Motion estimation from noisy image data

1904

In this paper a new algorithm to estimate dense displacement fields from a sequence of images is developed. The algorithm is based on modeling the displacement fields as Markov Random fields. The Markov Random fields-Gibbs equivalence is then used to convert the problem into one of finding an appropriate energy function that describes the motion and any constraints imposed on it. Mean field annealing, a technique which finds global minima in nonconvex optimization problems, is used to minimize the energy function, and solve for the optimum displacement fields. The algorithm results in accurate estimates even for scenes with noise or discontinuities.

Image Modeling, 1993

In this paper a new algorithm to estimate dense displacement fields from a sequence of images is developed. The algorithm is based on modeling the displacement fields as Markov Random fields. The Markov Random fields-Gibbs equivalence is then used to convert the problem into one of finding an appropriate energy function that describes the motion and any constraints imposed on it. Mean field annealing, a technique which finds global minima in nonconvex optimization problems, is used to minimize the energy function, and solve for the optimum displacement fields. The algorithm results in accurate estimates even for scenes with noise or discontinuities.

  Motion estimation can be formulated and solved as a Bayesian estimation problem. Bayesian estimation requires two probability density function models: observation model and motion field model. The optimization process for this method uses sequential approach, such as simulated annealing, iterated conditional mode, mean field annealing, and highest confidence first. In order to increase the speed of computation and to improve the result, we proposed a combination of the spatial and multiscale Markov random field modeling. The proposed framework can be used as an input to the Bayesian motion estimation. Results indicated one of the possible utilization of our strategy for Bayesian estimation method. Moreover, other strategies can be derived from our method.

1996 8th European Signal Processing Conference (EUSIPCO 1996), 1996

The 2D Markov Random Field (MRF) model, combined with the Bayesian estimation framework, has proved to be an efficient and reliable computing tool to the optical flow estimation problem. Specifically, we are investigating the multimodal approach, where complementary constraints are imposed on the optical flow model. However, this approach suffers from expensive computational requirements, which is the direct consequence of the large dimensions of the optimization problem. Recently, a deterministic optimization technique, namely the mean field approximation has been proposed, which not only provides satisfactory estimation result, but also reduces the computational cost drastically. Here we apply this new technique to the above mentioned multimodal motion estimation problem.

IEEE Transactions on Circuits and Systems for Video Technology, 1999

This paper presents a two-pass algorithm for estimating motion vectors from image sequences. In the proposed algorithm, the motion estimation is formulated as a problem of obtaining the maximum a posteriori in the Markov random field (MAP-MRF). An optimization method based on the mean field theory (MFT) is opted to conduct the MAP search. The estimation of motion vectors is modeled by only two MRF's, namely, the motion vector field and unpredictable field. Instead of utilizing the line field, a truncation function is introduced to handle the discontinuity between the motion vectors on neighboring sites. In this algorithm, a "double threshold" preprocessing pass is first employed to partition the sites into three regions, whereby the ensuing MFT-based pass for each MRF is conducted on one or two of the three regions. With this algorithm, no significant difference exists between the block-based and pixel-based MAP searches any more. Consequently, a good compromise between precision and efficiency can be struck with ease. To render our algorithm more resilient against noises, the mean absolute difference instead of mean square error is selected as the measure of difference, which is more reliable according to the knowledge of robust statistics. This is supported by our experimental results from both synthetic and real-world image sequences. The proposed two-pass algorithm is much faster than any other MAP-MRF motion estimation method reported in the literature so far.

1990

The estimation of 2D motion from spatio-temporally sampled image sequences is discussed, concentrating on the optimization aspect of the problem formulated through a Bayesian framework based on Markov random field (MRF) models. First, the Maximum A Posteriori Probability (MAP) formulation for motion estimation over discrete and continuous state spaces is reviewed along with the solution method using simulated annealing (SA). Then, instantaneous 'freezing' is applied to ,the stochastic algorithms resulting in well known deterministic methods. The stochastic algorithms are compared with their deterministic approximations over image sequences with natural data and synthetic as well as natural motion.

Image and Vision Computing, 1991

The estimation of 2D motion from spatio-temporally sampled image sequences is discussed, concentrating on the optimization aspect of the problem formulated through a Bayesian framework based on Markov random field (MRF) models. First, the Maximum A Posteriori Probability (MAP) formulation for motion estimation over discrete and continuous state spaces is reviewed along with the solution method using simulated annealing (SA). Then, instantaneous 'freezing' is applied to ,the stochastic algorithms resulting in well known deterministic methods. The stochastic algorithms are compared with their deterministic approximations over image sequences with natural data and synthetic as well as natural motion.

IEEE Transactions on Pattern Analysis and Machine Intelligence, 1993

The existing linear algorithms exhibit various high sensitivities to noise. The analysis presented in this paper provides insight into the causes for such high sensitivities. It is shown in this paper that even a small pixel-level perturbation may override the epipolar information that is essential for the linear algorithms to distinguish different motions. This analysis indicates the need for optimal estimation in the presence of noise. Then, we introduce methods for optimal motion and structure estimation under two situations of noise distribution: 1) known and 2) unknown. Computationally, the optimal estimation amounts to minimizing a nonlinear function. For the correct convergence of this nonlinear minimization, we use a two-step approach. The first step is using a linear algorithm to give a preliminary estimate for the parameters. The second step is minimizing the optimal objective function starting from that preliminary estimate as an initial guess. A remarkable accuracy improvement has been achieved by this two-step approach over using the linear algorithm alone. In order to assess the accuracy of the optimal solution, the error in the solution of the optimal estimation algorithm is compared with a theoretical lower error bound-CramCr-Rao bound. The simulations have shown that with Gaussian noise added to the coordinates of the image points, the actual error in the optimal solution is very close to the bound. In addition, we also use the CramCr-Rao bound to indicate the inherent instability of motion estimation from small image disparities, such as motion from optical flow. Finally, it is known that given the same nonlinear objective function and the same initial guess, different minimization methods may lead to different solutions. We investigate the performance difference between a batch least-squares technique (Levenberg-Marquardt) and a sequential least-squares technique (iterated extended Kalman filter) for this motion estimation problem, and the simulations showed that the former gives better results.

ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing, 1988

An orithm is presented for smoothadditive noise. Main feature is the combination of Markov k d o m Field (MRF) models, with Kalman Filtering (KF) techniques and Dynamic Programming (DP) in order to smooth and segment the data within the regions of stationarity without affecting the edges. Applications to one dimensional and two dimensional data are given, with particular emphasis on the segmentation of multiregion images.

1992

Abstract-This paper presents a new approach to the estimation of 2-D motion vector fields from time-varying 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 vector-binary Markov random fields.