Distortion Map Research Articles

Hybrid PET/MRI Insert: <formula formulatype="inline"><tex Notation="TeX">${B_0}$</tex></formula> Field Optimization by Applying Active and Passive Shimming on PET Detector Level

The design of an MRI (Magnetic Resonance Imaging) compatible PET (Positron Emission Tomography) detector is regarded to be a challenging task since both imaging devices are likely interacting with each other potentially leading to performance degradation. A typically expected consequence of this interaction is the distortion of the MRI system’s ${B_0}$ field homogeneity. The ${B_0}$ field gets distorted by any material with non-zero susceptibility brought into the MRI system. Typically, MRI machines have a so-called active shimming system available which allows the field optimization by using additional dedicated shim coils. However, this active shimming mechanism is limited and might not be capable to compensate localized higher order field patterns caused by e.g. a PET system. Since the high ${B_0}$ field quality is needed for an undisturbed MRI acquisition in general and especially for more advanced MR sequences (spectroscopic studies, sequences which utilizes spectral selective pre-pulses), the PET system’s hardware needs to be designed carefully. Consequently, the typical design paradigm regarding this ${B_0}$ field distortion is the careful selection of all components according to their susceptibility (as low as possible). This design paradigm certainly limits the flexibility of the system design since worse performing components might be chosen over better alternatives because of their higher susceptibility. To overcome this limitation and to retain the MRI capabilities, we propose the application of localized shimming on PET detector level, meaning that the distortion profile caused by PET modules is compensated using either additional components such as magnetic materials (passive shimming) or DC coils (active shimming) on the PET modules or by intelligently arranging the hardware components of the PET detector. We have implemented a software framework which covers three parts: firstly, it calculates the ${B_0}$ distortion of various objects (susceptibility objects, conductor configuration). Secondly, it allows the characterization of magnetic objects by fitting the implemented models to data and thirdly, it performs a ${B_0}$ field homogenization of measured distortion maps by superimposing field disturbances of additional simulated objects. We tested this software framework in a first attempt with a single PET module of the Hyperion-II $^ {\rm D}$ scanner. The measured distortion map of the single PET module shows a strong localized ${B_0}$ distortion with a volume RMS value of about $0.6~\hbox{ppm}$ . After optimization, the homogeneity of the simulated field distribution is strongly improved by a factor of 8 (volume RMS $ \approx 0.075~\hbox{ppm}$ ).

Simultaneous localization and calibration for electromagnetic tracking systems.

In clinical environments, field distortion can cause significant electromagnetic tracking errors. Therefore, dynamic calibration of electromagnetic tracking systems is essential to compensate for measurement errors. It is proposed to integrate the motion model of the tracked instrument with redundant EM sensor observations and to apply a simultaneous localization and mapping algorithm in order to accurately estimate the pose of the instrument and create a map of the field distortion in real-time. Experiments were conducted in the presence of ferromagnetic and electrically-conductive field distorting objects and results compared with those of a conventional sensor fusion approach. The proposed method reduced the tracking error from 3.94±1.61 mm to 1.82±0.62 mm in the presence of steel, and from 0.31±0.22 mm to 0.11±0.14 mm in the presence of aluminum. With reduced tracking error and independence from external tracking devices or pre-operative calibrations, the approach is promising for reliable EM navigation in various clinical procedures. Copyright © 2015 John Wiley & Sons, Ltd.

Mappings of finite distortion between metric measure spaces

We establish the basic analytic properties of mappings of finite distortion between proper Ahlfors regular metric measure spaces that support a ( 1 , 1 ) (1,1) -Poincaré inequality. As applications, we prove that under certain integrability assumption for the distortion function, the branch set of a mapping of finite distortion between generalized n n -manifolds of type A A has zero Hausdorff n n -measure.

Motionless electromagnetic phase stepping versus mechanical phase stepping in x-ray phase-contrast imaging with a compact source

X-ray phase contrast imaging based on grating interferometers detects the refractive index distribution of an object without relying on radiation attenuation, thereby having the potential for reduced radiation absorption. These techniques belong to the broader category of optical wavefront measurement, which requires stepping the phase of the interference pattern to obtain a pixel-wise map of the phase distortion of the wavefront. While phase stepping traditionally involves mechanical scanning of a grating or mirror, we developed electromagnetic phase stepping (EPS) for imaging with compact sources to obviate the need for mechanical movement. In EPS a solenoid coil is placed outside the x-ray tube to shift its focal spot with a magnetic field, causing a relative movement between the projection of the sample and the interference pattern in the image. Here we present two embodiments of this method. We verified experimentally that electromagnetic and mechanical phase stepping give the same results and attain the same signal-to-noise ratios under the same radiation dose. We found that the relative changes of interference fringe visibility were within 3.0% when the x-ray focal spot was shifted by up to 1.0 mm in either direction. We conclude that when using x-ray tube sources, EPS is an effective means of phase stepping without the need for mechanical movement.

Image processing for cameras with fiber bundle image relay.

Some high-performance imaging systems generate a curved focal surface and so are incompatible with focal plane arrays fabricated by conventional silicon processing. One example is a monocentric lens, which forms a wide field-of-view high-resolution spherical image with a radius equal to the focal length. Optical fiber bundles have been used to couple between this focal surface and planar image sensors. However, such fiber-coupled imaging systems suffer from artifacts due to image sampling and incoherent light transfer by the fiber bundle as well as resampling by the focal plane, resulting in a fixed obscuration pattern. Here, we describe digital image processing techniques to improve image quality in a compact 126° field-of-view, 30 megapixel panoramic imager, where a 12 mm focal length F/1.35 lens made of concentric glass surfaces forms a spherical image surface, which is fiber-coupled to six discrete CMOS focal planes. We characterize the locally space-variant system impulse response at various stages: monocentric lens image formation onto the 2.5 μm pitch fiber bundle, image transfer by the fiber bundle, and sensing by a 1.75 μm pitch backside illuminated color focal plane. We demonstrate methods to mitigate moiré artifacts and local obscuration, correct for sphere to plane mapping distortion and vignetting, and stitch together the image data from discrete sensors into a single panorama. We compare processed images from the prototype to those taken with a 10× larger commercial camera with comparable field-of-view and light collection.

Shape descriptors and mapping methods for full-field comparison of experimental to simulation data

Validation of computational solid mechanics simulations requires full-field comparison methodologies between numerical and experimental results. The continuous Zernike and Chebyshev moment descriptors are applied to decompose data obtained from numerical simulations and experimental measurements, in order to reduce the high amount of ‘raw’ data to a fairly modest number of features and facilitate their comparisons. As Zernike moments are defined over a unit disk space, a geometric transformation (mapping) of rectangular to circular domain is necessary, before Zernike decomposition is applied to non-circular geometry. Four different mapping techniques are examined and their decomposition/reconstruction efficiency is assessed. A deep mathematical investigation to the reasons of the different performance of the four methods has been performed, comprising the effects of image mapping distortion and the numerical integration accuracy. Special attention is given to the Schwarz–Christoffel conformal mapping, which in most cases is proven to be highly efficient in image description when combined to Zernike moment descriptors. In cases of rectangular structures, it is demonstrated that despite the fact that Zernike moments are defined on a circular domain, they can be more effective even from Chebyshev moments, which are defined on rectangular domains, provided that appropriate mapping techniques have been applied.

Absolute continuity of mappings with finite geometric distortion

Suppose that ⊂ R n is a domain with n ≥ 2. We show that a continuous, sense-preserving, open and discrete mapping of finite geometric outer distortion with KO(·,f) ∈ L 1/(n 1) loc () is absolutely continuous on almost every line parallel to the coordinate axes. Moreover, if U ⊂ is an open set with N(f,U) 0 depends only on n and on the maximum multiplicity N(f,U).

大口径离轴非球面补偿检测的畸变校正

大口径离轴非球面补偿检测的畸变校正

Comparative mapping and discovery of segregation distortion and linkage disequilibrium across the known fragrance chromosomal regions in a rice F2 population

Segregation distortion analysis in plant breeding is highly important because deviation factors are occasionally serious barriers for introgression of genes of interest into cultivated species. Also, the identification of major QTLs by high linkage disequilibrium is highly useful for breeders in order for crop improvement programs and the further fine mapping of particular genes. Consequently, simultaneous consideration of segregation distortion and linkage disequilibrium leads to developing fertile hybrids and normal inheritance of agronomically favorable genes. Hence, the goal of this study was to investigate genomic regions known to contain fragrance quantitative trait loci (QTLs) in terms of segregation distortion and linkage disequilibrium pattern, and to seek for a possible relationship between them using codominant markers on chromosomes 3, 4, and 8 in a set containing 189 F2 progenies. For the first time, we discovered the presence and extent of segregation distortion and linkage disequilibrium across the fragrance chromosomal areas of rice. The high frequency of skewed allelic segregations in the chromosomes 3 and 4 supports reports of possible gametic selection (ga) and hybrid sterility (S) genes. Finally, the highest linkage disequilibrium values, the lowest recombination frequency, and the shortest distances were observed in the chromosomal regions without segregation distortion. High linkage disequilibrium correlations between markers at short distances may show that such markers can maintain high linkage disequilibrium with linked QTLs and are influential for both MAS and QTL mapping analysis. Moreover, an indirect relationship between segregation distortion and linkage disequilibrium was detected, and thus linkage disequilibrium maps were introduced as useful diagnostic tools for segregation distortion.

Local distortion of M-conformal mappings

A conformal mapping in a plane domain locally maps circles to circles. More generally, quasiconformal mappings locally map circles to ellipses of bounded distortion. In this work, we study the corresponding situation for solutions to Stein–Weiss systems in the (n+1)D Euclidean space. This class of solutions is a transformation of a subset of monogenic locally quasiconformal mappings with nonvanishing Jacobian. In the theoretical part of this work, we prove that an M-conformal mapping locally maps the unit hypersphere onto explicitly characterized hyperellipsoids and vice versa. Then we discuss quasiconformal radial mappings and their relations with the Cauchy kernel and p-monogenic mappings. This is followed by the consideration of quadratic M-conformal mappings. In the applications part of this work, we provide the reader with some plot examples that demonstrate the effectiveness of our approach.

ICP 알고리즘을 이용한 2차원 격자지도 보정

This paper suggests using the ICP (Iterative Closet Point) algorithm to compensate a two-dimensional map. ICP algorithm is a typical algorithm method using matching distance data. When building a two-dimensional map, using data through the value of a laser scanner, it occurred warping and distortion of a two-dimensional map because of the difference of distance from the value of the sensor. It uses the ICP algorithm in order to reduce any error of line. It validated the proposed method through experiment involving matching a two-dimensional map based reference data and measured the two-dimensional map.

MRSA: a density-equalizing mapping analysis of the global research architecture.

Methicillin-resistant Staphylococcus aureus (MRSA) has evolved as an alarming public health thread due to its global spread as hospital and community pathogen. Despite this role, a scientometric analysis has not been performed yet. Therefore, the NewQIS platform was used to conduct a combined density-equalizing mapping and scientometric study. As database, the Web of Science was used, and all entries between 1961 and 2007 were analyzed. In total, 7671 entries were identified. Density equalizing mapping demonstrated a distortion of the world map for the benefit of the USA as leading country with a total output of 2374 publications, followed by the UK (1030) and Japan (862). Citation rate analysis revealed Portugal as leading country with a rate of 35.47 citations per article, followed by New Zealand and Denmark. Country cooperation network analyses showed 743 collaborations with US-UK being most frequent. Network citation analyses indicated the publications that arose from the cooperation of USA and France as well as USA and Japan as the most cited (75.36 and 74.55 citations per collaboration article, respectively). The present study provides the first combined density-equalizing mapping and scientometric analysis of MRSA research. It illustrates the global MRSA research architecture. It can be assumed that this highly relevant topic for public health will achieve even greater dimensions in the future.

Distortion of quasiconformal mappings with identity boundary values

Teichmüller's classical mapping problem for plane domains concerns finding a lower bound for the maximal dilatation of a quasiconformal homeomorphism which holds the boundary pointwise fixed, maps the domain onto itself and maps a given point of the domain to another given point of the domain. For a domain D ⊂ R n , n ⩾ 2 , we consider the class of all K-quasiconformal maps of D onto itself with identity boundary values and Teichmüller's problem in this context. Given a map f of this class and a point x ∈ D , we show that the maximal dilatation of f has a lower bound in terms of the distance of x and f ( x ) . We improve recent results for the unit ball and consider this problem in other more general domains. For instance, convex domains, bounded domains and domains with uniformly perfect boundaries are studied.

A method to correct coordinate distortion in EBSD maps

Drift during electron backscatter diffraction mapping leads to coordinate distortions in resulting orientation maps, which affects, in some cases significantly, the accuracy of analysis. A method, thin plate spline, is introduced and tested to correct such coordinate distortions in the maps after the electron backscatter diffraction measurements. The accuracy of the correction as well as theoretical and practical aspects of using the thin plate spline method is discussed in detail. By comparing with other correction methods, it is shown that the thin plate spline method is most efficient to correct different local distortions in the electron backscatter diffraction maps.

Hybrid PET/MRI insert: B0 field optimization by applying active and passive shimming on PET detector level.

Combining PET and MRI into a hybrid device is challenging since both systems might influence each other. A typical interference problem of such a combined device is the distortion of the MRI’s B0 field distribution due to the material brought inside the MRI’s FOV which is in particular challenging for small-bore PET-systems. High field homogeneity is needed for a good MRI acquisition in general as well as in certain applications. Typically, active shimming using dedicated coils is applied to improve the field homogeneity. However, these techniques are limited especially for localized distortion profiles with higher-order characteristics caused by PET/MRI inserts. As a consequence, we are exploring the potential application of shimming on PET detector level (for the Hyperion-IID PET/MRI insert), meaning that the distortion profile caused by PET modules is compensated using additional magnetic materials (passive shimming) and DC coils (active shimming). To explore the technique, B0 field measurements have been performed using a whole-body phantom in combination with the MRI body coil. An FFE sequence was used to measure distortion maps of DC loops and small magnetic objects (capacitors, ferrites). These distortion maps served as input for a software framework which has been written to perform the field optimization. The implementation was verified by measurements and fits were performed to extract characteristic parameters of the tested objects. Finally, the implemented software framework was used to homogenize a measured distortion map produced by a single PET module by superimposing distortion corrections from additional simulated materials. The resulting superimposed distortion map showed a significantly improved B0 field map quality (reduced spectral width and improved homogeneity). The simulated susceptibility distribution will be applied on PET module level and tested in experiments. Results and details about this study will be presented at the conference.

Highly accelerated Point-Spread Function mapping based on Finite Rate of Innovation for EPI distortion correction.

Hybrid MR-PET scans enable acquisition of both types of images within a session. Despite consistent subject positioning, image alignment can still be challenging. Functional MR images rely on echo-planar imaging (EPI) and present geometric distortions due to static B0 field inhomogeneities. Direct B0 [1] and Point Spread Function (PSF) mapping [2] (Figure ​(Figure1)1) have been proposed for distortion correction. The PSF method is more robust [3], but acquisition times are long even with previous acceleration approaches [4–7]. Figure 1 The PSF mapping sequence is repeated while varying the amplitude of the prewinder phase encode gradient (in red). We used the Finite Rate of Innovation (FRI) framework [8, 9] to detect the PSF peak position to sub-pixel precision using as few ks samples as possible. Images were acquired on a 3.0T Philips Achieva: 2.5×2.5×4.0 mm3, matrix 96×95, 95 ks steps with under-sampling retrospectively performed. PSF peak position was estimated using both the fully-sampled (zero-filled by a factor of 1000) and highly-undersampled data. To determine the PSF peak location, pattern matching was performed. The signal measured at each spatial location was compared to a predicted signal pattern accounting for the ks sampling scheme and the search progressively refined up to the intended precision. EPI images were undistorted as in [10]. Figure ​Figure22 shows example PSF peak shift maps (relative to expected undistorted positions). Figure ​Figure3A3A shows the original EPI slice matching Figure ​Figure2,2, and Figures 3B-E show the corrected images using each displacement map. Comparison with the GE image (Figure ​(Figure3F)3F) confirms accurate geometrical corrections. Figure 2 Maps of the PSF shifts (in pixels) estimated with: A0 2; B) 3; C) 4; D) all 95 ks Figure 3 EPI image (with corresponding outer contour in yellow); Undistorted EPI images estimating the displacement field from: B) 2; C) 3; D) 4 and E) all 95 ks samples and F) GE image (corresponding outer contour in yellow propagated to all undistorted EPI images) ... Using the proposed approach the position of the PSF peak can be estimated from a very small number of samples. In the future distortion map estimation could easily be incorporated into standard preparation phases. Making distortion correction of EPI images more practical would facilitate combining functional PET and MR information as well as structural connectivity information from diffusion-weighted MR images.

Locally injective parametrization with arbitrary fixed boundaries

We present an algorithm for mapping a triangle mesh, which is homeomorphic to a disk, to a planar domain with arbitrary fixed boundaries. The algorithm is guaranteed to produce a globally bijective map when the boundary is fixed to a shape that does not self-intersect. Obtaining a one-to-one map is of paramount importance for many graphics applications such as texture mapping. However, for other applications, such as quadrangulation, remeshing, and planar deformations, global bijectively may be unnecessarily constraining and requires significant increase on map distortion. For that reason, our algorithm allows the fixed boundary to intersect itself, and is guaranteed to produce a map that is injective locally (if such a map exists). We also extend the basic ideas of the algorithm to support the computation of discrete approximation for extremal quasiconformal maps. The algorithm is conceptually simple and fast. We demonstrate the superior robustness of our algorithm in various settings and configurations in which state-of-the-art algorithms fail to produce injective maps.

Latency and Distortion of Electromagnetic Trackers for Augmented Reality Systems

Augmented reality (AR) systems are often used to superimpose virtual objects or information on a scene to improve situational awareness. Delays in the display system or inaccurate registration of objects destroy the sense of immersion a user experiences when using AR systems. AC electromagnetic trackers are ideal for these applications when combined with head orientation prediction to compensate for display system delays. Unfortunately, these trackers do not perform well in environments that contain conductive or ferrous materials due to magnetic field distortion without expensive calibration techniques. In our work we focus on both the prediction and distortion compensation aspects of this application, developing a small footprint predictive filter for display lag compensation and a simplified calibration system for AC magnetic trackers. In the first phase of our study we presented a novel method of tracking angular head velocity from quaternion orientation using an Extended Kalman Filter in both single model (DQEKF) and multiple model (MMDQ) implementations. In the second phase of our work we have developed a new method of mapping the magnetic field generated by the tracker without high precision measurement equipment. This method uses simple fixtures with multiple sensors in a rigid geometry to collect magnetic field data in the tracking volume. We have developed a new algorithm to process the collected data and generate a map of the magnetic field distortion that can be used to compensate distorted measurement data.

SU‐C‐17A‐04: Distortion Characterization and Correction of MR‐SIM Images

Purpose:Distortions in MRI compromise spatial fidelity, potentially impacting delineation and dose calculation. We characterized 2D and 3D large field of view (FOV), system‐level distortion to implement correction maps for MR‐SIM treatment planning.Methods:For 2D in‐plane distortion characterization, a 36×43×2 cm3 phantom with 255 known landmarks (∼1 mm3) was scanned using 1.0T high‐field open MR‐SIM in the transverse, sagittal, and coronal axes (TE/TR/α = 30/500 ms/90°, voxel size =1.4×1.4×5mm3). A binary template (reference) was generated from phantom schematic. An automated program converted MR‐SIM images to binary via masking, thresholding, and testing for connectivity to identify landmarks. Distortion maps were generated by centroid mapping. Images were corrected via warping with inverse distortion maps. Temporal stability was assessed. 3D distortion was characterized using a 40×40×40 cm3 phantom (3D T1‐FFE, TE/TR/α= 3.83/9 ms/10°, voxel size=1 mm3) and performing B‐spline‐based deformable image registration to CT‐SIM (reference). Displacement vector fields describing vector distortion magnitude and distortion histograms were generated.Results:Over 9 months, B0‐field distortions (mm) were 0.51 ± 0.84 (maximum = 5.5), 0.18 ± 0.84 (maximum = 5.5), and 1.03 ± 0.50 (maximum = 3.6) in transverse, sagittal, and coronal planes, respectively. Maximum distortions occurred 18–24 cm from isocenter for all planes. After implementing correction maps, distortions (mm) were reduced to 0.14 ± 0.19 (maximum = 2.12), 0.01 ± 0.21 (maximum = 1.68), and 0.17 ± 0.21 (maximum = 3.00) in transverse, sagittal, and coronal planes, respectively. 3D vector distortion was 0.59 ± 0.32 mm (maximum = 1.65) within 5 cm of isocenter. Distortions were non‐negligible (mean = 1.57 ± 1.06 mm, maximum = 6.26), 10‐15 cm from isocenter.Conclusion:Assessment of 2D distortion was conducted, revealing the need to further correct the periphery of MR‐SIM images. Future work includes generating 3D corrections and quantifying objectinduced distortions to improve planning accuracy with MR‐SIM.Research supported in part by a grant from Philips HealthCare

Data-driven Expansion of Dense Regions – A Cartographic Approach in Literary Geography

Cartographic visualisation of the literary space is facing a major challenge resulting from different levels of detail within which the textual descriptions of settings are made by authors. Those range between very detailed descriptions within parts of a city to spatially spread events within a country, or long journeys across continents. Depending on the fictional texts, fictional action often concentrates on a few main places, resulting in high information density – in the form of various individual settings. As well, they are also embedded in a larger environment. When interactively analysing or choosing a section to print a literary map with individual spatial elements, the user has to choose a map scale, which will result in the output of either a detailed representation of a main place or the geographical overview of the fictional space having a small level of detail. However, it would be a great advantage to receive as much information as possible from one single map view. In order to achieve this, this paper presents a method that allows increasing the representable amount of information, depending on its density. Our method makes use of the diffusion algorithm that is used to create value-by-area cartograms. This algorithm is applied to an auxiliary density grid derived from the distribution of individual settings of a literary map that are to be displayed. The resulting distortion is subsequently transferred to the data of the literary map. Unlike the usual use of area cartograms, we do not aim to represent a statistical value; instead information density is used to provide space for the depiction of the information itself. Various parameters such as grid resolution, scale factor and a smoothing filter visually influence the final map distortion. On the basis of several map examples taken from the ‘Literary Atlas of Europe’ project database, distortion results generated from the application of different parameters are visually examined. Using this process, we improved the proposed approach and generalised an appropriate initial configuration for the automated generation of distorted maps through the usage of its information density.