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44
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 218 (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 98 (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.
Estimation of 3D left ventricular deformation from echocardiography,” Med
 Image Anal
, 2001
"... Abstract—The quantitative estimation of regional cardiac deformation from threedimensional (3D) image sequences has important clinical implications for the assessment of viability in the heart wall. We present here a generic methodology for estimating soft tissue deformation which integrates image ..."
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Cited by 44 (5 self)
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Abstract—The quantitative estimation of regional cardiac deformation from threedimensional (3D) image sequences has important clinical implications for the assessment of viability in the heart wall. We present here a generic methodology for estimating soft tissue deformation which integrates imagederived information with biomechanical models, and apply it to the problem of cardiac deformation estimation. The method is image modality independent. The images are segmented interactively and then initial correspondence is established using a shapetracking approach. A dense motion field is then estimated using a transversely isotropic, linearelastic model, which accounts for the muscle fiber directions in the left ventricle. The dense motion field is in turn used to calculate the deformation of the heart wall in terms of strain in cardiac specific directions. The strains obtained using this approach in openchest dogs before and after coronary occlusion, exhibit a high correlation with strains produced in the same animals using implanted markers. Further, they show good agreement with previously published results in the literature. This proposed method provides quantitative regional 3D estimates of heart deformation. Index Terms—Cardiac deformation, left ventricular motion estimation, magnetic resonance imaging, nonrigid motion estimation, validation. 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...
On Variable Brightness Optical Flow For Tagged MRI
 IN INFORMATION PROCESSING IN MEDICAL IMAGING
, 1995
"... The problem of computing velocity fields from tagged MR images is considered, with particular attention paid to the image brightness changes caused by tag pattern fading with time. Shortcomings of existing optical flow methods for this application are pointed out and Gennert and Negahdaripour's opt ..."
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Cited by 27 (4 self)
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The problem of computing velocity fields from tagged MR images is considered, with particular attention paid to the image brightness changes caused by tag pattern fading with time. Shortcomings of existing optical flow methods for this application are pointed out and Gennert and Negahdaripour's optical flow method is discussed. This method involves estimation of a local brightness transformation field in addition to the velocity field. Approximations for these transformations are developed, leading to a faster algorithm which does not require careful selection of the regularization coefficients. This method is validated by tests on both simulated and actual MR data, and is demonstrated to be computationally robust to inaccurate knowledge of MR parameters.
Deformable BSolids and Implicit Snakes for 3D Localization and Tracking of SPAMM MRIData
"... To date, MRISPAMM data from different image slices have been analyzed independently. In this paper, we propose an approach for 3D tag localization and tracking of SPAMM data by a novel deformable Bsolid. The solid is defined in terms of a 3D tensor product Bspline. The isoparametric curves of th ..."
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Cited by 24 (9 self)
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To date, MRISPAMM data from different image slices have been analyzed independently. In this paper, we propose an approach for 3D tag localization and tracking of SPAMM data by a novel deformable Bsolid. The solid is defined in terms of a 3D tensor product Bspline. The isoparametric curves of the Bspline solid have special importance. These are termed implicit snakes as they deform under image forces from tag lines in different image slices. The localization and tracking of tag lines is performed under constraints of continuity and smoothness of the Bsolid. To track motion from boundaries and restrict image forces to the myocardium, a volumetric model is employed as a pair of coupled endocardial and epicardial Bspline surfaces. To recover deformations of the Left Ventricle (LV) an energyminimization problem is posed where both tag and LV boundary data are used. The framework has been implemented on tag data from Short Axis (SA) cardiac images, as well as SA LV boundaries, and i...
3D cardiac deformation from ultrasound images
 in Medical Image Computing and Computer Aided Intervention (MICCAI
, 1999
"... Abstract. The quantitative estimation of regional cardiac deformation from 3D image sequences has important clinical implications for the assessment of viability in the heart wall. Such estimates have so far been obtained almost exclusively from Magnetic Resonance (MR) images, specifically MR taggin ..."
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Cited by 20 (4 self)
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Abstract. The quantitative estimation of regional cardiac deformation from 3D image sequences has important clinical implications for the assessment of viability in the heart wall. Such estimates have so far been obtained almost exclusively from Magnetic Resonance (MR) images, specifically MR tagging. In this paper we describe a methodology for estimating cardiac deformations from 3D ultrasound images. The images are segmented interactively and then initial correspondence is established using a shapetracking approach. A dense motion field is then estimated using an anisotropic linear elastic model, which accounts for the fiber directions in the leftventricle. The dense motion field is in turn used to calculate the deformation of the heart wall in terms of strain in cardiac specific directions. The strains obtained using this approach in openchest dogs before and after coronary occlusion related to changes in blood flow, show good agreement with previously published results in the literature. This proposed method provides quantitative regional 3D estimates of heart deformation from ultrasound images. 1
Cardiac Motion Simulator for Tagged MRI
 Proceedings of MMBIA
, 1996
"... This paper describes a computational simulator for use in cardiac imaging using tagged magnetic resonance imaging. The simulator incorporates a 13parameter model of leftventricular motion due to Arts et al. (1992) and applies it to a confocal prolate spherical shell, resembling the shape of the le ..."
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Cited by 18 (4 self)
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This paper describes a computational simulator for use in cardiac imaging using tagged magnetic resonance imaging. The simulator incorporates a 13parameter model of leftventricular motion due to Arts et al. (1992) and applies it to a confocal prolate spherical shell, resembling the shape of the left ventricle. Using parameters determined in other work, our model can be made to assume a configuration representing one of 60 phases in the cardiac cycle. In this paper, we determine the inverse motion map analytically, allowing pointwise correspondences to be made between two points at any two times. Using this mathematical relationship, we simulate the (tagged) magnetic resonance imaging process using a standard (tagged) spinecho imaging equation. Image sequences can be synthesized at arbitrary orientations at any phase. We currently synthesize a SPAMM tag pattern with arbitrary spatial frequency, but other patterns can be readily incorporated. To accommodate twodimensional motion esti...
Probabilistic and Sequential Computation of Optical Flow Using Temporal Coherence
 IEEE Transactions on Image Processing
, 1994
"... Abstruct In the computation of dense optical flow fields, spatial coherence constraints are commonly used to regularize otherwise illposed problem formulations, providing spatial integration of data. In this paper, we present a temporal, multiframe extension of the dense optical flow estimation fo ..."
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Cited by 15 (3 self)
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Abstruct In the computation of dense optical flow fields, spatial coherence constraints are commonly used to regularize otherwise illposed problem formulations, providing spatial integration of data. In this paper, we present a temporal, multiframe extension of the dense optical flow estimation formulation proposed by Horn and Schunck [l] in which we use a temporal coherence constraint to yield the optimal fusing of data from multiple frames of measurements. Conceptually, at least, standard Kalman filtering algorithms are applicable to the resulting multiframe optical flow estimation problem, providing a solution that is sequential and recursive in time. Experiments are presented to demonstrate that the resulting multiframe estimates are more robust to noise than those provided by the original, singleframe formulation. In addition, we demonstrate cases where the aperture problem of motion vision cannot be resolved satisfactorily without the temporal integration of data enabled by the proposed formulation. Practically, the large matrix dimensions involved in the problem prohibit exact implementation of the optimal Kalman filter. To overcome this limitation, we present a computationally efficient, yet near optimal approximation of the exact filtering algorithm. This approximation has a precise interpretation as the sequential estimation of a reducedorder spatial model for the optical flow estimation error process at each time step and arises from an estimationtheoretic treatment of the filtering problem. Experiments also demonstrate the efficacy of this near optimal filter. I.
Tracking Myocardial Deformation Using Phase Contrast MR Velocity Fields: A Stochastic Approach
 IEEE Transactions on Medical Imaging
"... In this paper, we propose a new approach for tracking the deformation of the Left Ventricular (LV) myocardium from twodimensional Magnetic Resonance (MR) phase contrast velocity fields. The use of phase contrast MR velocity data in cardiac motion problems has been introduced by others [1] and shown ..."
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Cited by 15 (4 self)
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In this paper, we propose a new approach for tracking the deformation of the Left Ventricular (LV) myocardium from twodimensional Magnetic Resonance (MR) phase contrast velocity fields. The use of phase contrast MR velocity data in cardiac motion problems has been introduced by others [1] and shown to be potentially useful for tracking discrete tissue elements, and therefore characterizing LV motion. However, we show here that these velocity data i.) are extremely noisy near the LV borders and ii.) cannot alone be used to estimate the motion and the deformation of the entire myocardium due to noise in the velocity fields. In this new approach, we use the natural spatial constraints of the endocardial and epicardial contours, detected semiautomatically in each image frame, to help remove noisy velocity vectors at the LV contours. The information from both the boundaries and the phase contrast velocity data is then integrated into a deforming mesh that is placed over the myocardium at ...