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21
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 2675 (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.
Estimation of 3D left ventricular deformation from echocardiography,” Med
 Image Anal
, 2001
"... Abstract—The quantitative estimation of regional cardiac deformation from threedimensional (3D) image sequences has important clinical implications for the assessment of viability in the heart wall. We present here a generic methodology for estimating soft tissue deformation which integrates image ..."
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Cited by 62 (6 self)
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Abstract—The quantitative estimation of regional cardiac deformation from threedimensional (3D) image sequences has important clinical implications for the assessment of viability in the heart wall. We present here a generic methodology for estimating soft tissue deformation which integrates imagederived information with biomechanical models, and apply it to the problem of cardiac deformation estimation. The method is image modality independent. The images are segmented interactively and then initial correspondence is established using a shapetracking approach. A dense motion field is then estimated using a transversely isotropic, linearelastic model, which accounts for the muscle fiber directions in the left ventricle. The dense motion field is in turn used to calculate the deformation of the heart wall in terms of strain in cardiac specific directions. The strains obtained using this approach in openchest dogs before and after coronary occlusion, exhibit a high correlation with strains produced in the same animals using implanted markers. Further, they show good agreement with previously published results in the literature. This proposed method provides quantitative regional 3D estimates of heart deformation. Index Terms—Cardiac deformation, left ventricular motion estimation, magnetic resonance imaging, nonrigid motion estimation, validation. I.
Adaptive Multidimensional Filtering
 LINKÖPING UNIVERSITY, SWEDEN
, 1992
"... This thesis contains a presentation and an analysis of adaptive filtering strategies for multidimensional data. The size, shape and orientation of the filter are signal controlled and thus adapted locally to each neighbourhood according to a predefined model. The filter is constructed as a linear we ..."
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Cited by 31 (1 self)
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This thesis contains a presentation and an analysis of adaptive filtering strategies for multidimensional data. The size, shape and orientation of the filter are signal controlled and thus adapted locally to each neighbourhood according to a predefined model. The filter is constructed as a linear weighting of fixed oriented bandpass filters having the same shape but different orientations. The adaptive filtering methods have been tested on both real data and synthesized test data in 2D, e.g. still images, 3D, e.g. image sequences or volumes, with good results. In 4D, e.g. volume sequences, the algorithm is given in its mathematical form. The weighting coefficients are given by the inner products of a tensor representing the local structure of the data and the tensors representing the orientation of the filters. The procedure and filter design in estimating the representation tensor are described. In 2D, the tensor contains information about the local energy, the optimal orientation and a certainty of the orientation. In 3D, the information in the tensor is the energy, the normal to the best fitting local plane and the tangent to the best fitting line, and certainties of these orientations. In the case of time sequences, a quantitative comparison of the proposed method and other (optical flow) algorithms is presented. The estimation of control information is made in different scales. There are two main reasons for this. A single filter has a particular limited pass band which may or may not be tuned to the different sized objects to describe. Second, size or scale is a descriptive feature in its own right. All of this requires the integration of measurements from different scales. The increasing interest in wavelet theory supports the idea that a multiresolution approach is necessary. Hence the resulting adaptive filter will adapt also in size and to different orientations in different scales.
Fast And Accurate ThreeDimensional Reconstruction From ConeBeam Projection Data Using Algebraic Methods
, 1998
"... Conebeam computed tomography (CT) is an emerging imaging technology, as it provides all projections needed for threedimensional (3D) reconstruction in a single spin of the Xray sourcedetector pair. This facilitates fast, lowdose data acquisition as required for imaging fast moving objects, such ..."
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Cited by 10 (1 self)
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Conebeam computed tomography (CT) is an emerging imaging technology, as it provides all projections needed for threedimensional (3D) reconstruction in a single spin of the Xray sourcedetector pair. This facilitates fast, lowdose data acquisition as required for imaging fast moving objects, such as the heart, and intraoperative CT applications. Current conebeam reconstruction algorithms mainly employ the FilteredBackprojection (FBP) approach. In this dissertation, a different class of reconstruction algorithms is studied: the algebraic reconstruction methods. Algebraic reconstruction starts from an initial guess for the reconstructed object and then performs a sequence of iterative grid projections and correction backprojections until the reconstruction has converged. Algebraic methods have many advantages over FBP, such as better noise tolerance and better handling of sparse and nonuniformly distributed projection datasets. So far, the main repellant for using algebraic methods...
ARTICLE NO. IV960489 Shape from Radiological Density
, 1994
"... detected in each slice by means of surface fitting or interpoIn this paper we propose a strategy to solve the problem of lation methods [7–15]. Surface fitting approaches can also recovering the 3D shape of anatomical structures from single be used for the recovery of the approximate shape of an X ..."
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detected in each slice by means of surface fitting or interpoIn this paper we propose a strategy to solve the problem of lation methods [7–15]. Surface fitting approaches can also recovering the 3D shape of anatomical structures from single be used for the recovery of the approximate shape of an Xray images, i.e., the problem of Shape from Radiological anatomical structure from a small set of tomographic or Density (SFRD). In order to overcome the noninvertibility of radiographic images when the boundaries of such a structhe process of image generation, we formulate a minimal set ture or other surface landmarks (obtained, for example, of physical assumptions that are used to constrain SFRD and by matching fiducial points in different views) are availto transform it into a wellposed problem. Our shape recovery able [16–19]. strategy requires the solution of four problems: (a) linearization of the process of Xray image generation, (b) image segmenta The abovementioned methods use the output data of a tion, (c) estimation of a map of the local thickness of each segmentation or a featurematching algorithm as geometric anatomical structure of interest, and (d) recovery of the 3D constraints for the recovery of 3D shape. However, in the shape of each structure from its boundaries and thickness map. case of Xray projective imaging, an additional, important In this paper we assume that problems (a) and (b) have already source of 3D information is available: the selective absorpbeen faced, and propose a solution for problems (c) and (d). tion of Xray photons by the different tissues being imaged. Experimental results on synthetic images, Xray images of Such a source of information is used, for example, in phantoms, and real radiograms are reported. © 1997 Academic Press computed tomography for the reconstruction of a density image from a complete set of projections on the grounds 1.
CI Cardiac index.
"... Abstract—Threedimensional (3D) imaging of the heart is a rapidly developing area of research in medical imaging. Advances in hardware and methods for fast spatiotemporal cardiac imaging are extending the frontiers of clinical diagnosis and research on cardiovascular diseases. In the last few year ..."
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Abstract—Threedimensional (3D) imaging of the heart is a rapidly developing area of research in medical imaging. Advances in hardware and methods for fast spatiotemporal cardiac imaging are extending the frontiers of clinical diagnosis and research on cardiovascular diseases. In the last few years, many approaches have been proposed to analyze images and extract parameters of cardiac shape and function from a variety of cardiac imaging modalities. In particular, techniques based on spatiotemporal geometric models have received considerable attention. This paper surveys the literature of two decades of research on cardiac modeling. The contribution of the paper is threefold: 1) to serve as a tutorial of the field for both clinicians and technologists, 2) to provide an extensive account of modeling techniques in a comprehensive and systematic manner, and 3) to critically review these approaches in terms of their performance and degree of clinical evaluation with respect to the final goal of cardiac functional analysis. From this review it is concluded that whereas 3D modelbased approaches have the capability to improve the diagnostic value of cardiac images, issues as robustness, 3D interaction, computational complexity and clinical validation still require significant attention. Index Terms—Cardiac imaging, functional analysis, modelbased image analysis.
Resonance, Ultrasound, and XRay CT images. Estimation of 3D Left Ventricular Deformation from Medical Images Using Biomechanical Models
, 2000
"... The noninvasive quantitative estimation of regional cardiac deformation has important clinical implications for the assessment of viability in the heart wall. In this work we describe a general framework for estimating soft tissue deformation from sequences of threedimensional medical images. We a ..."
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The noninvasive quantitative estimation of regional cardiac deformation has important clinical implications for the assessment of viability in the heart wall. In this work we describe a general framework for estimating soft tissue deformation from sequences of threedimensional medical images. We also explore some of their theoretical constraints which can be used to guide the selection of an appropriate model for the displacement field. We then apply this framework to the problem of estimating left ventricular deformations from sequences of 3D image sequences. The images are segmented interactively to extract the endocardial and epicardial surfaces. Then, initial frametoframe correspondences are established between points on the surfaces using a shapetracking approach. The myocardium is modeled using a transversely isotropic linear elastic model, which accounts for the preferential stiffness of the left ventricular myocardium along its fiber directions. The measurements and the model are integrated within a Bayesian estimation framework. The resulting equations are solved using the finite element method, to produce a dense displacement field for the whole of the left ventricle. The dense displacement field is, in turn, used to calculate the deformation of the heart wall in terms of the strains.
4 Measurement of Projection Data
"... The mathematical algorithms for tomographic reconstructions described in Chapter 3 are based on projection data. These projections can represent, for example, the attenuation of xrays through an object as in conventional xray tomography, the decay of radioactive nucleoids in the body as in emissio ..."
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The mathematical algorithms for tomographic reconstructions described in Chapter 3 are based on projection data. These projections can represent, for example, the attenuation of xrays through an object as in conventional xray tomography, the decay of radioactive nucleoids in the body as in emission tomography, or the refractive index variations as in ultrasonic tomography. This chapter will discuss the measurement of projection data with energy that travels in straight lines through objects. This is always the case when a human body is illuminated with xrays and is a close approximation to what happens when ultrasonic tomography is used for the imaging of soft biological tissues (e.g., the female breast). Projection data, by their very nature, are a result of interaction between the radiation used for imaging and the substance of which the object is composed. To a first approximation, such interactions can be modeled as measuring integrals of some characteristic of the object. A simple example of this is the attenuation a beam of xrays undergoes as it travels through an object. A line
Research Article ConeBeam CompositeCircling Scan and Exact Image Reconstruction for a QuasiShort Object
, 2007
"... Here we propose a conebeam compositecircling mode to solve the quasishort object problem, which is to reconstruct a short portion of a long object from longitudinally truncated conebeam data involving the short object. In contrast to the saddle curve conebeam scanning, the proposed scanning mod ..."
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Here we propose a conebeam compositecircling mode to solve the quasishort object problem, which is to reconstruct a short portion of a long object from longitudinally truncated conebeam data involving the short object. In contrast to the saddle curve conebeam scanning, the proposed scanning mode requires that the Xray focal spot undergoes a circular motion in a plane facing the short object, while the Xray source is rotated in the gantry main plane. Because of the symmetry of the proposed mechanical rotations and the compatibility with the physiological conditions, this new mode has significant advantages over the saddle curve from perspectives of both engineering implementation and clinical applications. As a feasibility study, a backprojection filtration (BPF) algorithm is developed to reconstruct images from data collected along a compositecircling trajectory. The initial simulation results demonstrate the correctness of the proposed exact reconstruction method and the merits of the proposed mode. Copyright © 2007 H. Yu and G. Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.