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Robust Motion Vector Relaxation for X-Ray Fluoroscopy Using Generalized Gauss-Markov Random Fields
Abstract
. We describe a Bayesian motion estimation algorithm which is part of a temporally recursive noise reduction filter for X-ray fluoroscopy images. Our algorithm draws its robustness against high quantum noise levels from a statistical regularization, where a priori expectations about the spatial and temporal smoothness of motion vector fields are modelled by generalized Gauss-Markov random fields. We show that by using generalized Gauss-Markov random fields both smoothness and motion edges can be captured, without the need to specify an often critical edge detection threshold. Instead, our algorithm controls edges by a single parameter by means of which the regularization can be tuned from a median-filter like behaviour to a linear-filter like one. Keywords: fluoroscopy, image restoration, Bayesian motion estimation, generalized Gauss-Markov random fields, thresholdless edge model. 1 Introduction We describe a robust X-ray fluoroscopy motion estimator which we use within a motion comp...
... Minimization of this criterion by appropriately finding the motion field V t can be regarded as finding the maximum a posteriori (MAP) estimate of the motion field, 11,17 where the prior expectations on the sought motion fields are modelled by a Generalized Gauss-Markov random field within the image plane, and by a Markov chain along the temporal axis. The remaining noise in the motion-compensated difference images is characterized by the above approximation to the Poisson model. ...
One advantage of flat-panel X-ray detectors is the immediate availability of the acquired images for display. Current limitations in large-area active-matrix manufacturing technology, however, require that the images read out from such detectors be processed to correct for inactive pixels. In static radiographs, these defects can only be interpolated by spatial filtering. Moving X-ray image modalities, such as fluoroscopy or cine-angiography, permit to use temporal information as well. This paper describes interframe defect interpolation algorithms based on motion compensation and filtering. Assuming the locations of the defects to be known, we fill in the defective areas from past frames, where the missing information was visible due to motion. The motion estimator is based on regularized block matching, with speedup obtained by successive elimination and related measures. To avoid the motion estimator locking on to static defects, these are cut out of each block during matching. Once motion is estimated, three methods are available for defect interpolation: direct filling-in by the motion-compensated predecessor, filling-in by a 3D-multilevel median filtered value, and spatiotemporal mean filtering. Results are shown for noisy fluoroscopy sequences acquired in clinical routine with varying amounts of motion and simulated defects up to six lines wide. They show that the 3D-multilevel median filter appears as the method of choice since it causes the least blur of the interpolated data, is robust with respect to motion estimation errors and works even in non-moving areas.
Visual Reconstruction presents a unified and highly original approach to the treatment of continuity in vision. It introduces, analyzes, and illustrates two new concepts. The first—the weak continuity constraint—is a concise, computational formalization of piecewise continuity. It is a mechanism for expressing the expectation that visual quantities such as intensity, surface color, and surface depth vary continuously almost everywhere, but with occasional abrupt changes. The second concept—the graduated nonconvexity algorithm—arises naturally from the first. It is an efficient, deterministic (nonrandom) algorithm for fitting piecewise continuous functions to visual data. The book first illustrates the breadth of application of reconstruction processes in vision with results that the authors' theory and program yield for a variety of problems. The mathematics of weak continuity and the graduated nonconvexity (GNC) algorithm are then developed carefully and progressively.
Contents Modeling Piecewise Continuity • Applications of Piecewise Continuous Reconstruction • Introducing Weak Continuity Constraints • Properties of the Weak String and Membrane • Properties of Weak Rod and Plate • The Discrete Problem • The Graduated Nonconvexity (GNC) Algorithm • Appendixes: Energy Calculations for the String and Membrane • Noise Performance of the Weak Elastic String • Energy Calculations for the Rod and Plate • Establishing Convexity • Analysis of the GNC Algorithm
Visual Reconstruction is included in the Artificial Intelligence series, edited by Michael Brady and Patrick Winston.
A continuous two‐dimensional region is partitioned into a fine rectangular array of sites or “pixels”, each pixel having a particular “colour” belonging to a prescribed finite set. The true colouring of the region is unknown but, associated with each pixel, there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model. The aim is to reconstruct the true scene, with the additional knowledge that pixels close together tend to have the same or similar colours. In this paper, it is assumed that the local characteristics of the true scene can be represented by a non‐degenerate Markov random field. Such information can be combined with the records by Bayes' theorem and the true scene can be estimated according to standard criteria. However, the computational burden is enormous and the reconstruction may reflect undesirable large‐scale properties of the random field. Thus, a simple, iterative method of reconstruction is proposed, which does not depend on these large‐scale characteristics. The method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field. Some complications, including parameter estimation, are discussed. Potential applications are mentioned briefly.
In clinical x-ray fluoroscopy, moving images are acquired at very low x-ray dose so that only 10-500 x-ray quanta contribute to each pixel. The resulting Poisson statistic causes the images to be strongly aected by quantum noise, which, in the observed images, is spatially cor- related and signal-dependent. In this contribution, we develop a spatial frequency domain method for intra- frame quantum noise reduction, which takes the non- white noise power spectrum into account. Each image is subjected to a block DFT or DCT. The magnitude of each observed spectral coecient is compared to the expected noise variance for it, which is derived from a suitable quantum noise model. Depending on this com- parison, each coecient is more or less attenuated, leav- ing the phase unchanged. Finally, the image is back- transformed and re-assembled. Using this method, noise power reductions of 60% are possible.
A continuous two-dimensional region is partitioned into a fine rectangular array of sites, or ‘pixels', each pixel having a particular '‘colour’ belonging to a prescribed finite set. The true colouring of the region is unknown but, associated with each pixel, there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model. The aim is to reconstruct the true scene, with the additional knowledge that pixels close together tend to have the same or similar colours. In this paper, it is assumed that the local characteristics of the true scene can be represented by a non-degenerate Markov random field. Such information can be combined with the records by Bayes' theorem and the true scene can be estimated according to standard criteria. However, the computational burden is enormous and the reconstruction may reflect undesirable large-scale properties of the random field. Thus, a simple, iterative method of reconstruction is proposed, which does not depend on these large-scale characteristics. The method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field. Some complications, including parameter estimation, are discussed. Potential applications are mentioned briefly.
Noise in television signals degrades both the image quality and the performance of image coding algorithms. This paper describes a nonlinear temporal filtering algorithm using motion compensation for reducing noise in image sequences. A specific implementation for NTSC composite television signals is described, and simulation results on several video sequences are presented. This approach is shown to be successful in improving image quality and also improving the efficiency of subsequent image coding operations.
This contribution discusses a selection of today's techniques and future concepts for digital x-ray imaging in medicine. Advantages of digital imaging over conventional analog methods include the possibility to archive and transmit images in digital information systems as well as to digitally process pictures before display, for example, to enhance low contrast details. After reviewing two digital x- ray radiography systems for the capture of still x-ray images, we examine the real time acquisition of dynamic x- ray images (x-ray fluoroscopy). Here, particular attention is paid to the implications of introducing charge-coupled device cameras. We then present a new unified radiography/fluoroscopy solid-state detector concept. As digital image quality is predominantly determined by the relation of signal and noise, aspects of signal transfer, noise, and noise-related quality measures like detective quantum efficiency feature prominently in our discussions. Finally, we describe a digital image processing algorithm for the reduction of noise in images acquired with low x-ray dose.
Includes index. Bibliography: p. [173]-181. Andrew Blake and Andrew Zisserman.
The authors present a Markov random field model which allows realistic edge modeling while providing stable maximum a posterior (MAP) solutions. The model, referred to as a generalized Gaussian Markov random field (GGMRF), is named for its similarity to the generalized Gaussian distribution used in robust detection and estimation. The model satisfies several desirable analytical and computational properties for map estimation, including continuous dependence of the estimate on the data, invariance of the character of solutions to scaling of data, and a solution which lies at the unique global minimum of the a posteriori log-likelihood function. The GGMRF is demonstrated to be useful for image reconstruction in low-dosage transmission tomography.<
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Describes a method for displacement estimation in stereoscopic
images, which is closely coupled with a segmentation of the pictures
into homogeneously displaced regions. The technique is driven by a
statistical optimization criterion which assesses the quality of the
disparity estimate and of the segmentation, thus improving both of these
simultaneously. In addition, the optimization criterion explicitly takes
occluded areas into consideration. With the additional help of two
constraints, this enables the algorithm to locate regions corresponding
to occlusions accurately