Results 1  10
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14
Marching cubes: A high resolution 3D surface construction algorithm
 COMPUTER GRAPHICS
, 1987
"... We present a new algorithm, called marching cubes, that creates triangle models of constant density surfaces from 3D medical data. Using a divideandconquer approach to generate interslice connectivity, we create a case table that defines triangle topology. The algorithm processes the 3D medical d ..."
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Cited by 2070 (4 self)
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We present a new algorithm, called marching cubes, that creates triangle models of constant density surfaces from 3D medical data. Using a divideandconquer approach to generate interslice connectivity, we create a case table that defines triangle topology. The algorithm processes the 3D medical data in scanline order and calculates triangle vertices using linear interpolation. We find the gradient of the original data, normalize it, and use it as a basis for shading the models. The detail in images produced from the generated surface models is the result of maintaining the interslice connectivity, surface data, and gradient information present in the original 3D data. Results from computed tomography (CT), magnetic resonance (MR), and singlephoton emission computed tomography (SPECT) illustrate the quality and functionality of marching cubes. We also discuss improvements that decrease processing time and add solid modeling capabilities.
Noise Removal Using FourthOrder Partial Differential Equations with Applications to Medical Magnetic Resonance Images in Space and Time
 IEEE Trans. Imag. Proc
, 2003
"... In this paper we introduce a new method for image smoothing based on a fourth order PDE model. The method is tested on a broad range of medical magnetic resonance images, both in space and time, as well as on nonmedical test images. Our algorithm demonstrates good noise suppression with preservatio ..."
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Cited by 43 (5 self)
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In this paper we introduce a new method for image smoothing based on a fourth order PDE model. The method is tested on a broad range of medical magnetic resonance images, both in space and time, as well as on nonmedical test images. Our algorithm demonstrates good noise suppression with preservation of edges and contours and without destruction of important anatomical or functional detail, even at poor signaltonoise ratios. We have also compared our method with a related secondorder PDE model and nd our method to perform overall better on the images being tested.
Statistical issues in fMRI for brain imaging
 International Statistical Review
, 2001
"... Functional magnetic resonance imaging is a technique developed in the last decade and used in the elds of cognitive psychology and neuroscience, among others, to study the processes underlying the working of the human brain. In this paper we examine some of the statistical issues in functional magne ..."
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Cited by 8 (1 self)
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Functional magnetic resonance imaging is a technique developed in the last decade and used in the elds of cognitive psychology and neuroscience, among others, to study the processes underlying the working of the human brain. In this paper we examine some of the statistical issues in functional magnetic resonance imaging for brain research. We start by giving a brief introduction to the physics of magnetic resonance imaging. Using a psychological experiment as a case study, we then describe questions of design and statistical analysis. The data obtained from functional magnetic resonance imaging studies are of a highly complex nature, displaying both spatial and temporal correlation, as well as high levels of noise from di erent sources. Given this, the scope for statistics is vast, and is not limited to simple analysis of the data, once collected.
MRI Geometric Distortion: a simple approach to correcting the effects of nonlinear gradient fields
 J. Magn. Reson. Imaging
, 1999
"... We present a method to correct intensity variations and voxel shifts caused by nonlinear gradient fields in Magnetic Resonance Images. The principal sources of distortion are briefly exposed, as well as the methods of correction currently in use. The implication of the gradient fields nonlineariti ..."
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Cited by 7 (0 self)
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We present a method to correct intensity variations and voxel shifts caused by nonlinear gradient fields in Magnetic Resonance Images. The principal sources of distortion are briefly exposed, as well as the methods of correction currently in use. The implication of the gradient fields nonlinearities on the signal equations are described in a detailed way for the case of 2D and 3D Fourier imagery. A model of these nonlinearities, derived from the geometry of the gradient coils, is proposed and then applied in postprocessing to correct any images regardless of the acquisition sequence. Initial position errors, as large as 4 mm (i.e. 4 voxels of 1x1x1.4 mm ) before correction, are reduced to less than the voxel sizes after correction. Keywords Magnetic resonance imaging . Image distortion correction . Nonlinear gradient fields
Algorithms in Tomography
 The State of the Art in Numerical Analysis
, 1997
"... this paper is as follows. In section 2 we survey the mathematical models used in tomography. In section 3 we give a fairly detailed survey on 2D reconstruction algorithm which still are the work horse of tomography. In section 4 we describe recent developments in 3D reconstruction. In section 5 we m ..."
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Cited by 3 (0 self)
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this paper is as follows. In section 2 we survey the mathematical models used in tomography. In section 3 we give a fairly detailed survey on 2D reconstruction algorithm which still are the work horse of tomography. In section 4 we describe recent developments in 3D reconstruction. In section 5 we make a few remarks on the beginning development of algorithms for nonstraight line tomography. 2 Mathematical Models in Tomography
A �space analysis of MR tagging
 J Magn. Reson
, 2000
"... We present a kspace approximation that directly relates a pulse sequence to its residual pattern of zdirected magnetization M z, in a manner akin to the kspace approximation for small tipangle excitation. Our approximation is particularly useful for the analysis and design of tagging sequences, ..."
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Cited by 2 (1 self)
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We present a kspace approximation that directly relates a pulse sequence to its residual pattern of zdirected magnetization M z, in a manner akin to the kspace approximation for small tipangle excitation. Our approximation is particularly useful for the analysis and design of tagging sequences, in which M z is the important quantity—as opposed to the transverse magnetization components M x and M y considered in selective excitation. We demonstrate that our approximation provides new insights into tagging, can be used to design novel tag patterns, and, more generally, may be applied to selective presaturation sequences for purposes other than tagging. © 2000 Academic Press Key Words: tagging; pulse sequences; small tipangle approximation; k space; presaturation.
Computerized Tomography and its Applications: a Guided Tour
 Special Issue on Image Processing, Nieuw Archief voor Wiskunde
, 1992
"... this paper is as follows. The first part is devoted to an overview of the mathematical principles of CT (Section 2). We present the Radon transform, related transforms, inversion formulas, uniqueness, the ranges, illposedness, sampling, reconstruction algorithms and diffraction tomography; then a n ..."
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Cited by 2 (0 self)
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this paper is as follows. The first part is devoted to an overview of the mathematical principles of CT (Section 2). We present the Radon transform, related transforms, inversion formulas, uniqueness, the ranges, illposedness, sampling, reconstruction algorithms and diffraction tomography; then a number of generalizations are mentioned and we finish with some historical remarks. The second part (Section 3) contains a case study of magnetic resonance imaging, a field in which we have gained some personal experience over the last years. 2 The Mathematics
NonFourier Encoded Parallel MRI Using Multiple Receiver Coils
"... This paper describes a general theoretical framework combining nonFourier spatially encoded MR imaging with multichannel acquisition parallel MR imaging. The two spatial encoding mechanisms are physically and analytically separable, allowing nonFourier encoding to be expressed as complementary to ..."
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This paper describes a general theoretical framework combining nonFourier spatially encoded MR imaging with multichannel acquisition parallel MR imaging. The two spatial encoding mechanisms are physically and analytically separable, allowing nonFourier encoding to be expressed as complementary to the inherent encoding imposed by RF receiver coil sensitivities. Consequently, the number of nonFourier spatial encoding steps necessary to fully encode a FOV is reduced. Furthermore, by casting the FOV reduction of parallel imaging techniques as a dimensionality reduction of the kspace that is nonFourier encoded, a speedup of each digital nonFourier spatial excitation may be obtained in addition to imaging acceleration. Images acquired at speedup factors of 2x to 8x using a 4element RF receiver coil array demonstrate use of the framework and the efficiency afforded by it. Key words: NonFourier spatial encoding; Parallel Imaging;
Stochastic Estimation of Deformable Motion from Magnetic Resonance Tagged Cardiac Images
, 1994
"... The estimation of heart motion from image sequence data has received a great deal of attention in recent years because cardiac motion is complex and analysis of cardiac motion can be used to diagnose damage to the heart muscle caused by a heart attack. Magnetic resonance imaging has shown great prom ..."
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The estimation of heart motion from image sequence data has received a great deal of attention in recent years because cardiac motion is complex and analysis of cardiac motion can be used to diagnose damage to the heart muscle caused by a heart attack. Magnetic resonance imaging has shown great promise for imaging cardiac motion because of a technique called tagging. Tagged images appear with a spatially encoded pattern that moves with the heart tissue as it moves through the heart cycle. In this dissertation we develop two new approaches to cardiac motion estimation that exploit MR tagging techniques. Both approaches are developed within a stochastic estimation framework, which serves as an important unifying theme. In the first approach, we use Horn and Schunck's optical flow (HSOF) algorithm to estimate motion and design a continuously varying tag pattern that is optimal for the HSOF algorithm. An optimal tag pattern is determined by formulating HSOF as a stochastic linear smoother ...
Image Segmentation with Kohonen Neural Network SelfOrganising Maps.
"... Kohonen [1,2] has developed an algorithm with selforganising properties for a network of adaptive elements. These elements receive signals from an event space and the signal representations are automatically mapped onto a set of output responses in such a way that these responses acquire the same to ..."
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Kohonen [1,2] has developed an algorithm with selforganising properties for a network of adaptive elements. These elements receive signals from an event space and the signal representations are automatically mapped onto a set of output responses in such a way that these responses acquire the same topological order as that of the primary events. Images can be processed to become the input signals for the SelfOrganising Maps (SOM) and the output neurones that have adapted to the image, present interesting features such as contourextraction and edge detection. In this work the Kohonen algorithm was programmed and medical images were used as input to prove the convergence of the algorithm. Keywords: Neural Networks, Image Segmentation, Self  Organising Maps. 1.