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14
Bayesian Estimation Of Motion Vector Fields
 IEEE Trans. Pattern Anal. Machine Intell
, 1992
"... This paper presents a new approach to the estimation of twodimensional motion vector fields from timevarying images. The approach is stochastic, both in its formulation and in the solution method. The formulation involves the specification of a deterministic structural model, along with stochastic ..."
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Cited by 130 (19 self)
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This paper presents a new approach to the estimation of twodimensional motion vector fields from timevarying images. The approach is stochastic, both in its formulation and in the solution method. The formulation involves the specification of a deterministic structural model, along with stochastic observation and motion field models. Two motion models are proposed: a globally smooth model based on vector Markov random fields and a piecewise smooth model derived from coupled vectorbinary Markov random fields. Two estimation criteria are studied. In the Maximum A Posteriori Probability (MAP) estimation the a posteriori probability of motion given data is maximized, while in the Minimum Expected Cost (MEC) estimation the expectation of a certain cost function is minimized. The MAP estimation is performed via simulated annealing, while the MEC algorithm performs iterationwise averaging. Both algorithms generate sample fields by means of stochastic relaxation implemented via the Gibbs s...
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 ..."
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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.
Motion Estimation Using a ComplexValued Wavelet Transform
, 1998
"... This paper describes a new motion estimation algorithm which is potentially useful for both computer vision and video compression applications. It is hierarchical in structure, using a separable 2d Discrete Wavelet Transform (DWT) on each frame to efficiently construct a multiresolution pyramid of ..."
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Cited by 52 (7 self)
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This paper describes a new motion estimation algorithm which is potentially useful for both computer vision and video compression applications. It is hierarchical in structure, using a separable 2d Discrete Wavelet Transform (DWT) on each frame to efficiently construct a multiresolution pyramid of subimages. The DWT is based on a complexvalued pair of 4tap FIR filters with Gaborlike characteristics. The resulting Complex DWT (CDWT) effectively implements an analysis by an ensemble of Gaborlike filters with a variety of orientations and scales. The phase difference between the subband coefficients of each frame at a given subpel bears a predictable relation to a local translation in the region of the reference frame subtended by that subpel. That relation is used to estimate the displacement field at the coarsest scale of the multiresolution pyramid. Each estimate is accompanied by a directional confidence measure in the form of the parameters of a quadratic matching surface. The i...
Estimating Motion in Image Sequences  A tutorial on modeling and computation of 2D motion
 IEEE Signal Processing Magazine
, 1999
"... this paper should be helpful to researchers and practitioners working in the fields of video compression and processing, as well as in computer vision. Although the understanding of issues involved in the computation of motion has significantly increased over the last decade, we are still far from g ..."
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Cited by 43 (0 self)
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this paper should be helpful to researchers and practitioners working in the fields of video compression and processing, as well as in computer vision. Although the understanding of issues involved in the computation of motion has significantly increased over the last decade, we are still far from generic, robust, realtime motion estimation algorithms. The selection of the best motion estimator is still highly dependent on the application. Nevertheless, a broad variety of estimation models, criteria and optimization schemes can be treated in a unified framework presented here, thus allowing a direct comparison and leading to a deeper understanding of the properties of the resulting estimators.
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 30 (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...
J: Estimation of 2D motion fields from image sequences with application to motioncompensated processing
 In Motion Analysis and Image Sequence Processing Edited by: Lagendijk MISRL
"... c ○ 1993 Kluwer Academic Publishers. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component ..."
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Cited by 29 (12 self)
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c ○ 1993 Kluwer Academic Publishers. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the Kluwer Academic Publishers. 3
Estimation of Accelerated Motion and Occlusions from TimeVarying Images
, 1994
"... This thesis addresses the problem of modeling and computing dense 2D velocity and acceleration fields from timevarying images and applying them to motioncompensated interpolation. Unlike in many other approaches that assume motion to be locally translational, the approach proposed here uses a quad ..."
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Cited by 3 (2 self)
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This thesis addresses the problem of modeling and computing dense 2D velocity and acceleration fields from timevarying images and applying them to motioncompensated interpolation. Unlike in many other approaches that assume motion to be locally translational, the approach proposed here uses a quadratic motion trajectory model that incorporates both velocity and acceleration. This model corresponds better to natural image sequences especially when processing over multiple frames is considered. One of the advantages of using accelerated motion over linear trajectories is in motioncompensated processing over multiple images. This is due to the fact that over longer time frame, a quadratic motion model is capable of providing a better intensity match along trajectories than the linear model. The side effect is, however, that with more images used for estimation occlusion effects play a more dominant role. Therefore, another motion model is proposed to account for occlusions and motion d...
Use of Colour in GradientBased Estimation of Dense TwoDimensional Motion
 in Proc. Conf. Vision Interface VI'92
, 1992
"... This chapter presents a gradientbased approach to the multiconstraint estimation of dense twodimensional (2D) motion. The formulation is based on two assumptions: that at least one feature exists that is constant along motion trajectories and that motion vectors are smooth functions of spatial c ..."
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Cited by 2 (1 self)
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This chapter presents a gradientbased approach to the multiconstraint estimation of dense twodimensional (2D) motion. The formulation is based on two assumptions: that at least one feature exists that is constant along motion trajectories and that motion vectors are smooth functions of spatial coordinates. From these assumptions matching and smoothness errors are derived and combined to obtain a cost function. The cost function is minimized using a sequence of quadratic approximations of the matching error and solving the resulting linear system by deterministic relaxation. The structural model used (relating the motion vectors and data) permits the use of multiple image features as the input, for example intensity and colours, or subbands of a spectral decomposition. The motion model reduces illposedness of the problem through a smoothness constraint. The proposed algorithm is a generalization of the Horn and Schunck algorithm [5] to the case of vector data. Results of applicat...
On GibbsMarkov Models for Motion Computation
, 1997
"... In this chapter we present GibbsMarkov models for 2D motion in the context of their application to video coding and processing. We study nonlinear trajectory model that incorporates both velocity and acceleration. Although the maximum a posteriori probability criterion is the preferred choice for ..."
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Cited by 1 (0 self)
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In this chapter we present GibbsMarkov models for 2D motion in the context of their application to video coding and processing. We study nonlinear trajectory model that incorporates both velocity and acceleration. Although the maximum a posteriori probability criterion is the preferred choice for most motion estimation algorithms based on GibbsMarkov models, we discuss the more general Bayesian criterion, including the merits of several loss functions. We describe various models for the likelihood and prior probability distributions, but we concentrate on pixel, block and regionbased motion models. We propose a new motion model that incorporates acceleration into the affine model. This contribution is mainly theoretical, however we present some experimental results to underline essential differences between models discussed.
Bayesian Estima tion of Mo tion Vector F ields
"... AbstractThis paper presents a new approach to the estimation of 2D motion vector fields from timevarying images. The approach is stochastic both in its formulation and in the solution method. The formulation involves the specification of a deterministic structural model along ivith stochastic ob ..."
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AbstractThis paper presents a new approach to the estimation of 2D motion vector fields from timevarying images. The approach is stochastic both in its formulation and in the solution method. The formulation involves the specification of a deterministic structural model along ivith stochastic observation and motion field models. Two motion models are proposed: a globally smooth model based on vector Markov random fields and a piecewise smooth model derived from coupled vectorbinary Markov random fields. Two estimation criteria are studied. In the max imum a posteriori probability (MAP) estimation, the a posteriori probability of motion given data is maximized, whereas in the min imum expected cost (MEC) estimation, the expectation of a certain cost function is minimized. The MAP estimation is performed via simulated annealing, whereas the MEC algorithm performs iterationwise averaging. Both algorithms generate sample fields by means of stochustic relaxation implemented via the Gibbs sampler. Two versions are developed: one for a discrete state space and the other for a continuous state space. The MAP estimation is incorporated into a hierarchical environment to deal efficiently with large displacements. Numerous experimental results of application of these algorithms to natural and computergenerated images with natural and synthetic motion are shown. Index Terms Bayesian estimation, Markov random fields, motion estimation, motion modeling, optical flow, simulated annealing, stochastic relaxation, 2D motion. I.