Showing papers on "Iterative reconstruction published in 1996"

Imaging Through Turbulence

Abstract: Introduction Overview of the Problem Area Historical Overview of Imaging Through Turbulence Overview of the Book Background: Fourier and Statistical Optics Fourier Optics Statistical Optics Turbulence Effects on Imaging Systems Index of Refraction Fluctuations in the Atmosphere Statistics of Index of Refraction Fluctuations Wave Propagation through Random Media First-Order Turbulence Effects on Incoherent Imaging Modal Expansions of Phase Perturbation Phase Screen Generation Speckle Imaging Techniques Introduction Overview of Speckle Imaging Speckle Interferometry Fourier Phase Estimation Techniques Image Reconstruction for Speckle Imaging Conclusion Adaptive Optical Imaging Systems Introduction Factors that Degrade AOI Systems Performance Adaptive Optical System Components and Models AOI System Performance Modeling Summary Hybrid Imaging Techniques Introduction Deconvolution from Wavefront Sensing Methods Involving Adaptive Optics Conclusion Index

A review of wavelets in biomedical applications

Abstract: We present an overview of the various uses of the wavelet transform (WT) in medicine and biology. We start by describing the wavelet properties that are the most important for biomedical applications. In particular we provide an interpretation of the the continuous wavelet transform (CWT) as a prewhitening multiscale matched filter. We also briefly indicate the analogy between the WT and some of the the biological processing that occurs in the early components of the auditory and visual system. We then review the uses of the WT for the analysis of 1-D physiological signals obtained by phonocardiography, electrocardiography (ECG), mid electroencephalography (EEG), including evoked response potentials. Next, we provide a survey of wavelet developments in medical imaging. These include biomedical image processing algorithms (e.g., noise reduction, image enhancement, and detection of microcalcifications in mammograms), image reconstruction and acquisition schemes (tomography, and magnetic resonance imaging (MRI)), and multiresolution methods for the registration and statistical analysis of functional images of the brain (positron emission tomography (PET) and functional MRI (fMRI)). In each case, we provide the reader with same general background information and a brief explanation of how the methods work.

MicroPET: a high resolution PET scanner for imaging small animals

Abstract: MicroPET is a high resolution positron emission tomography (PET) scanner designed for imaging small laboratory animals. It consists of a ring of 30 position-sensitive scintillation detectors, each with an 8/spl times/8 array of small lutetium oxyorthosilicate (LSO) crystals coupled via optical fibers to a multi-channel photomultiplier tube. The detectors have an intrinsic resolution averaging 1.68 mm, an energy resolution between 15 and 25% and 2.4 ns timing resolution at 511 keV. The detector ring diameter of microPET is 17.2 cm with an imaging field of view of 112 mm transaxially by 18 mm axially. The scanner has no septa and operates exclusively in 3D mode. Reconstructed image resolution 1 cm from the center of the scanner is 2.0 mm and virtually isotropic, yielding a volume resolution of 8 mm/sup 3/. For comparison, the volume resolution of state-of-the-art clinical PET systems is in the range of 50-75 mm/sup 3/. Initial images of phantoms have been acquired and are reported. A computer controlled bed is under construction and will incorporate a small wobble motion to improve spatial sampling. This is projected to further enhance spatial resolution. MicroPET is the first PET scanner to incorporate the new scintillator LSO and to our knowledge is the highest resolution multi-ring PET scanner currently in existence.

Spatial resolution properties of penalized-likelihood image reconstruction: space-invariant tomographs

Abstract: This paper examines the spatial resolution properties of penalized-likelihood image reconstruction methods by analyzing the local impulse response. The analysis shows that standard regularization penalties induce space-variant local impulse response functions, even for space-invariant tomographic systems. Paradoxically, for emission image reconstruction, the local resolution is generally poorest in high-count regions. We show that the linearized local impulse response induced by quadratic roughness penalties depends on the object only through its projections. This analysis leads naturally to a modified regularization penalty that yields reconstructed images with nearly uniform resolution. The modified penalty also provides a very practical method for choosing the regularization parameter to obtain a specified resolution in images reconstructed by penalized-likelihood methods.

A unified approach to statistical tomography using coordinate descent optimization

Abstract: Over the past years there has been considerable interest in statistically optimal reconstruction of cross-sectional images from tomographic data. In particular, a variety of such algorithms have been proposed for maximum a posteriori (MAP) reconstruction from emission tomographic data. While MAP estimation requires the solution of an optimization problem, most existing reconstruction algorithms take an indirect approach based on the expectation maximization (EM) algorithm. We propose a new approach to statistically optimal image reconstruction based on direct optimization of the MAP criterion. The key to this direct optimization approach is greedy pixel-wise computations known as iterative coordinate decent (ICD). We propose a novel method for computing the ICD updates, which we call ICD/Newton-Raphson. We show that ICD/Newton-Raphson requires approximately the same amount of computation per iteration as EM-based approaches, but the new method converges much more rapidly (in our experiments, typically five to ten iterations). Other advantages of the ICD/Newton-Raphson method are that it is easily applied to MAP estimation of transmission tomograms, and typical convex constraints, such as positivity, are easily incorporated.

On image analysis by moments

Abstract: Research has been performed investigating the use of moments for pattern recognition in recent years. The basic problem of the influence of discretization and noise on moment accuracy as object descriptors, has been barely investigated. In this paper, the detailed error analysis involved in the moment method is discussed. Several new techniques to increase the accuracy and efficiency of moment descriptor are proposed. We utilize these results for the problem of image reconstruction from the orthogonal Legendre moments computed from discrete and noisy data. The automatic selection of an optimal number of moments is also discussed.

Iterative deblurring for CT metal artifact reduction

Abstract: Iterative deblurring methods using the expectation maximization (EM) formulation and the algebraic reconstruction technique (ART), respectively, are adapted for metal artifact reduction in medical computed tomography (CT). In experiments with synthetic noise-free and additive noisy projection data of dental phantoms, it is found that both simultaneous iterative algorithms produce superior image quality as compared to filtered backprojection after linearly fitting projection gaps. Furthermore, the EM-type algorithm converges faster than the ART-type algorithm in terms of either the I-divergence or Euclidean distance between ideal and reprojected data in the authors' simulation. Also, for a given iteration number, the EM-type deblurring method produces better image clarity but stronger noise than the ART-type reconstruction. The computational complexity of EM- and ART-based iterative deblurring is essentially the same, dominated by reprojection and backprojection. Relevant practical and theoretical issues are discussed.

Tissue elasticity reconstruction using linear perturbation method

Abstract: A new method to reconstruct the elastic modulus of soft tissue subjected to an external static compression is presented. In this approach the Newton-Raphson method is used to vary a finite element (FE) model of the elasticity equations to fit, in a least squared sense, a set of axial tissue displacement fields estimated using a correlation technique applied to ultrasound signals. The ill-conditioning of the Hessian matrix is eliminated using the Tikhonov regularization technique. This regularization provides a compromise between fidelity to the observed data and a priori information of the solution. Using an echographic image formation model, it is shown that the method converges within a few iterations (8-10) and that strain images artifacts which are common in elastography are significantly reduced after the resolution of the inverse problem.

Spectrum-blind minimum-rate sampling and reconstruction of multiband signals

Abstract: We propose a universal sampling pattern and corresponding reconstruction algorithms that guarantee well-conditioned reconstruction of all multiband signals with a given spectral occupancy bound without prior knowledge of the spectral support. It is shown that such a universal sampling pattern can asymptotically achieve the Nyquist-Landau (1957) minimal sampling rate. Also, the new design method replaces the nonaliasing or packability criterion for a reconstructive sampling pattern with a more lenient criterion, allowing reconstruction of signals aliased by sampling.

Practical considerations for 3-D image reconstruction using spherically symmetric volume elements

Abstract: Spherically symmetric volume elements with smooth tapering of the values near their boundaries are alternatives to the more conventional voxels for the construction of volume images in the computer. Their use, instead of voxels, introduces additional parameters which enable the user to control the shape of the volume element (blob) and consequently to control the characteristics of the images produced by iterative methods for reconstruction from projection data. For images composed of blobs, efficient algorithms have been designed for the projection and discrete back-projection operations, which are the crucial parts of iterative reconstruction methods. The authors have investigated the relationship between the values of the blob parameters and the properties of images represented by the blobs. Experiments show that using blobs in iterative reconstruction methods leads to substantial improvement in the reconstruction performance, based on visual quality and on quantitative measures, in comparison with the voxel case. The images reconstructed using appropriately chosen blobs are characterized by less image noise for both noiseless data and noisy data, without loss of image resolution.

EigenTracking: Robust Matching and Tracking of Articulated Objects Using a View-Based Representation

Abstract: This paper describes an approach for tracking rigid and articulated objects using a view-based representation The approach builds on and extends work on eigenspace representations, robust estimation techniques, and parameterized optical flow estimation First, we note that the least-squares image reconstruction of standard eigenspace techniques has a number of problems and we reformulate the reconstruction problem as one of robust estimation Second we define a “subspace constancy assumption” that allows us to exploit techniques for parameterized optical flow estimation to simultaneously solve for the view of an object and the affine transformation between the eigenspace and the image To account for large affine transformations between the eigenspace and the image we define a multi-scale eigenspace representation and a coarse-to-fine matching strategy Finally, we use these techniques to track objects over long image sequences in which the objects simultaneously undergo both affine image motions and changes of view In particular we use this “EigenTracking” technique to track and recognize the gestures of a moving hand

Electrical impedance tomography: regularized imaging and contrast detection

Abstract: Dynamic electrical impedance tomography (EIT) images changes in the conductivity distribution of a medium from low frequency electrical measurements made at electrodes on the medium surface. Reconstruction of the conductivity distribution is an under-determined and ill-posed problem, typically requiring either simplifying assumptions or regularization based on a priori knowledge. This paper presents a maximum a posteriori (MAP) approach to linearized image reconstruction using knowledge of the noise variance of the measurements and the covariance of the conductivity distribution. This approach has the advantage of an intuitive interpretation of the algorithm parameters as well as fast (near real time) image reconstruction. In order to compare this approach to existing algorithms, the authors develop figures of merit to measure the reconstructed image resolution, the noise amplification of the image reconstruction, and the fidelity of positioning in the image. Finally, the authors develop a communications systems approach to calculate the probability of detection of a conductivity contrast in the reconstructed image as a function of the measurement noise and the reconstruction algorithm used.

Real-time focus range sensor

Abstract: Structures of dynamic scenes can only be recovered using a real-time range sensor. Depth from defocus offers an effective solution to fast and dense range estimation. However, accurate depth estimation requires theoretical and practical solutions to a variety of problems including recovery of textureless surfaces, precise blur estimation, and magnification variations caused by defocusing. Both textured and textureless surfaces are recovered using an illumination pattern that is projected via the same optical path used to acquire images. The illumination pattern is optimized to maximize accuracy and spatial resolution in computed depth. The relative blurring in two images is computed using a narrow-band linear operator that is designed by considering all the optical, sensing, and computational elements of the depth from defocus system. Defocus invariant magnification is achieved by the use of an additional aperture in the imaging optics. A prototype focus range sensor has been developed that has a workspace of 1 cubic foot and produces up to 512/spl times/480 depth estimates at 30 Hz with an average RMS error of 0.2%. Several experimental results are included to demonstrate the performance of the sensor.

Optimization-based reconstruction of a 3D object from a single freehand line drawing

Abstract: This paper describes an optimization-based algorithm for reconstructing a 3D model from a single, inaccurate, 2D edge-vertex graph. The graph, which serves as input for the reconstruction process, is obtained from an inaccurate freehand sketch of a 3D wireframe object. Compared with traditional reconstruction methods based on line labelling, the proposed approach is more tolerant of faults in handling both inaccurate vertex positioning and sketches with missing entities. Furthermore, the proposed reconstruction method supports a wide scope of general (manifold and non-manifold) objects containing flat and cylindrical faces. Sketches of wireframe models usually include enough information to reconstruct the complete body. The optimization algorithm is discussed, and examples from a working implementation are given.

Optical image reconstruction using frequency-domain data: simulations and experiments

Abstract: Optical image reconstruction in a heterogeneous turbid medium with the use of frequency-domain measurements is investigated in detail. A finite-element reconstruction algorithm for optical data based on a diffusion equation approximation is presented and confirmed by a series of simulations and experiments using phantoms having optical properties in the range of those expected for tissues. Simultaneous reconstruction of absorption and scattering coefficients is achieved both theoretically and experimentally. Images with different target locations and contrast levels between target and background are also successfully recovered. All reconstructed images from both simulated and experimental data are derived directly from absolute optical data in which no differential measurement scheme is used. Results from the use of simulated and measured data suggest that quantitative images can be produced in terms of absorption and scattering coefficient values and location, size, and shape of heterogeneities within a circular background region over a range of contrast levels. Further, the effects of modulation frequency are found to be relatively modest, although boundary conditions appear to be important factors.

Bayesian reconstruction and use of anatomical a priori information for emission tomography

Abstract: A Bayesian method is presented for simultaneously segmenting and reconstructing emission computed tomography (ECT) images and for incorporating high-resolution, anatomical information into those reconstructions. The anatomical information is often available from other imaging modalities such as computed tomography (CT) or magnetic resonance imaging (MRI). The Bayesian procedure models the ECT radiopharmaceutical distribution as consisting of regions, such that radiopharmaceutical activity is similar throughout each region. It estimates the number of regions, the mean activity of each region, and the region classification and mean activity of each voxel. Anatomical information is incorporated by assigning higher prior probabilities to ECT segmentations in which each ECT region stays within a single anatomical region. This approach is effective because anatomical tissue type often strongly influences radiopharmaceutical uptake. The Bayesian procedure is evaluated using physically acquired single-photon emission computed tomography (SPECT) projection data and MRI for the three-dimensional (3-D) Hoffman brain phantom. A clinically realistic count level is used. A cold lesion within the brain phantom is created during the SPECT scan but not during the MRI to demonstrate that the estimation procedure can detect ECT structure that is not present anatomically.

A new method for modeling the spatially-variant, object-dependent scatter response function in SPECT

Abstract: Scatter compensation using iterative reconstruction results in improved image quality and quantitative accuracy compared to subtraction-based methods, However, this requires knowledge of the spatially-varying, object-dependent scatter response function (SRF), We have previously developed a method, slab derived scatter estimation (SDSE) for estimating the SRF. However, this method has reduced accuracy for nonuniform attenuators and Tl-201 imaging. In this paper we present a new method which provides better modeling of the SRF for Tl-201 SPECT, and should provide improved accuracy for nonuniform attenuators. The method requires 3 image space convolutions and an attenuated projection for each viewing angle. Implementation in a projector-backprojector pair for use with an iterative reconstruction algorithm would require 2 image space Fourier transforms and 6 image space inverse Fourier transforms per iteration. We observed good agreement between SRFs and projection data estimated using this new model compared to those obtained using Monte Carlo simulations.

Bayesian reconstruction of PET images: methodology and performance analysis.

Abstract: We describe a practical statistical methodology for the reconstruction of PET images. Our approach is based on a Bayesian formulation of the imaging problem. The data are modelled as independent Poisson random variables and the image is modelled using a Markov random field smoothing prior. We describe a sequence of calibration procedures which are performed before reconstruction: (i) calculation of accurate attenuation correction factors from re-projected Bayesian reconstructions of the transmission image; (ii) estimation of the mean of the randoms component in the data; and (iii) computation of the scatter component in the data using a Klein - Nishina-based scatter estimation method. The Bayesian estimate of the PET image is then reconstructed using a pre-conditioned conjugate gradient method. We performed a quantitation study with a multi-compartment chest phantom in a Siemens/CTI ECAT931 system. Using 40 1 min frames, we computed the ensemble mean and variance over several regions of interest from images reconstructed using the Bayesian and a standard filtered backprojection (FBP) protocol. The values for the region of interest were compared with well counter data for each compartment. These results show that the Bayesian protocol can produce substantial improvements in relative quantitation over the standard FBP protocol, particularly when short transmission scans are used. An example showing the application of the method to a clinical chest study is also given.

High resolution device and method for imaging concealed objects within an obscuring medium

Abstract: A method and apparatus are provided for imaging and identifying concealed objects within an obscuring medium using radiation (optical, photo-acoustic, ionizing, and/or acoustic) optimized for imaging (e.g. temporal properties, spectral bandwidth, directionality, polarization, etc.). Radiation propagates through, interacts with, exits the medium and the object, and is detected/imaged. Image quality can be improved if radiation is collimated and/or if transmission and/or backscattered measurements from a number of perspectives are used to improved image reconstruction. Coupling materials can be employed during image acquisition to enhance radiation coupling as well as providing desirable absorption and scattering properties. Contrast materials and agents can also aid in the detection of concealed objects. Adaptive methods, e.g. using reference objects, including implementations based on the concept of guide stars, can improve the imaging process. The surface can be monitored and groomed to enhance the imaging process. Tomosynthesis techniques can be used to reconstruct images. Acousto-optic effects may be observed when both optical radiation and acoustic radiation are introduce into the medium. A laser vibrometry, speckle, or holographic interferometry imaging technique can be used to readout the acoustic waveform exiting the medium surface directly or after interacting with a deformable mirrored or reflective layer coupled to the medium. The medium may be prepared prior to imaging in order to reduce surface irregularities and roughness. Multilayer mirrors and capillary optics can be used to enhance imaging systems which use ionizing radiation. Resistance images can be obtained using probes to penetrate the medium.

A three-dimensional ultrasound prostate imaging system

Abstract: We have developed a three-dimensional (3D) transrectal ultrasound imaging system, based on using a motorized 5 MHz transducer assembly, rotated under microcomputer control, to collect a series of 100 two-dimensional (2D) images, digitized by a video frame-grabber. These are then reconstructed into a 3D image on a computer workstation, permitting the prostate anatomy to be visualized in three dimensions, and distance and volume measurements to be performed. The accuracy of the distance measurements was assessed with a string test phantom, and that of the volume measurements with balloons of known sizes. Also, the resolution degradation engendered by the reconstruction algorithm was assessed by comparing the full-width at half-maximum (FWHM) of string cross-sectional images in the 3D image to their 2D counterparts. The results show that distance and volume measurements are both accurate to about +/- 1%, and that the reconstruction algorithm increases the mean FWHM by 8 +/- 3% axially and 3 +/- 3% laterally.

An overview of electromagnetic inductance tomography: Description of three different systems

Abstract: This paper presents a general overview of electromagnetic inductance tomography (EMT). A general introduction is given together with a description of the theoretical background of the technique. Three examples of different EMT systems are discussed and images produced using several different image reconstruction techniques are presented. A discussion of the main features of the techniques is included and some potential applications are suggested.

Euclidean reconstruction from constant intrinsic parameters

Abstract: A new method for Euclidean reconstruction from sequences of images taken by uncalibrated cameras, with constant intrinsic parameters, is described. Our approach leads to a variant of the so called Kruppa equations. It is shown that it is possible to calculate the intrinsic parameters as well as the Euclidean reconstruction from at least three images. The novelty of our approach is that we build our calculation on a projective reconstruction obtained without the assumption on constant intrinsic parameters. This assumption simplifies the analysis, because a projective reconstruction is already obtained and we need "only" to find the correct Euclidean reconstruction among all possible projective reconstructions.

Microwave tomography: two-dimensional system for biological imaging

Abstract: Microwave tomographic imaging is one of the new technologies which has the potential for important applications in medicine. Microwave tomographically reconstructed images may potentially provide information about the physiological state of tissue as well as the anatomical structure of an organ. A two-dimensional (2-D) prototype of a quasi real-time microwave tomographic system was constructed. It was utilized to reconstruct images of physiologically active biological tissues such as an explanted canine perfused heart. The tomographic system consisted of 64 special antennae, divided into 32 emitters and 32 receivers which were electronically scanned. The cylindrical microwave chamber had an internal diameter of 360 mm and was filled with various solutions, including deionized water. The system operated on a frequency of 2.45 GHz. The polarization of the incident electromagnetic field was linear in the vertical direction. Total acquisition time was less than 500 ms. Both accurate and approximation methods of image reconstruction were used. Images of 2-D phantoms, canine hearts, and beating canine hearts have been achieved. In the worst-case situation when the 2-D diffraction model was used for an attempt to "slice" three-dimensional (3-D) object reconstruction, the authors still achieved spatial resolution of 1 to 2 cm and contrast resolution of 5%.

Microwave Tomography: Two-Dimensiorial System for Biological 1magin.g

Abstract: Microwave tomographic imaging is one of the new technologies which has the potential for important applications in medicine. Microwave tomographically reconstructed images may potentially provide information about the physiological state of tissue as well as the anatomical structure of an organ. A two-dimensional (2-D) prototype of a quasi real-time microwave tomographic system was constructed. It was utilized to recon- struct images of physiologically active biological tissues such as an explanted canine perfused heart. The tomographic system consisted of 64 special antennae, divided into 32 emitters and 32 receivers which were electronically scanned. The cylindrical microwave chamber had an internal diameter of 360 mm and was filled with various solutions, including deionized water. The system operated on a frequency of 2.45 GHz. The polarization of the incident electromagnetic field was linear in the vertical direction. Total acquisition time was less than 500 ms. Both accur,ate and approximation methods of image reconstruction were used. Images of 2-D phantoms, canine hearts, and beating canine hearts have been achieved. In the worst-case situation when the 2-D diffraction model was used for an attempt to '*slice" three-dimensional (3-D) object reconstruction, we still achieved spatial resolution of 1 to 2 cm and contrast resolution of 5%.

Microwave imaging for tissue assessment: initial evaluation in multitarget tissue-equivalent phantoms

Abstract: A prototype microwave imaging system is evaluated for its ability to recover two-dimensional (2-D) electrical property distributions under transverse magnetic (TM) illumination using multitarget tissue equivalent phantoms. Experiments conducted in a surrounding lossy saline tank, demonstrate that simultaneous recovery of both the real and imaginary components of the electrical property distribution is possible using absolute imaging procedures over a frequency range of 300-700 MHz. Further, image reconstructions of embedded tissue-equivalent targets are found to be quantitative not only with respect to geometrical factors such as object size and location but also electrical composition. Quantitative assessments based on full-width half-height criteria reveal that errors in diameter estimates of reconstructed targets are less than 10 mm in all cases, whereas, positioning errors are less than 1 mm in single object experiments but degrade to 4-10 mm when multiple targets are present. Recovery of actual electrical properties is found to be frequency dependent for the real and imaginary components with background values being typically within 10-20% of their correct size and embedded object having similar accuracies as a percentage of the electrical contrast, although errors as high as 50% can occur. The quantitative evaluation of imaging performance has revealed potential advantages in a two-tiered receiver antenna configuration whose measured field values are more sensitive to target region changes than the typical tomographic type of approach which uses reception sites around the full target region perimeter. This measurement strategy has important implications for both the image reconstruction algorithm where there is a premium on minimizing problem size without sacrificing image quality and the hardware system design which seeks to economize on the amount of measured data required for quantitative image reconstruction while maximizing its sensitivity to target perturbations.

Euclidean shape and motion from multiple perspective views by affine iterations

Abstract: We describe a method for solving the Euclidean reconstruction problem with a perspective camera model by incrementally performing Euclidean reconstruction with either a weak or a paraperspective camera model. With respect to other methods that compute shape and motion from a sequence of images with a calibrated camera, this method converges in a few iterations, is computationally efficient, and solves for the sign (reversal) ambiguity. We give a detailed account of the method, analyze its convergence, and test it with both synthetic and real data.

Correction for scatter in 3D brain PET using a dual energy window method

Abstract: A method for scatter correction using dual energy window acquisition has been developed and implemented on data collected with a brain-PET tomograph operated in the septa retracted, 3D mode. Coincidence events are assigned to (i) an upper energy window where both photons deposit energy between 380 keV and 850 keV or (ii) a lower energy window where one or both photons deposit within 200 keV and 380 keV. Scaling parameters are derived from measurements of the ratios of counts from line sources due to scattered and unscattered events in the two energy windows in head-sized phantoms. A scaled subtraction of the two energy windows produces a distribution of scatter which is smoothed prior to subtraction from the upper energy window. In phantoms, the correction was found to restore the uniformity, contrast and linearity of activity concentration. Relative activity concentrations were restored to within 7% of their true values in a multicompartment phantom. The method was found to provide accurate correction for scattered events arising from activity outside the direct detector field of view. In a three-compartment phantom containing water, and scanned in dynamic, multiframe mode, the half-lives of the two isotopes were restored to within 2% of their true value.

Scanning-beam x-ray imaging system

Abstract: An x-ray imaging system according to the present invention comprising a stepped scanning-beam x-ray source and a multi-detector array. The output of the multi-detector array is input to an image reconstruction engine which combines the outputs of the multiple detectors over selected steps of the x-ray beam to generate an x-ray image of the object. A collimating element, preferably in the form of a perforated grid containing an array of apertures, interposed between the x-ray source and an object to be x-rayed. A maneuverable positioner incorporating an x-ray sensitive marker allowing the determination of the precise position coordinates of the maneuverable positioner.