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Efficient multiscale regularization with applications to the computation of optical flow
 IEEE Trans. Image Process
, 1994
"... AbsfruetA new approach to regularization methods for image processing is introduced and developed using as a vehicle the problem of computing dense optical flow fields in an image sequence. Standard formulations of this problem require the computationally intensive solution of an elliptic partial d ..."
Abstract

Cited by 98 (33 self)
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AbsfruetA new approach to regularization methods for image processing is introduced and developed using as a vehicle the problem of computing dense optical flow fields in an image sequence. Standard formulations of this problem require the computationally intensive solution of an elliptic partial differential equation that arises from the often used “smoothness constraint” ’yl”. regularization. The interpretation of the smoothness constraint is utilized as a “fractal prior ” to motivate regularization based on a recently introduced class of multiscale stochastic models. The solution of the new problem formulation is computed with an efficient multiscale algorithm. Experiments on several image sequences demonstrate the substantial computational savings that can be achieved due to the fact that the algorithm is noniterative and in fact has a per pixel computational complexity that is independent of image size. The new approach also has a number of other important advantages. Specifically, multiresolution flow field estimates are available, allowing great flexibility in dealing with the tradeoff between resolution and accuracy. Multiscale error covariance information is also available, which is of considerable use in assessing the accuracy of the estimates. In particular, these error statistics can be used as the basis for a rational procedure for determining the spatiallyvarying optimal reconstruction resolution. Furthermore, if there are compelling reasons to insist upon a standard smoothness constraint, our algorithm provides an excellent initialization for the iterative algorithms associated with the smoothness constraint problem formulation. Finally, the usefulness of our approach should extend to a wide variety of illposed inverse problems in which variational techniques seeking a “smooth ” solution are generally Used. I.
Image Processing with Multiscale Stochastic Models
, 1993
"... In this thesis, we develop image processing algorithms and applications for a particular class of multiscale stochastic models. First, we provide background on the model class, including a discussion of its relationship to wavelet transforms and the details of a twosweep algorithm for estimation. A ..."
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Cited by 29 (3 self)
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In this thesis, we develop image processing algorithms and applications for a particular class of multiscale stochastic models. First, we provide background on the model class, including a discussion of its relationship to wavelet transforms and the details of a twosweep algorithm for estimation. A multiscale model for the error process associated with this algorithm is derived. Next, we illustrate how the multiscale models can be used in the context of regularizing illposed inverse problems and demonstrate the substantial computational savings that such an approach offers. Several novel features of the approach are developed including a technique for choosing the optimal resolution at which to recover the object of interest. Next, we show that this class of models contains other widely used classes of statistical models including 1D Markov processes and 2D Markov random fields, and we propose a class of multiscale models for approximately representing Gaussian Markov random fields...
Sequential filtering for multiframe visual reconstruction
, 1992
"... We describe an extension of the singleframe visual field reconstruction problem in which we consider how to efficiently and optimally fuse multiple frames of measurements obtained from images arriving sequentially over time. Specifically we extend the notion of spatial coherence constraints, used t ..."
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Cited by 23 (7 self)
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We describe an extension of the singleframe visual field reconstruction problem in which we consider how to efficiently and optimally fuse multiple frames of measurements obtained from images arriving sequentially over time. Specifically we extend the notion of spatial coherence constraints, used to regularize singleframe problems, to the time axis yielding temporal coherence constraints. An information form variant of the Kalman filter is presented which yields the optimal maximum likelihood estimate of the field at each time instant and is tailored to the visual field reconstruction problem. Propagation and even storage of the optimal information matrices for visual problems is prohibitive, however, since their size is on the order of 104 x 104 to 106 x 106. To cope with this dimensionality problem a practical yet nearoptimal filter is presented. The key to this solution is the observation that the information matrix, i.e. the inverse of the covariance matrix, of a vector of samples of a spatially distributed process may be precisely interpreted as specifying a Markov random field model for the estimation error process. This insight leads directly to the idea of obtaining loworder approximate models for the estimation error in a recursive filter through the recursive approximation of the information matrix by an appropriate sparse, spatially localized matrix. Numerical experiments are presented to demonstrate the efficacy of the proposed filter and approximations.
A Distributed and Iterative Method for Square Root Filtering in SpaceTime Estimation
 AUTOMATICA
, 1995
"... An efficient, approximate algorithm for square root Kalman filter is presented. Largescale, spacetime estimation can be performed sequentially over time by spatially distributed and local computation. ..."
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Cited by 6 (2 self)
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An efficient, approximate algorithm for square root Kalman filter is presented. Largescale, spacetime estimation can be performed sequentially over time by spatially distributed and local computation.