Non-rigid Free-Form 2D-3D Registration Using Statistical Deformation Model

This paper presents a non-rigid free-from 2D-3D registration approach using statistical deformation model (SDM). In our approach the SDM is first constructed from a set of training data using a non-rigid registration algorithm based on b-spline free-form deformation to encode a priori information about the underlying anatomy. A novel intensity-based non-rigid 2D-3D registration algorithm is then presented to iteratively fit the 3D b-spline-based SDM to the 2D X-ray images of an unseen subject, which requires a computationally expensive inversion of the instantiated deformation in each iteration. In this paper, we propose to solve this challenge with a fast B-spline pseudo-inversion algorithm that is implemented on graphics processing unit (GPU). Experiments conducted on C-arm and X-ray images of cadaveric femurs demonstrate the efficacy of the present approach.

Comparison of Routine Brain Imaging at 3 T and 7 T.

OBJECTIVE The aim of this study was to compare quantitative and semiquantitative parameters (signal-to-noise ratio [SNR], contrast-to-noise ratio [CNR], image quality, diagnostic confidence) from a standard brain magnetic resonance imaging examination encompassing common neurological disorders such as demyelinating disease, gliomas, cerebrovascular disease, and epilepsy, with comparable sequence protocols and acquisition times at 3 T and at 7 T. MATERIALS AND METHODS Ten healthy volunteers and 4 subgroups of 40 patients in total underwent comparable magnetic resonance protocols with standard diffusion-weighted imaging, 2D and 3D turbo spin echo, 2D and 3D gradient echo and susceptibility-weighted imaging of the brain (10 sequences) at 3 T and 7 T. The subgroups comprised patients with either lesional (n = 5) or nonlesional (n = 4) epilepsy, intracerebral tumors (n = 11), demyelinating disease (n = 11) (relapsing-remitting multiple sclerosis [MS, n = 9], secondary progressive MS [n = 1], demyelinating disease not further specified [n = 1]), or chronic cerebrovascular disorders [n = 9]). For quantitative analysis, SNR and CNR were determined. For a semiquantitative assessment of the diagnostic confidence, a 10-point scale diagnostic confidence score (DCS) was applied. Two experienced radiologists with additional qualification in neuroradiology independently assessed, blinded to the field strength, 3 pathology-specific imaging criteria in each of the 4 disease groups and rated their diagnostic confidence. The overall image quality was semiquantitatively assessed using a 4-point scale taking into account whether diagnostic decision making was hampered by artifacts or not. RESULTS Without correction for spatial resolution, SNR was higher at 3 T except in the T2 SPACE 3D, DWI single shot, and DIR SPACE 3D sequences. The SNR corrected by the ratio of 3 T/7 T voxel sizes was higher at 7 T than at 3 T in 10 of 11 sequences (all except for T1 MP2RAGE 3D).In CNR, there was a wide variation between sequences and patient cohorts, but average CNR values were broadly similar at 3 T and 7 T.DCS values for all 4 pathologic entities were higher at 7 T than at 3 T. The DCS was significantly higher at 7 T for diagnosis and exclusion of cortical lesions in vascular disease. A tendency to higher DCS at 7 T for cortical lesions in MS was observed, and for the depiction of a central vein and iron deposits within MS lesions. Despite motion artifacts, DCS values were higher at 7 T for the diagnosis and exclusion of hippocampal sclerosis in mesial temporal lobe epilepsy (improved detection of the hippocampal subunits). Interrater agreement was 69.7% at 3 T and 93.3% at 7 T. There was no significant difference in the overall image quality score between 3 T and 7 T taking into account whether diagnostic decision making was hampered by artifacts or not. CONCLUSIONS Ultra-high-field magnetic resonance imaging at 7 T compared with 3 T yielded an improved diagnostic confidence in the most frequently encountered neurologic disorders. Higher spatial resolution and contrast were identified as the main contributory factors.

A parallel implementation of 3D Zernike moment analysis

Zernike polynomials are a well known set of functions that find many applications in image or pattern characterization because they allow to construct shape descriptors that are invariant against translations, rotations or scale changes. The concepts behind them can be extended to higher dimension spaces, making them also fit to describe volumetric data. They have been less used than their properties might suggest due to their high computational cost. We present a parallel implementation of 3D Zernike moments analysis, written in C with CUDA extensions, which makes it practical to employ Zernike descriptors in interactive applications, yielding a performance of several frames per second in voxel datasets about 2003 in size. In our contribution, we describe the challenges of implementing 3D Zernike analysis in a general-purpose GPU. These include how to deal with numerical inaccuracies, due to the high precision demands of the algorithm, or how to deal with the high volume of input data so that it does not become a bottleneck for the system.

Advances in the Simultaneous Multiple Surface optical design method for imaging and non-imaging applications

Classical imaging optics has been developed over centuries in many areas, such as its paraxial imaging theory and practical design methods like multi-parametric optimization techniques. Although these imaging optical design methods can provide elegant solutions to many traditional optical problems, there are more and more new design problems, like solar concentrator, illumination system, ultra-compact camera, etc., that require maximum energy transfer efficiency, or ultra-compact optical structure. These problems do not have simple solutions from classical imaging design methods, because not only paraxial rays, but also non-paraxial rays should be well considered in the design process. Non-imaging optics is a newly developed optical discipline, which does not aim to form images, but to maximize energy transfer efficiency. One important concept developed from non-imaging optics is the “edge-ray principle”, which states that the energy flow contained in a bundle of rays will be transferred to the target, if all its edge rays are transferred to the target. Based on that concept, many CPC solar concentrators have been developed with efficiency close to the thermodynamic limit. When more than one bundle of edge-rays needs to be considered in the design, one way to obtain solutions is to use SMS method. SMS stands for Simultaneous Multiple Surface, which means several optical surfaces are constructed simultaneously. The SMS method was developed as a design method in Non-imaging optics during the 90s. The method can be considered as an extension to the Cartesian Oval calculation. In the traditional Cartesian Oval calculation, one optical surface is built to transform an input wave-front to an out-put wave-front. The SMS method however, is dedicated to solve more than 1 wave-fronts transformation problem. In the beginning, only 2 input wave-fronts and 2 output wave-fronts transformation problem was considered in the SMS design process for rotational optical systems or free-form optical systems. Usually “SMS 2D” method stands for the SMS procedure developed for rotational optical system, and “SMS 3D” method for the procedure for free-form optical system. Although the SMS method was originally employed in non-imaging optical system designs, it has been found during this thesis that with the improved capability to design more surfaces and control more input and output wave-fronts, the SMS method can also be applied to imaging system designs and possesses great advantage over traditional design methods. In this thesis, one of the main goals to achieve is to further develop the existing SMS-2D method to design with more surfaces and improve the stability of the SMS-2D and SMS-3D algorithms, so that further optimization process can be combined with SMS algorithms. The benefits of SMS plus optimization strategy over traditional optimization strategy will be explained in details for both rotational and free-form imaging optical system designs. Another main goal is to develop novel design concepts and methods suitable for challenging non-imaging applications, e.g. solar concentrator and solar tracker. This thesis comprises 9 chapters and can be grouped into two parts: the first part (chapter 2-5) contains research works in the imaging field, and the second part (chapter 6-8) contains works in the non-imaging field. In the first chapter, an introduction to basic imaging and non-imaging design concepts and theories is given. Chapter 2 presents a basic SMS-2D imaging design procedure using meridian rays. In this chapter, we will set the imaging design problem from the SMS point of view, and try to solve the problem numerically. The stability of this SMS-2D design procedure will also be discussed. The design concepts and procedures developed in this chapter lay the path for further improvement. Chapter 3 presents two improved SMS 3 surfaces’ design procedures using meridian rays (SMS-3M) and skew rays (SMS-1M2S) respectively. The major improvement has been made to the central segments selections, so that the whole SMS procedures become more stable compared to procedures described in Chapter 2. Since these two algorithms represent two types of phase space sampling, their image forming capabilities are compared in a simple objective design. Chapter 4 deals with an ultra-compact SWIR camera design with the SMS-3M method. The difficulties in this wide band camera design is how to maintain high image quality meanwhile reduce the overall system length. This interesting camera design provides a playground for the classical design method and SMS design methods. We will show designs and optical performance from both classical design method and the SMS design method. Tolerance study is also given as the end of the chapter. Chapter 5 develops a two-stage SMS-3D based optimization strategy for a 2 freeform mirrors imaging system. In the first optimization phase, the SMS-3D method is integrated into the optimization process to construct the two mirrors in an accurate way, drastically reducing the unknown parameters to only few system configuration parameters. In the second optimization phase, previous optimized mirrors are parameterized into Qbfs type polynomials and set up in code V. Code V optimization results demonstrates the effectiveness of this design strategy in this 2-mirror system design. Chapter 6 shows an etendue-squeezing condenser optics, which were prepared for the 2010 IODC illumination contest. This interesting design employs many non-imaging techniques such as the SMS method, etendue-squeezing tessellation, and groove surface design. This device has theoretical efficiency limit as high as 91.9%. Chapter 7 presents a freeform mirror-type solar concentrator with uniform irradiance on the solar cell. Traditional parabolic mirror concentrator has many drawbacks like hot-pot irradiance on the center of the cell, insufficient use of active cell area due to its rotational irradiance pattern and small acceptance angle. In order to conquer these limitations, a novel irradiance homogenization concept is developed, which lead to a free-form mirror design. Simulation results show that the free-form mirror reflector has rectangular irradiance pattern, uniform irradiance distribution and large acceptance angle, which confirm the viability of the design concept. Chapter 8 presents a novel beam-steering array optics design strategy. The goal of the design is to track large angle parallel rays by only moving optical arrays laterally, and convert it to small angle parallel output rays. The design concept is developed as an extended SMS method. Potential applications of this beam-steering device are: skylights to provide steerable natural illumination, building integrated CPV systems, and steerable LED illumination. Conclusion and future lines of work are given in Chapter 9. Resumen La óptica de formación de imagen clásica se ha ido desarrollando durante siglos, dando lugar tanto a la teoría de óptica paraxial y los métodos de diseño prácticos como a técnicas de optimización multiparamétricas. Aunque estos métodos de diseño óptico para formación de imagen puede aportar soluciones elegantes a muchos problemas convencionales, siguen apareciendo nuevos problemas de diseño óptico, concentradores solares, sistemas de iluminación, cámaras ultracompactas, etc. que requieren máxima transferencia de energía o dimensiones ultracompactas. Este tipo de problemas no se pueden resolver fácilmente con métodos clásicos de diseño porque durante el proceso de diseño no solamente se deben considerar los rayos paraxiales sino también los rayos no paraxiales. La óptica anidólica o no formadora de imagen es una disciplina que ha evolucionado en gran medida recientemente. Su objetivo no es formar imagen, es maximazar la eficiencia de transferencia de energía. Un concepto importante de la óptica anidólica son los “rayos marginales”, que se pueden utilizar para el diseño de sistemas ya que si todos los rayos marginales llegan a nuestra área del receptor, todos los rayos interiores también llegarán al receptor. Haciendo uso de este principio, se han diseñado muchos concentradores solares que funcionan cerca del límite teórico que marca la termodinámica. Cuando consideramos más de un haz de rayos marginales en nuestro diseño, una posible solución es usar el método SMS (Simultaneous Multiple Surface), el cuál diseña simultáneamente varias superficies ópticas. El SMS nació como un método de diseño para óptica anidólica durante los años 90. El método puede ser considerado como una extensión del cálculo del óvalo cartesiano. En el método del óvalo cartesiano convencional, se calcula una superficie para transformar un frente de onda entrante a otro frente de onda saliente. El método SMS permite transformar varios frentes de onda de entrada en frentes de onda de salida. Inicialmente, sólo era posible transformar dos frentes de onda con dos superficies con simetría de rotación y sin simetría de rotación, pero esta limitación ha sido superada recientemente. Nos referimos a “SMS 2D” como el método orientado a construir superficies con simetría de rotación y llamamos “SMS 3D” al método para construir superficies sin simetría de rotación o free-form. Aunque el método originalmente fue aplicado en el diseño de sistemas anidólicos, se ha observado que gracias a su capacidad para diseñar más superficies y controlar más frentes de onda de entrada y de salida, el SMS también es posible aplicarlo a sistemas de formación de imagen proporcionando una gran ventaja sobre los métodos de diseño tradicionales. Uno de los principales objetivos de la presente tesis es extender el método SMS-2D para permitir el diseño de sistemas con mayor número de superficies y mejorar la estabilidad de los algoritmos del SMS-2D y SMS-3D, haciendo posible combinar la optimización con los algoritmos. Los beneficios de combinar SMS y optimización comparado con el proceso de optimización tradicional se explican en detalle para sistemas con simetría de rotación y sin simetría de rotación. Otro objetivo importante de la tesis es el desarrollo de nuevos conceptos de diseño y nuevos métodos en el área de la concentración solar fotovoltaica. La tesis está estructurada en 9 capítulos que están agrupados en dos partes: la primera de ellas (capítulos 2-5) se centra en la óptica formadora de imagen mientras que en la segunda parte (capítulos 6-8) se presenta el trabajo del área de la óptica anidólica. El primer capítulo consta de una breve introducción de los conceptos básicos de la óptica anidólica y la óptica en formación de imagen. El capítulo 2 describe un proceso de diseño SMS-2D sencillo basado en los rayos meridianos. En este capítulo se presenta el problema de diseñar un sistema formador de imagen desde el punto de vista del SMS y se intenta obtener una solución de manera numérica. La estabilidad de este proceso se analiza con detalle. Los conceptos de diseño y los algoritmos desarrollados en este capítulo sientan la base sobre la cual se realizarán mejoras. El capítulo 3 presenta dos procedimientos para el diseño de un sistema con 3 superficies SMS, el primero basado en rayos meridianos (SMS-3M) y el segundo basado en rayos oblicuos (SMS-1M2S). La mejora más destacable recae en la selección de los segmentos centrales, que hacen más estable todo el proceso de diseño comparado con el presentado en el capítulo 2. Estos dos algoritmos representan dos tipos de muestreo del espacio de fases, su capacidad para formar imagen se compara diseñando un objetivo simple con cada uno de ellos. En el capítulo 4 se presenta un diseño ultra-compacto de una cámara SWIR diseñada usando el método SMS-3M. La dificultad del diseño de esta cámara de espectro ancho radica en mantener una alta calidad de imagen y al mismo tiempo reducir drásticamente sus dimensiones. Esta cámara es muy interesante para comparar el método de diseño clásico y el método de SMS. En este capítulo se presentan ambos diseños y se analizan sus características ópticas. En el capítulo 5 se describe la estrategia de optimización basada en el método SMS-3D. El método SMS-3D calcula las superficies ópticas de manera precisa, dejando sólo unos pocos parámetros libres para decidir la configuración del sistema. Modificando el valor de estos parámetros se genera cada vez mediante SMS-3D un sistema completo diferente. La optimización se lleva a cabo variando los mencionados parámetros y analizando el sistema generado. Los resultados muestran que esta estrategia de diseño es muy eficaz y eficiente para un sistema formado por dos espejos. En el capítulo 6 se describe un sistema de compresión de la Etendue, que fue presentado en el concurso de iluminación del IODC en 2010. Este interesante diseño hace uso de técnicas propias de la óptica anidólica, como el método SMS, el teselado de las lentes y el diseño mediante grooves. Este dispositivo tiene un límite teórica en la eficiencia del 91.9%. El capítulo 7 presenta un concentrador solar basado en un espejo free-form con irradiancia uniforme sobre la célula. Los concentradores parabólicos tienen numerosas desventajas como los puntos calientes en la zona central de la célula, uso no eficiente del área de la célula al ser ésta cuadrada y además tienen ángulos de aceptancia de reducido. Para poder superar estas limitaciones se propone un novedoso concepto de homogeneización de la irrandancia que se materializa en un diseño con espejo free-form. El análisis mediante simulación demuestra que la irradiancia es homogénea en una región rectangular y con mayor ángulo de aceptancia, lo que confirma la viabilidad del concepto de diseño. En el capítulo 8 se presenta un novedoso concepto para el diseño de sistemas afocales dinámicos. El objetivo del diseño es realizar un sistema cuyo haz de rayos de entrada pueda llegar con ángulos entre ±45º mientras que el haz de rayos a la salida sea siempre perpendicular al sistema, variando únicamente la posición de los elementos ópticos lateralmente. Las aplicaciones potenciales de este dispositivo son varias: tragaluces que proporcionan iluminación natural, sistemas de concentración fotovoltaica integrados en los edificios o iluminación direccionable con LEDs. Finalmente, el último capítulo contiene las conclusiones y las líneas de investigación futura.

Analytic free-form lens design in 3D: coupling three ray sets using two lens surfaces

The two-dimensional analytic optics design method presented in a previous paper [Opt. Express 20, 5576–5585 (2012)] is extended in this work to the three-dimensional case, enabling the coupling of three ray sets with two free-form lens surfaces. Fermat’s principle is used to deduce additional sets of functional differential equations which make it possible to calculate the lens surfaces. Ray tracing simulations demonstrate the excellent imaging performance of the resulting free-form lenses described by more than 100 coefficients.

Single optical surface imaging designs with unconstrained object to image mapping

In this work, novel imaging designs with a single optical surface (either refractive or reflective) are presented. In some of these designs, both object and image shapes are given but mapping from object to image is obtained as a result of the design. In other designs, not only the mapping is obtained in the design process, but also the shape of the object is found. In the examples considered, the image is virtual and located at infinity and is seen from known pupil, which can emulate a human eye. In the first introductory part, 2D designs have been done using three different design methods: a SMS design, a compound Cartesian oval surface, and a differential equation method for the limit case of small pupil. At the point-size pupil limit, it is proven that these three methods coincide. In the second part, previous 2D designs are extended to 3D by rotation and the astigmatism of the image has been studied. As an advanced variation, the differential equation method is used to provide the freedom to control the tangential rays and sagittal rays simultaneously. As a result, designs without astigmatism (at the small pupil limit) on a curved object surface have been obtained. Finally, this anastigmatic differential equation method has been extended to 3D for the general case, in which freeform surfaces are designed.

Dysfunctional 3D model based on structural and neuropsychological information

Acquired brain injury (ABI) 1-2 refers to any brain damage occurring after birth. It usually causes certain damage to portions of the brain. ABI may result in a significant impairment of an individuals physical, cognitive and/or psychosocial functioning. The main causes are traumatic brain injury (TBI), cerebrovascular accident (CVA) and brain tumors. The main consequence of ABI is a dramatic change in the individuals daily life. This change involves a disruption of the family, a loss of future income capacity and an increase of lifetime cost. One of the main challenges in neurorehabilitation is to obtain a dysfunctional profile of each patient in order to personalize the treatment. This paper proposes a system to generate a patient s dysfunctional profile by integrating theoretical, structural and neuropsychological information on a 3D brain imaging-based model. The main goal of this dysfunctional profile is to help therapists design the most suitable treatment for each patient. At the same time, the results obtained are a source of clinical evidence to improve the accuracy and quality of our rehabilitation system. Figure 1 shows the diagram of the system. This system is composed of four main modules: image-based extraction of parameters, theoretical modeling, classification and co-registration and visualization module.

3D Frangi-based lung vessel enhancement filter penalizing airways

This paper describes a fully automatic simultaneous lung vessel and airway enhancement filter. The approach consists of a Frangi-based multiscale vessel enhancement filtering specifically designed for lung vessel and airway detection, where arteries and veins have high contrast with respect to the lung parenchyma, and airway walls are hollow tubular structures with a non negative response using the classical Frangi's filter. The features extracted from the Hessian matrix are used to detect centerlines and approximate walls of airways, decreasing the filter response in those areas by applying a penalty function to the vesselness measure. We validate the segmentation method in 20 CT scans with different pathological states within the VESSEL12 challenge framework. Results indicate that our approach obtains good results, decreasing the number of false positives in airway walls.

Identification of pore spaces in 3D CT soil images using a PFCM partitional clustering

Recent advances in non-destructive imaging techniques, such as X-ray computed tomography (CT), make it possible to analyse pore space features from the direct visualisation from soil structures. A quantitative characterisation of the three-dimensional solid-pore architecture is important to understand soil mechanics, as they relate to the control of biological, chemical, and physical processes across scales. This analysis technique therefore offers an opportunity to better interpret soil strata, as new and relevant information can be obtained. In this work, we propose an approach to automatically identify the pore structure of a set of 200-2D images that represent slices of an original 3D CT image of a soil sample, which can be accomplished through non-linear enhancement of the pixel grey levels and an image segmentation based on a PFCM (Possibilistic Fuzzy C-Means) algorithm. Once the solids and pore spaces have been identified, the set of 200-2D images is then used to reconstruct an approximation of the soil sample by projecting only the pore spaces. This reconstruction shows the structure of the soil and its pores, which become more bounded, less bounded, or unbounded with changes in depth. If the soil sample image quality is sufficiently favourable in terms of contrast, noise and sharpness, the pore identification is less complicated, and the PFCM clustering algorithm can be used without additional processing; otherwise, images require pre-processing before using this algorithm. Promising results were obtained with four soil samples, the first of which was used to show the algorithm validity and the additional three were used to demonstrate the robustness of our proposal. The methodology we present here can better detect the solid soil and pore spaces on CT images, enabling the generation of better 2D?3D representations of pore structures from segmented 2D images.

Anastigmatic imaging with unconstrained object to image mapping

Anastigmatic imaging of an object to an image surfaces without the point-to-point mapping prescription and using a single optical surface is analyzed in 2D and 3D geometries (free-form and rotational-symmetric). Several design techniques are shown.

Basement structure of the Hontomín CO2 storage site (Spain) determined by integration of microgravity and 3D seismic data

We dedicate this paper to the memory of Prof. Andres Perez Estaún, who was a great and committed scientist, wonderful colleague and even better friend. The datasets in this work have been funded by Fundación Ciudad de la Energía (Spanish Government, www.ciuden.es) and by the European Union through the “European Energy Programme 15 for Recovery” and the Compostilla OXYCFB300 project. Dr. Juan Alcalde is currently funded by NERC grant NE/M007251/1. Simon Campbell and Samuel Cheyney are acknowledged for thoughtful comments on gravity inversion

3D Visual Data-Driven Spatiotemporal Deformations for Non-Rigid Object Grasping Using Robot Hands

Sensing techniques are important for solving problems of uncertainty inherent to intelligent grasping tasks. The main goal here is to present a visual sensing system based on range imaging technology for robot manipulation of non-rigid objects. Our proposal provides a suitable visual perception system of complex grasping tasks to support a robot controller when other sensor systems, such as tactile and force, are not able to obtain useful data relevant to the grasping manipulation task. In particular, a new visual approach based on RGBD data was implemented to help a robot controller carry out intelligent manipulation tasks with flexible objects. The proposed method supervises the interaction between the grasped object and the robot hand in order to avoid poor contact between the fingertips and an object when there is neither force nor pressure data. This new approach is also used to measure changes to the shape of an object’s surfaces and so allows us to find deformations caused by inappropriate pressure being applied by the hand’s fingers. Test was carried out for grasping tasks involving several flexible household objects with a multi-fingered robot hand working in real time. Our approach generates pulses from the deformation detection method and sends an event message to the robot controller when surface deformation is detected. In comparison with other methods, the obtained results reveal that our visual pipeline does not use deformations models of objects and materials, as well as the approach works well both planar and 3D household objects in real time. In addition, our method does not depend on the pose of the robot hand because the location of the reference system is computed from a recognition process of a pattern located place at the robot forearm. The presented experiments demonstrate that the proposed method accomplishes a good monitoring of grasping task with several objects and different grasping configurations in indoor environments.

Susac's syndrome: Leptomeningeal enhancement on 3D FLAIR MRI

BACKGROUND Contrast-enhanced (ce) fluid-attenuated inversion recovery magnetic resonance imaging (FLAIR MRI) has recently been shown to identify leptomeningeal pathology in multiple sclerosis. OBJECTIVE To demonstrate leptomeningeal enhancement on three-dimensional (3D) FLAIR in a case of Susac's syndrome. METHODS Leptomeningeal enhancement was correlated with clinical activity over 20 months and compared to retinal fluorescein angiography. RESULTS The size, number, and location of leptomeningeal enhancement varied over time and generally correlated with symptom severity. The appearance was remarkably similar to that of retinal vasculopathy. CONCLUSION Ce 3D FLAIR may aid in diagnosis and understanding of pathophysiology in Susac's syndrome and may serve as a biomarker for disease activity.

A novel phantom and method for comprehensive 3-dimensional measurement and correction of geometric distortion in magnetic resonance imaging

A phantom that can be used for mapping geometric distortion in magnetic resonance imaging (MRI) is described. This phantom provides an array of densely distributed control points in three-dimensional (3D) space. These points form the basis of a comprehensive measurement method to correct for geometric distortion in MR images arising principally from gradient field non-linearity and magnet field inhomogeneity. The phantom was designed based on the concept that a point in space can be defined using three orthogonal planes. This novel design approach allows for as many control points as desired. Employing this novel design, a highly accurate method has been developed that enables the positions of the control points to be measured to sub-voxel accuracy. The phantom described in this paper was constructed to fit into a body coil of a MRI scanner, (external dimensions of the phantom were: 310 mm x 310 mm x 310 mm), and it contained 10,830 control points. With this phantom, the mean errors in the measured coordinates of the control points were on the order of 0.1 mm or less, which were less than one tenth of the voxel's dimensions of the phantom image. The calculated three-dimensional distortion map, i.e., the differences between the image positions and true positions of the control points, can then be used to compensate for geometric distortion for a full image restoration. It is anticipated that this novel method will have an impact on the applicability of MRI in both clinical and research settings. especially in areas where geometric accuracy is highly required, such as in MR neuro-imaging. (C) 2004 Elsevier Inc. All rights reserved.

Geometric distortion in clinical MRI systems - Part II: correction using a 3D phantom

In this paper, we present the correction of the geometric distortion measured in the clinical magnetic resonance imaging (MRI) systems reported in the preceding paper (Part 1) using a 3D method based on the phantom-mapped geometric distortion data. This method allows the correction to be made on phantom images acquired without or with the vendor correction applied. With the vendor's 2D correction applied, the method corrects for both the residual geometric distortion still present in the plane in which the correction method was applied (the axial plane) and the uncorrected geometric distortion along the axis non-nal to the plane. The evaluation of the effectiveness of the correction using this new method was carried out through analyzing the residual geometric distortion in the corrected phantom images. The results show that the new method can restore the distorted images in 3D nearly to perfection. For all the MRI systems investigated, the mean absolute deviations in the positions of the control points (along x-, y- and z-axes) measured on the corrected phantom images were all less than 0.2 mm. The maximum absolute deviations were all below similar to0.8 mm. As expected, the correction of the phantom images acquired with the vendor's correction applied in the axial plane performed equally well. Both the geometric distortion still present in the axial plane after applying the vendor's correction and the uncorrected distortion along the z-axis have all been restored. (C) 2004 Elsevier Inc. All rights reserved.