31 research outputs found

    3D Mesh Skeleton Extraction Using Topological and Geometrical Analyses

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    International audienceThis paper describes a novel and unified approach for Reeb graph construction and simplification as well as constriction approximation on 3D polygonal meshes. The key idea of our algorithm is that discrete contours - curves carried by the edges of the mesh and approximating the continuous contours of a mapping function - encode both topological and geometrical shape characteristics. Firstly, mesh feature points are computed. Then they are used as geodesic origins for the computation of an invariant mapping function that reveals the shape most significant features. Secondly, for each vertex in the mesh, its discrete contour is computed. As the set of discrete contours recovers the whole surface, each of them can be analyzed, both to detect topological changes or constrictions. Constriction approximations enable Reeb graphs refinement into more visually meaningful skeletons, that we refer as enhanced topological skeletons. Without pre-processing stages and without input parameters, our method provides nice-looking and affine- invariant skeletons, with satisfactory execution times. This makes enhanced topological skeletons good candidates for applications needing high level shape representations, such as mesh deformation (experimented in this paper), retrieval, compression, metamorphosis, etc

    Numerical Methods in Shape Spaces and Optimal Branching Patterns

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    The contribution of this thesis is twofold. The main part deals with numerical methods in the context of shape space analysis, where the shape space at hand is considered as a Riemannian manifold. In detail, we apply and extend the time-discrete geodesic calculus (established by Rumpf and Wirth [WBRS11, RW15]) to the space of discrete shells, i.e. triangular meshes with fixed connectivity. The essential building block is a variational time-discretization of geodesic curves, which is based on a local approximation of the squared Riemannian distance on the manifold. On physical shape spaces this approximation can be derived e.g. from a dissimilarity measure. The dissimilarity measure between two shell surfaces can naturally be defined as an elastic deformation energy capturing both membrane and bending distortions. Combined with a non-conforming discretization of a physically sound thin shell model the time-discrete geodesic calculus applied to the space of discrete shells is shown to be suitable to solve important problems in computer graphics and animation. To extend the existing calculus, we introduce a generalized spline functional based on the covariant derivative along a curve in shape space whose minimizers can be considered as Riemannian splines. We establish a corresponding time-discrete functional that fits perfectly into the framework of Rumpf and Wirth, and prove this discretization to be consistent. Several numerical simulations reveal that the optimization of the spline functional—subject to appropriate constraints—can be used to solve the multiple interpolation problem in shape space, e.g. to realize keyframe animation. Based on the spline functional, we further develop a simple regression model which generalizes linear regression to nonlinear shape spaces. Numerical examples based on real data from anatomy and botany show the capability of the model. Finally, we apply the statistical analysis of elastic shape spaces presented by Rumpf and Wirth [RW09, RW11] to the space of discrete shells. To this end, we compute a Fréchet mean within a class of shapes bearing highly nonlinear variations and perform a principal component analysis with respect to the metric induced by the Hessian of an elastic shell energy. The last part of this thesis deals with the optimization of microstructures arising e.g. at austenite-martensite interfaces in shape memory alloys. For a corresponding scalar problem, Kohn and Müller [KM92, KM94] proved existence of a minimizer and provided a lower and an upper bound for the optimal energy. To establish the upper bound, they studied a particular branching pattern generated by mixing two different martensite phases. We perform a finite element simulation based on subdivision surfaces that suggests a topologically different class of branching patterns to represent an optimal microstructure. Based on these observations we derive a novel, low dimensional family of patterns and show—numerically and analytically—that our new branching pattern results in a significantly better upper energy bound

    Patient-Specific Identification of Atrial Flutter Vulnerability–A Computational Approach to Reveal Latent Reentry Pathways

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    Atypical atrial flutter (AFlut) is a reentrant arrhythmia which patients frequently develop after ablation for atrial fibrillation (AF). Indeed, substrate modifications during AF ablation can increase the likelihood to develop AFlut and it is clinically not feasible to reliably and sensitively test if a patient is vulnerable to AFlut. Here, we present a novel method based on personalized computational models to identify pathways along which AFlut can be sustained in an individual patient. We build a personalized model of atrial excitation propagation considering the anatomy as well as the spatial distribution of anisotropic conduction velocity and repolarization characteristics based on a combination of a priori knowledge on the population level and information derived from measurements performed in the individual patient. The fast marching scheme is employed to compute activation times for stimuli from all parts of the atria. Potential flutter pathways are then identified by tracing loops from wave front collision sites and constricting them using a geometric snake approach under consideration of the heterogeneous wavelength condition. In this way, all pathways along which AFlut can be sustained are identified. Flutter pathways can be instantiated by using an eikonal-diffusion phase extrapolation approach and a dynamic multifront fast marching simulation. In these dynamic simulations, the initial pattern eventually turns into the one driven by the dominant pathway, which is the only pathway that can be observed clinically. We assessed the sensitivity of the flutter pathway maps with respect to conduction velocity and its anisotropy. Moreover, we demonstrate the application of tailored models considering disease-specific repolarization properties (healthy, AF-remodeled, potassium channel mutations) as well as applicabiltiy on a clinical dataset. Finally, we tested how AFlut vulnerability of these substrates is modulated by exemplary antiarrhythmic drugs (amiodarone, dronedarone). Our novel method allows to assess the vulnerability of an individual patient to develop AFlut based on the personal anatomical, electrophysiological, and pharmacological characteristics. In contrast to clinical electrophysiological studies, our computational approach provides the means to identify all possible AFlut pathways and not just the currently dominant one. This allows to consider all relevant AFlut pathways when tailoring clinical ablation therapy in order to reduce the development and recurrence of AFlut

    Patient-Specific Identification of Atrial Flutter Vulnerability–A Computational Approach to Reveal Latent Reentry Pathways

    Get PDF
    Atypical atrial flutter (AFlut) is a reentrant arrhythmia which patients frequently develop after ablation for atrial fibrillation (AF). Indeed, substrate modifications during AF ablation can increase the likelihood to develop AFlut and it is clinically not feasible to reliably and sensitively test if a patient is vulnerable to AFlut. Here, we present a novel method based on personalized computational models to identify pathways along which AFlut can be sustained in an individual patient. We build a personalized model of atrial excitation propagation considering the anatomy as well as the spatial distribution of anisotropic conduction velocity and repolarization characteristics based on a combination of a priori knowledge on the population level and information derived from measurements performed in the individual patient. The fast marching scheme is employed to compute activation times for stimuli from all parts of the atria. Potential flutter pathways are then identified by tracing loops from wave front collision sites and constricting them using a geometric snake approach under consideration of the heterogeneous wavelength condition. In this way, all pathways along which AFlut can be sustained are identified. Flutter pathways can be instantiated by using an eikonal-diffusion phase extrapolation approach and a dynamic multifront fast marching simulation. In these dynamic simulations, the initial pattern eventually turns into the one driven by the dominant pathway, which is the only pathway that can be observed clinically. We assessed the sensitivity of the flutter pathway maps with respect to conduction velocity and its anisotropy. Moreover, we demonstrate the application of tailored models considering disease-specific repolarization properties (healthy, AF-remodeled, potassium channel mutations) as well as applicabiltiy on a clinical dataset. Finally, we tested how AFlut vulnerability of these substrates is modulated by exemplary antiarrhythmic drugs (amiodarone, dronedarone). Our novel method allows to assess the vulnerability of an individual patient to develop AFlut based on the personal anatomical, electrophysiological, and pharmacological characteristics. In contrast to clinical electrophysiological studies, our computational approach provides the means to identify all possible AFlut pathways and not just the currently dominant one. This allows to consider all relevant AFlut pathways when tailoring clinical ablation therapy in order to reduce the development and recurrence of AFlut

    Generating anatomical substructures for physically-based facial animation.

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    Physically-based facial animation techniques are capable of producing realistic facial deformations, but have failed to find meaningful use outside the academic community because they are notoriously difficult to create, reuse, and art-direct, in comparison to other methods of facial animation. This thesis addresses these shortcomings and presents a series of methods for automatically generating a skull, the superficial musculoaponeurotic system (SMAS – a layer of fascia investing and interlinking the mimic muscle system), and mimic muscles for any given 3D face model. This is done toward (the goal of) a production-viable framework or rig-builder for physically-based facial animation. This workflow consists of three major steps. First, a generic skull is fitted to a given head model using thin-plate splines computed from the correspondence between landmarks placed on both models. Second, the SMAS is constructed as a variational implicit or radial basis function surface in the interface between the head model and the generic skull fitted to it. Lastly, muscle fibres are generated as boundary-value straightest geodesics, connecting muscle attachment regions defined on the surface of the SMAS. Each step of this workflow is developed with speed, realism and reusability in mind

    QUANTIFICATION OF CORONARY FLOW VELOCITY VIA CONTRAST DISPERSION PATTERNS: INSIGHTS FROM COMPUTATIONAL MODELING AND COMPUTED TOMOGRAPHY EXPERIMENTS

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    Advances in multi-detector cardiac computed tomography (CT) have expanded its use beyond coronary atherosclerosis to a suite of functional myocardial imaging options that now closely parallels magnetic resonance imaging; including ventricular function, viability and perfusion. Despite these advances, there are currently no existing CT based methods to assess coronary luminal blood flow/hemodynamics. Recent studies have shown that CT derived axial transluminal contrast gradients (TCG) are greater in coronary arteries with atherosclerotic lesions when compared with normal arteries; suggesting TCG may be related to local coronary hemodynamics. Despite this provocative observation, the basic mechanisms responsible for TCG and their possible connection with coronary hemodynamics have not been explained. In the current work, we hypothesize that TCG is related to the temporal gradients of the contrast bolus and that TCG encodes coronary flow velocity. An analytical relationship between spatial (TCG) and temporal measurements of contrast dispersion is proposed and this allows for estimation of coronary flow velocity from TCG. This is a novel method (called transluminal attenuation flow encoding-TAFE) integrates: a) anatomic features of the coronary vessels, b) TCG and c) temporal gradients in contrast associated with the arterial input function (AIF) that are readily available in conventional CT to allow non-invasive CT derived coronary flow quantification. The TAFE formulation is validated in computational models as well as in CT-compatible experimental phantom studies with configurations that mimic coronary vessels. The experimental studies revealed factors that were absent in computational modeling including imaging artifacts and imaging reconstruction kernels where by imaging analysis TAFE has been modified. In addition, computational simulations of the aortic arch including a semi-patient specific aortic valve model were performed to study contrast dispersion through the arch. This study was done to assess a key assumption in TAFE, that the clinically available AIF at the descending aorta can be used as an accurate estimate of the AIF at the coronary ostium.. The work provides support for the ability of TAFE to provide quantitative estimates of coronary flow velocity but also reveals a number of issues that require further assessment for improved accuracy of TAFE

    Generating anatomical substructures for physically-based facial animation

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    Physically-based facial animation techniques are capable of producing realistic facial deformations, but have failed to find meaningful use outside the academic community because they are notoriously difficult to create, reuse, and art-direct, in comparison to other methods of facial animation. This thesis addresses these shortcomings and presents a series of methods for automatically generating a skull, the superficial musculoaponeurotic system (SMAS – a layer of fascia investing and interlinking the mimic muscle system), and mimic muscles for any given 3D face model. This is done toward (the goal of) a production-viable framework or rig-builder for physically-based facial animation. This workflow consists of three major steps. First, a generic skull is fitted to a given head model using thin-plate splines computed from the correspondence between landmarks placed on both models. Second, the SMAS is constructed as a variational implicit or radial basis function surface in the interface between the head model and the generic skull fitted to it. Lastly, muscle fibres are generated as boundary-value straightest geodesics, connecting muscle attachment regions defined on the surface of the SMAS. Each step of this workflow is developed with speed, realism and reusability in mind.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

    Generating anatomical substructures for physically-based facial animation

    Get PDF
    Physically-based facial animation techniques are capable of producing realistic facial deformations, but have failed to find meaningful use outside the academic community because they are notoriously difficult to create, reuse, and art-direct, in comparison to other methods of facial animation. This thesis addresses these shortcomings and presents a series of methods for automatically generating a skull, the superficial musculoaponeurotic system (SMAS – a layer of fascia investing and interlinking the mimic muscle system), and mimic muscles for any given 3D face model. This is done toward (the goal of) a production-viable framework or rig-builder for physically-based facial animation. This workflow consists of three major steps. First, a generic skull is fitted to a given head model using thin-plate splines computed from the correspondence between landmarks placed on both models. Second, the SMAS is constructed as a variational implicit or radial basis function surface in the interface between the head model and the generic skull fitted to it. Lastly, muscle fibres are generated as boundary-value straightest geodesics, connecting muscle attachment regions defined on the surface of the SMAS. Each step of this workflow is developed with speed, realism and reusability in mind.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

    From a Closed Piecewise Geodesic to a Constriction on a Closed Triangulated Surface

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    http://www.computer.org/Constrictions on a surface are defined as simple closed curves whose length is locally minimal. In particular, constrictions are periodic geodesics. We use constrictions in order to segment objects. In [Hetroy and Attali, VisSym 2003], we proposed an approach based on progressive surface simplification and local geodesic computation. The drawback of this approach is that constrictions are approximated by closed piecewise geodesics which are not necessarily periodic geodesics. In this paper, we compute constrictions starting from the closed piecewise geodesics previously computed and moving them on the surface. We compare the location of the initial closed piecewise geodesics to the location of the constrictions. Finally, we define and compute different types of constrictions on a surface
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