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18
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 2119 (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 47 (5 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 (0 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 9 (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...
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
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.
an der Technischen Universität Wien, Fakultät für Technische Naturwissenschaften und Informatik,
"... eines Doktors der technischen Wissenschaften unter der Leitung von ..."
3 Algorithms for Reconstruction
"... In this chapter we will deal with the mathematical basis of tomography with nondiffracting sources. We will show how one can go about recovering the image of the cross section of an object from the projection data. In ideal situations, projections are a set of measurements of the integrated values o ..."
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In this chapter we will deal with the mathematical basis of tomography with nondiffracting sources. We will show how one can go about recovering the image of the cross section of an object from the projection data. In ideal situations, projections are a set of measurements of the integrated values of some parameter of the objectintegrations being along straight lines through the object and being referred to as line integrals. We will show that the key to tomographic imaging is the Fourier Slice Theorem which relates the measured projection data to the twodimensional Fourier transform of the object cross section. This chapter will start with the definition of line integrals and how they are combined to form projections of an object. By finding the Fourier transform of a projection taken along parallel lines, we will then derive the Fourier Slice Theorem. The reconstruction algorithm used depends on the type of projection data measured; we will discuss algorithms based on parallel beam projection data and two types of fan beam data. 3.1 Line Integrals and Projections A line integral, as the name implies, represents the integral of some parameter of the object along a line. In this chapter we will not concern ourselves with the physical phenomena that generate line integrals, but a typical example is the attenuation of xrays as they propagate through biological tissue. In this case the object is modeled as a twodimensional (or threedimensional) distribution of the xray attenuation constant and a line integral represents the total attenuation suffered by a beam of xrays as it travels in a straight line through the object. More details of this process and other examples will be presented in Chapter 4. We will use the coordinate system defined in Fig. 3.1 to describe line integrals and projections. In this example the object is represented by a twodimensional function f(x, y) and each line integral by the (6, t) parameters. The equation of line AB in Fig. 3.1 is x cos 8+y sin O=t (1)
3D nonrigid motion analysis under small deformations
"... We present a novel method for estimating motion parameters and point correspondences between 3D surfaces under small nonrigid motion. A vector point function is utilized as the motion parameter, called the displacement function. Differentialgeometric changes of surfaces are then used in tracking sm ..."
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We present a novel method for estimating motion parameters and point correspondences between 3D surfaces under small nonrigid motion. A vector point function is utilized as the motion parameter, called the displacement function. Differentialgeometric changes of surfaces are then used in tracking small deformations. Discriminant (of first fundamental form), unitnormal and Gaussian curvature are the invariant differentialgeometric parameters that have been utilized for nonrigid motion analysis. Tests were performed by generating nonrigid motion on a simulated data set to illustrate performance and accuracy of our algorithms. Experiments were then performed on a Cyberware range data sequence of facial motion. A total of 16 sets of facial motion images were used in our experiments, belonging to eight different persons, each having two facial expressions. We have demonstrated the correct point correspondence recovery by tracking features of the face during each facial expression and comparing against the manual tracking of feature points by different users. In addition, nonrigid motion segmentation and interpolation of intermediate frames of data were successfully performed on these images. We have also performed experiments on cardiac data in order to estimate the motion parameters related to the abnormality in cardiac motion. Two sets of volumetric CT data of the left ventricle of a dog’s heart in cardiac cycle were used in our experiments. All our experiments indicate that the system performs very well and proves to be extremely useful in other nonrigid motion analysis applications.