Level set diagrams of polyhedral objects

Lazarus, Francis; Verroust, Anne

doi:10.1145/304012.304025

Cited by 107 publications

(84 citation statements)

References 22 publications

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“…The second reference length L 2 is defined as the distance between the bifurcating point of the skeleton branches and the apex of the anastomosis, the location where the graft and the proximal branches separate. The apex location is found by calculating the shortest distance from the centroid of the distal branch exit over the surface of the graft [34]. The apex is the location where the contours of equal distance from the exit last join before dividing into the graft and proximal branches.…”

Section: Topology Characterization Via Skeletonizationmentioning

confidence: 99%

Reconstruction of shape and its effect on flow in arterial conduits

Gambaruto

Peiró

Doorly

et al. 2007

Numerical Methods in Fluids

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SUMMARYThe geometry of arterial conduits derived from in vivo image data is subject to acquisition and reconstruction errors. This results in a degree of uncertainty in defining the bounding geometry for a patient-specific anatomical conduit. In applying computational fluid dynamics to model the flow in specific anatomical configurations, the effect of the uncertainty in boundary definition should be considered, particularly if the objective is to extract quantitative measures of the local haemodynamics.Taking an example of a bypass graft configuration, we examine the effects of image threshold, surface smoothing and semi-idealization on the modelled geometry and the resulting flow. Procedures for reconstruction from medical images are outlined and applied with different parameter values within the image uncertainty range to create alternative models from the same data set.Methods to characterize the flow structure and wall shear stress (WSS) are introduced and used to provide quantitative comparison of the different haemodynamic environments associated with the varying model geometries. Comparable effects on the WSS distribution are found to occur with progressively increased surface smoothing and semi-idealization of the geometry by elliptical section fitting. Significant differences in WSS correspond to different threshold choices.

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Section: Topology Characterization Via Skeletonizationmentioning

confidence: 99%

Reconstruction of shape and its effect on flow in arterial conduits

Gambaruto

Peiró

Doorly

et al. 2007

Numerical Methods in Fluids

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“…An equivalent statement of our Index Theorem appeared independently in [30]. A special case was obtained by Banchoff [1] and used by Lazarus and Verroust [28]. However, their theorem applies only to so-called null-cohomologous one-forms (arising from the differences of a scalar potential field defined on the mesh vertices) over a triangle mesh, and thus does not consider faces of non-zero index.…”

Section: Sign Changes and Indicesmentioning

confidence: 99%

Discrete one-forms on meshes and applications to 3D mesh parameterization

Gortler

Gotsman

Thurston

2006

Computer Aided Geometric Design

109

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We describe how some simple properties of discrete one-forms directly relate to some old and new results concerning the parameterization of 3D mesh data. Our first result is an easy proof of Tutte's celebrated "spring-embedding" theorem for planar graphs, which is widely used for parameterizing meshes with the topology of a disk as a planar embedding with a convex boundary. Our second result generalizes the first, dealing with the case where the mesh contains multiple boundaries, which are free to be non-convex in the embedding. We characterize when it is still possible to achieve an embedding, despite these boundaries being non-convex. The third result is an analogous embedding theorem for meshes with genus 1 (topologically equivalent to the torus). Applications of these results to the parameterization of meshes with disk and toroidal topologies are demonstrated. Extensions to higher genus meshes are discussed.

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“…A good criterion to decide which points to disregard is determining a length of reference L as the distance between the junction point and the apex of the junction. This can be done by automatically locating a saddle point on the surface as described in [9]. The exclusion of these points leads to measures that are more representative of the angles defined by the axes of the branches of the model bifurcation.…”

Section: Reconstruction and Analysis Of A Model Anastomosismentioning

confidence: 99%

Classification of peripheral distal by-pass geometries obtained via reconstruction from MRI

Giordana¹,

Peiró²,

Sherwin³

et al. 2002

ESAIM: Proc.

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Abstract. This paper discusses the application of a set of computer graphics tools to the reconstruction of three-dimensional models from medical images. Specifically, this work is focused on in-vivo Magnetic Resonance Imaging (MRI) of the distal anastomosis of peripheral by-pass grafts. The aim of this study is the morphological classification of different anastomoses and the identification of correlations between shape, or more precisely a set of parameters representing shape, and blood flow patterns. Flows patterns are calculated using computational fluid dynamics (CFD) techniques on suitable computer representations of the reconstructed geometries. The reconstruction of a three-dimensional model of an anastomosis starts from a stack of planar sections of the lumen of the blood vessels produced by segmenting the MR images. An implicit function is fitted through the sections and it is chosen so that its zero-level contour is the interpolating surface of minimum curvature. A skeletonization algorithm extracts an approximation to the medial line of the threedimensional models. This medial line is used to determine the angles that blood vessels form at the anastomosis. The deviation of the medial line of the grafted vessel from the plane of the anastomosis yields a measure of planarity. These parameters allow a preliminary classification of shape. Scanning the same patient at different times postoperatively also allows to monitor changes in the shape of an anastomosis. Furthermore, scanning the same patient more than once, in different MRI scanners and at different resolutions constitutes an experimental validation of the reconstruction technique.

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Level set diagrams of polyhedral objects

Cited by 107 publications

References 22 publications

Reconstruction of shape and its effect on flow in arterial conduits

Reconstruction of shape and its effect on flow in arterial conduits

Discrete one-forms on meshes and applications to 3D mesh parameterization

Classification of peripheral distal by-pass geometries obtained via reconstruction from MRI

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