Two-dimensional image motion is the projection of the three-dimensional motion of objects, relative to a visual sensor, onto its image plane. Sequences of time-ordered images allow the estimation of projected two-dimensional image motion as either instantaneous image velocities or discrete image displacements. These are usually called the optical flow field or the image velocity field. Provided that optical flow is a reliable approximation to two-dimensional image motion, it may then be used to recover the three-dimensional motion of the visual sensor (to within a scale factor) and the three-dimensional surface structure (shape or relative depth) through assumptions concerning the structure of the optical flow field, the three-dimensional environment and the motion of the sensor. Optical flow may also be used to perform motion detection, object segmentation, time-to-collision and focus of expansion calculations, motion compensated encoding and stereo disparity measurement. We investiga...

Absfruet-A 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 spatially-varying 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 ill-posed inverse problems in which variational techniques seeking a “smooth ” solution are generally Used. I.

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 two-sweep 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 ill-posed 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 1-D Markov processes and 2-D Markov random fields, and we propose a class of multiscale models for approximately representing Gaussian Markov random fields...

First, we examined a number of methods to perform forward and backward image reconstruction using optical flow. Given an image and its optical flow, we used these methods to generate the next image in the sequence. The RMS differences between the actual next images and their reconstructed versions for 3 synthetic image sequences, for which the correct flows were known, allowed us to determine which of our reconstruction methods performed their task well. Second, we examined the suitability of using good image reconstruction methods as an error metric for optical flow fields computed from image sequences for which the correct flow is unknown. Again, the RMS differences between the actual next images and their reconstructed versions, which were created using the flows computed by one of 4 well known optical flow methods, were recovered for both the set of synthetic and a set of 4 real image sequences. RMS error was found to be a good indicator of optical flow error for the better reconst...

. Retinal image motion and optical ow as its approximation are fundamental concepts in the eld of vision, perceptual and computational. However, the computation of optical ow remains a challenging problem as image motion includes discontinuities and multiple values mostly due to scene geometry, surface translucency and various photometric eects such as reectance. In this contribution, we analyze image motion in the frequency space with respect to motion discontinuities and translucence. We derive the frequency structure of motion discontinuities due to occlusion and we demonstrate its various geometrical properties. The aperture problem is investigated and we show that the information content of an occlusion almost always disambiguates the velocity of an occluding signal suering from the aperture problem. In addition, the theoretical framework can describe the exact frequency structure of Non-Fourier motion and bridges the gap between Non-Fourier visual phenomena and their understanding in the frequency domain. Keywords: Image motion, optical ow, occlusion, aperture problem, non-Fourier motion 1.

This paper presents new methods for use of dense motion fields for motion compensation of interlaced video. The motion is estimated using previously decoded field-images. An initial motion compensated prediction is produced using the assumption that the motion is predictable in time. The motion estimation algorithm is phase-based and uses two or three field-images to achieve motion estimates with sub-pixel accuracy. To handle non-constant motion and the specific characteristics of the field-image to be coded, the initially predicted image is refined using forward motion compensation, based on block-matching. Tests show that this approach achieves higher PSNR than forward block-based motion estimation, when coding the residual with the same coder. The subjective performance is also better. 1.

Retinal image motion and optical flow as its approximation are fundamental concepts in the field of vision, perceptual and computational. However, the computation of optical flow remains a challenging problem as image motion includes discontinuities and multiple values mostly due to scene geometry, surface translucency and various photometric effects such as surface reflectance. In this contribution, we analyze image motion in the frequency space with respect to motion discontinuities and surface translucence. We derive, under models of constant and linear optical flow, the frequency structure of motion discontinuities due to occlusion and we demonstrate its various geometrical properties. The aperture problem is investigated and we show that the information content of an occlusion almost always disambiguates the velocity of an occluding signal suffering from the aperture problem. In addition, the theoretical framework can describe the exact frequency structure of Non-Fourier motion an...

Currently existing subpixel motion estimation algorithms require interpolation of inter-pixel values which undesirably increases the overall complexity and data flow and deteriorates estimation accuracy. In this paper, we develop DCT-based techniques to estimate subpel motion at different desired subpel levels of accuracy in DCT domain without interpolation. We show that subpixel motion information is preserved in the DCT of a shifted signal under some condition in the form of pseudo phases and establish subpel sinusoidal orthogonal principles to extract this information. Though applicable to other areas as well, the resulted algorithms from these techniques for video coding are flexible and scalable in terms of estimation accuracy with very low computational complexity O(N 2 ) compared to O(N 4 ) for Full Search Block Matching Approach and its subpixel versions. Above all, motion estimation in DCT domain instead of spatial domain simplifies the conventional hybrid DCT-based video ...

This thesis is concerned primarily with the development of algorithms for estimating and segmenting image motion fields that contain discontinuities. An error-weighted regularization algorithm for image motion field estimation is proposed as a computationally attractive alternative to stochastic optimization based schemes. Block matching errors in the local motion measurement process are used in the regularization functional in order to avoid oversmoothing across motion boundaries. A second algorithm, anisotropic regularization, improves on the local measurement process, by employing alternative matching criteria and matching window organization. A selective confidence measure derived from anisotropic local measurements is used to further improve the error-weighted regularization.

Motion estimation is a common component of machine vision systems. Given the number of motion estimation algorithms available, selection of an appropriate algorithm is a difficult process. A quantitative measurement of the performance of motion estimation algorithms on real unlabelled data allows for more realistic comparison of motion estimation algorithms than the current situation. At present the most common measure of a motion estimation algorithm involves comparing a measured to a known motion field. Szeliski suggested treating motion estimation as a registration process. The motion between two successive images is computed and used to warp one of the images onto the other. The registration error is then used as a quantitative measure of the motion estimation algorithm. An extension to the Szeliski metric is examined. Examples will be shown where algorithms are selected and the tunable parameters are optimised for some test sequences. 1