ranges of cardiac behavior that share some common feature with respect to the purpose of the signal processing. The statistical approach has the advantage that, coupled with a statistical performance criterion, it specifies an optimal signal-processing algorithm. These optimal algorithms are often computationally intractable, however, especially for real-time use in instruments. Approximations are therefore crucial. The mathematical form of the model is then important since, even if two forms generate identical statistics, the approximations that are natural in different forms can be quite different. Two different mathematical formulations are described--stochastic Petri nets and interacting Markov chains--and the different types of approximately optimal signal-processing algorithms that are natural in these two frameworks are discussed.