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Realtime Volumetric Deformable Models for Surgery Simulation using Finite Elements and Condensation
 Computer Graphics Forum
, 1996
"... This paper discusses the application of 3D solid volumetric Finite Element models to surgery simulation. In particular it presents three new approaches to the problem of achieving realtime performance for these models. The simulation system we have developed is described and we demonstrate realtim ..."
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Cited by 182 (11 self)
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This paper discusses the application of 3D solid volumetric Finite Element models to surgery simulation. In particular it presents three new approaches to the problem of achieving realtime performance for these models. The simulation system we have developed is described and we demonstrate realtime deformation using the methods developed in the paper. Keywords: Virtual Surgery, RealTime Deformation, Solid Volumetric Deformable Models, Virtual Reality, Finite Element Models. 1 Introduction Speed is overriding concern in Surgery Simulation and it is only in the last few years that realtime surgery simulation has become practically possible. The big problem in surgery simulation is modeling the deformation of solid volumetric objects, which often can have very complex forms, in realtime, ie. 1520 frames/second. Since human organs and tissue have very complex elastic behaviour it has only been possible to model these using very simplistic models. Almost all the attempts have used s...
Arbitrary topology shape reconstruction from planar cross sections
 Graphical Models and Image Processing
, 1996
"... In computed tomography, magnetic resonance imaging and ultrasound imaging, reconstruction of the 3D object from the 2D scalarvalued slices obtained by the imaging system is di cult because of the large spacings between the 2D slices. The aliasing that results from this undersampling in the directio ..."
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Cited by 85 (12 self)
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In computed tomography, magnetic resonance imaging and ultrasound imaging, reconstruction of the 3D object from the 2D scalarvalued slices obtained by the imaging system is di cult because of the large spacings between the 2D slices. The aliasing that results from this undersampling in the direction orthogonal to the slices leads to two problems known as the correspondence problem and the tiling problem. A third problem, known as the branching problem, arises because of the structure of the objects being imaged in these applications. Existing reconstruction algorithms typically address only one or two of these problems. In this paper, we approach all three of these problems simultaneously. This is accomplished by imposing a set of three constraints on the reconstructed surface and then deriving precise correspondence and tiling rules from these constraints. The constraints ensure that the regions tiled by these rules obey physical constructs and have a natural appearance. Regions which cannot be tiled by these rules without breaking one or more constraints are tiled with their medial axis (edge Voronoi diagram). Our implementation of the above approach generates triangles of 3D isosurfaces from input which is either a set of contour data or a volume of image slices. Results obtained with synthetic and actual medical data are presented. There are still speci c cases in which our new approach can generate distorted results, but these cases are much less likely to occur than those which cause distortions in other tiling approaches. 2 1
Structural and functional analyses of human cerebral cortex using a surfacebased atlas.
 J Neurosci
, 1997
"... We have analyzed the geometry, geography, and functional organization of human cerebral cortex using surface reconstructions and cortical flat maps of the left and right hemispheres generated from a digital atlas (the Visible Man). The total surface area of the reconstructed Visible Man neocortex i ..."
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Cited by 83 (2 self)
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We have analyzed the geometry, geography, and functional organization of human cerebral cortex using surface reconstructions and cortical flat maps of the left and right hemispheres generated from a digital atlas (the Visible Man). The total surface area of the reconstructed Visible Man neocortex is 1570 cm 2 (both hemispheres), ϳ70% of which is buried in sulci. By linking the Visible Man cerebrum to the Talairach stereotaxic coordinate space, the locations of activation foci reported in neuroimaging studies can be readily visualized in relation to the cortical surface. The associated spatial uncertainty was empirically shown to have a radius in three dimensions of ϳ10 mm. Application of this approach to studies of visual cortex reveals the overall patterns of activation associated with different aspects of visual function and the relationship of these patterns to topographically organized visual areas. Our analysis supports a distinction between an anterior region in ventral occipitotemporal cortex that is selectively involved in form processing and a more posterior region (in or near areas VP and V4v) involved in both form and color processing. Foci associated with motion processing are mainly concentrated in a region along the occipitotemporal junction, the ventral portion of which overlaps with foci also implicated in form processing. Comparisons between flat maps of human and macaque monkey cerebral cortex indicate significant differences as well as many similarities in the relative sizes and positions of cortical regions known or suspected to be homologous in the two species.
Registration of 3D Intraoperative MR Images of the Brain Using a Finite Element Biomechanical Model
 IEEE Transactions on Medical Imaging
, 2001
"... . We present a new algorithm for the nonrigid registration of 3D Magnetic Resonance (MR) intraoperative image sequences showing brain shift. The algorithm tracks key surfaces (cortical surface and the lateral ventricles) in the image sequence using an active surface algorithm. The volumetric def ..."
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Cited by 77 (19 self)
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. We present a new algorithm for the nonrigid registration of 3D Magnetic Resonance (MR) intraoperative image sequences showing brain shift. The algorithm tracks key surfaces (cortical surface and the lateral ventricles) in the image sequence using an active surface algorithm. The volumetric deformation field of the objects the surfaces are embedded in is then inferred from the displacements at the boundary surfaces using a biomechanical finite element model of these objects. The biomechanical model allows us to analyse characteristics of the deformed tissues, such as stress measures. Initial experiments on an intraoperative sequence of brain shift show a good correlation of the internal brain structures after deformation using our algorithm, and a good capability of measuring surface as well as subsurface shift. We measured distances between landmarks in the deformed initial image and the corresponding landmarks in the target scan. The surface shift was recovered from up ...
Multiscale Medial Loci and Their Properties
"... Blum's medial axes have great strengths, in principle, in intuitively describing object shape in terms of a quasihierarchy of figures. But it is well known that, derived from a boundary, they are damagingly sensitive to detail in that boundary. The development of notions of spatial scale has le ..."
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Cited by 60 (8 self)
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Blum's medial axes have great strengths, in principle, in intuitively describing object shape in terms of a quasihierarchy of figures. But it is well known that, derived from a boundary, they are damagingly sensitive to detail in that boundary. The development of notions of spatial scale has led to some definitions of multiscale medial axes different from the Blum medial axis that considerably overcame the weakness. Three major multiscale medial axes have been proposed: iteratively pruned trees of Voronoi edges [Ogniewicz 1993, Székely 1996, Näf 1996], shock loci of reactiondiffusion equations [Kimia et al. 1995, Siddiqi & Kimia 1996], and height ridges of medialness (cores) [Fritsch et al. 1994, Morse et al. 1993, Pizer et al. 1998]. These are different from the Blum medial axis, and each has different mathematical properties of generic branching and ending properties, singular transitions, and geometry of implied boundary, and they have different strengths and weaknesses for computing object descriptions from images or from object boundaries. These mathematical properties and computational abilities are laid out and compared and contrasted in this paper.
Automatic Landmark Identification using a New Method of Nonrigid Correspondence
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1997
"... . A method for corresponding the boundaries of two shapes is presented. The algorithm locates a matching pair of sparse polygonal approximations, one for each of a pair of boundaries, by minimising a cost function using a greedy algorithm. The cost function expresses the dissimilarity in both the sh ..."
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Cited by 52 (8 self)
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. A method for corresponding the boundaries of two shapes is presented. The algorithm locates a matching pair of sparse polygonal approximations, one for each of a pair of boundaries, by minimising a cost function using a greedy algorithm. The cost function expresses the dissimilarity in both the shape and representation error (with respect to the defining boundary) of the sparse polygons. Results are presented for three classes of shape which exhibit various types of nonrigid deformation. The algorithm is also applied to an automatic landmark identification task for the construction of statistical shape models. 1 Introduction A frequently encountered problem in computer vision is that of finding the transformation which maps the boundary of one object onto that of another. In our case, the two boundaries represent different examples from the same class of object (e.g. two hands) and the mapping is a nonrigid transformation. The application which motivates our work is that of genera...
3D Image Matching Using a Finite Element Based Elastic Deformation Model
 In Proc. of MICCAI’99, LNCS 1679
, 1999
"... . We present a new approach for the computation of the deformation field between three dimensional (3D) images. The deformation field locally minimizes the sum of the squared differences between the images to be matched and is constrained by the physical properties of the different objects repres ..."
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Cited by 45 (8 self)
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. We present a new approach for the computation of the deformation field between three dimensional (3D) images. The deformation field locally minimizes the sum of the squared differences between the images to be matched and is constrained by the physical properties of the different objects represented by the image. The objects are modeled as elastic bodies. Compared to optical flow methods, this approach distinguishes itself by three main characteristics: it can account for the actual physical properties of the objects to be deformed, it can provide us with physical properties of the deformed objects (i.e. stress tensors), and computes a global solution to the deformation instead of a set of local solutions. This latter characteristic is achieved through a finiteelement based scheme. The finite element approach requires the different objects in the images to be meshed. Therefore, a tetrahedral mesh generator using a precomputed case table and specifically suited for segme...
Computational methods for reconstructing and unfolding the cerebral cortex
 Cerb. Cortex
"... We describe computational methods for constructing threedimensional models and unfolded, twodimensional maps of the cerebral cortex. These methods consist of four procedures, including (1) sampling of a surface within the cortex, (2) reconstruction of a threedimensional model of that surface, (3 ..."
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Cited by 41 (0 self)
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We describe computational methods for constructing threedimensional models and unfolded, twodimensional maps of the cerebral cortex. These methods consist of four procedures, including (1) sampling of a surface within the cortex, (2) reconstruction of a threedimensional model of that surface, (3) unfolding of the surface to generate a twodimensional cortical map, and (4) visualization of data on the model and the map. These methods produce structurally accurate representations of tile cortex and have practical advantages over previous manual and automated approaches for flattening the cortex. We illustrate the application of these methods to neuroanatomical data obtained from histological sections of cerebral cortex in the macaque monkey. The approach should be equally useful for structural and functional studies in other species, including humans. In many mammalian species, the cerebral cortex occupies a sufficiently large surface area that it must be extensively fold
Geometric Methods for Vessel Visualization and Quantification  A Survey
 IN GEOMETRIC MODELLING FOR SCIENTIFIC VISUALIZATION
, 2002
"... ... This paper surveys several geometric methods to solve basic visualization and quantification problems like centerline computation, boundary detection, projection techniques, and geometric model generation. ..."
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Cited by 36 (1 self)
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... This paper surveys several geometric methods to solve basic visualization and quantification problems like centerline computation, boundary detection, projection techniques, and geometric model generation.
R.H.: Anatomybased registration of CTscan and intraoperative Xray images for guiding a surgical robot
 IEEE Trans. Med. Imaging
, 1998
"... Abstract — We describe new methods for rigid registration of a preoperative computed tomography (CT)scan image to a set of intraoperative Xray fluoroscopic images, for guiding a surgical robot to its trajectory planned from CT. Our goal is to perform the registration, i.e., compute a rotation and ..."
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Cited by 25 (2 self)
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Abstract — We describe new methods for rigid registration of a preoperative computed tomography (CT)scan image to a set of intraoperative Xray fluoroscopic images, for guiding a surgical robot to its trajectory planned from CT. Our goal is to perform the registration, i.e., compute a rotation and translation of one data set with respect to the other to within a prescribed accuracy, based upon bony anatomy only, without external fiducial markers. With respect to previous approaches, the following aspects are new: 1) we correct the geometric distortion in fluoroscopic images and calibrate them directly with respect to the robot by affixing to it a new calibration device designed as a radiolucent rod with embedded metallic markers, and by moving the device along two planes, while radiographs are being acquired at regular intervals; 2) the registration uses an algorithm for computing the best transformation between a set of lines in three space, the (intraoperative) Xray paths, and a set of points on the surface of the bone (imaged preoperatively), in a statistically robust fashion, using the Cayley parameterization of a rotation; and 3) to find corresponding sets of points to the Xray paths on the surfaces, our new approach consists of extracting the surface apparent contours for a given viewpoint, as a set of closed threedimensional nonplanar curves, before registering the apparent contours to Xray paths. Aside from algorithms, there are a number of major technical difficulties associated with engineering a clinically viable system using anatomy and imagebased registration. To detect and solve them, we have so far conducted two experiments with the surgical robot in an operating room (OR), using CT and fluoroscopic image data of a cadaver bone, and attempting to faithfully simulate clinical conditions. Such experiments indicate that intraoperative Xraybased registration is a promising alternative to markerbased registration for clinical use with our proposed method. Index Terms — Anatomy and imagebased registration, CT, revision total hip replacement surgery, ROBODOC®, Xray fluoroscopy. I.