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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 99 (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...
3D Kalman Filter for Image Motion Estimation
 IEEE Trans. Image Processing
, 1998
"... This paper presents a new 3D Markov model for motion vector fields. The three dimensions consist of the two space dimensions plus a scale dimension. We use a compound signal model to handle motion discontinuity in this 3D Markov random field. For motion estimation, we use an extended Kalman filter ..."
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Cited by 5 (1 self)
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This paper presents a new 3D Markov model for motion vector fields. The three dimensions consist of the two space dimensions plus a scale dimension. We use a compound signal model to handle motion discontinuity in this 3D Markov random field. For motion estimation, we use an extended Kalman filter as a pelrecursive estimator. Since a single observation can be sensitive to local image characteristics, especially the model is not accurate, we employ windowed multiple observations at each pixel to increase accuracy. These multiple observations employ different weighting values for each observation, since the uncertainty in each observation is different. Finally, we compare this 3D model with earlier proposed 1D (coarsetofine scale) and 2D spatial compound models, in terms of motion estimation performance on a synthetic and a real image sequence. Keywords 3D Markov random field, pelrecursive motion estimation, extended Kalman filter, multiscale, compound model, multiple obser...
Dynamical Systems and Motion Vision
, 1988
"... In this paper we show how the theory of dynamical systems can be employed to solve problems in motion vision. In particular we develop algorithms for recovery of dense depth maps and motion parameters using state space observers or filters. We begin with a review of previous, related work followe ..."
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Cited by 4 (0 self)
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In this paper we show how the theory of dynamical systems can be employed to solve problems in motion vision. In particular we develop algorithms for recovery of dense depth maps and motion parameters using state space observers or filters. We begin with a review of previous, related work followed by n overview of relevant aspects of the theory of dynamical systems. Three dynamical models of the imaging situation are presented: In the first model we assume that motion is known and a reflectance model for the surface is given. Depth is recovered directly from brightness measurements with nonlinear Kalman filter.