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20
The Computation of Optical Flow
, 1995
"... Twodimensional image motion is the projection of the threedimensional motion of objects, relative to a visual sensor, onto its image plane. Sequences of timeordered images allow the estimation of projected twodimensional image motion as either instantaneous image velocities or discrete image dis ..."
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Cited by 292 (10 self)
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Twodimensional image motion is the projection of the threedimensional motion of objects, relative to a visual sensor, onto its image plane. Sequences of timeordered images allow the estimation of projected twodimensional 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 twodimensional image motion, it may then be used to recover the threedimensional motion of the visual sensor (to within a scale factor) and the threedimensional surface structure (shape or relative depth) through assumptions concerning the structure of the optical flow field, the threedimensional environment and the motion of the sensor. Optical flow may also be used to perform motion detection, object segmentation, timetocollision and focus of expansion calculations, motion compensated encoding and stereo disparity measurement. We investiga...
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 106 (36 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 34 (4 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...
Image Reconstruction Error for Optical Flow
 In Vision Interface
, 1994
"... 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 f ..."
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Cited by 11 (2 self)
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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...
On the Fourier Properties of Discontinuous Motion
 Journal of Mathematical Imaging and Vision
, 2000
"... . 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, surf ..."
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Cited by 10 (0 self)
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. 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 NonFourier motion and bridges the gap between NonFourier visual phenomena and their understanding in the frequency domain. Keywords: Image motion, optical ow, occlusion, aperture problem, nonFourier motion 1.
Interpolationfree subpixel motion estimation techniques in DCT domain
 IEEE Trans. Circuits and Systems for Video Technology
, 1998
"... Abstract — Currently existing subpixel motion estimation algorithms require interpolation of interpixel values which undesirably increases the overall complexity and data flow and deteriorates estimation accuracy. In this paper, we develop discrete cosine transform (DCT)based techniques to estimate ..."
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Cited by 5 (1 self)
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Abstract — Currently existing subpixel motion estimation algorithms require interpolation of interpixel values which undesirably increases the overall complexity and data flow and deteriorates estimation accuracy. In this paper, we develop discrete cosine transform (DCT)based techniques to estimate subpel motion at different desired subpel levels of accuracy in the 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 pseudophases, and we establish subpel sinusoidal orthogonal principles to extract this information. The proposed subpixel techniques are flexible and scalable in terms of estimation accuracy with very low computational complexity O(N 2) compared to O(N 4) for the fullsearch blockmatching approach and its subpixel versions. Above all, motion estimation in the DCT domain instead of the spatial domain simplifies the conventional hybrid DCTbased video coder, especially the heavily loaded feedback loop in the conventional design, resulting in a fully DCTbased highthroughput video codec. In addition, the computation of pseudophases is local, and thus a highly parallel architecture is feasible for the DCTbased algorithms. Finally, simulation on video sequences of different characteristics shows comparable performance of the proposed algorithms to blockmatching approaches. Index Terms—Motion estimation, shift measurement, subpixel accuracy, video coding, video compression. I.
Backwardforward motion compensated prediction
 in: Advanced Concepts for Intelligent Vision Systems (ACIVS’02
, 2002
"... This paper presents new methods for use of dense motion fields for motion compensation of interlaced video. The motion is estimated using previously decoded fieldimages. An initial motion compensated prediction is produced using the assumption that the motion is predictable in time. The motion esti ..."
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Cited by 4 (3 self)
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This paper presents new methods for use of dense motion fields for motion compensation of interlaced video. The motion is estimated using previously decoded fieldimages. An initial motion compensated prediction is produced using the assumption that the motion is predictable in time. The motion estimation algorithm is phasebased and uses two or three fieldimages to achieve motion estimates with subpixel accuracy. To handle nonconstant motion and the specific characteristics of the fieldimage to be coded, the initially predicted image is refined using forward motion compensation, based on blockmatching. Tests show that this approach achieves higher PSNR than forward blockbased motion estimation, when coding the residual with the same coder. The subjective performance is also better. 1.
On the Fourier Properties of Discontinuous Visual Motion
 Journal of Mathematical Imaging and Vision
, 2000
"... 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, ..."
Abstract

Cited by 4 (1 self)
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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 NonFourier motion an...
A Theoretical Framework for Discontinuous Visual Motion
"... 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, ..."
Abstract
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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. In addition, 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. We conclude by showing that additive translucency phenomena may be reduced to special cases o...