Feature Lines for Illustrating Medical Surface Models: Mathematical Background and Survey

This paper provides a tutorial and survey for a specific kind of illustrative visualization technique: feature lines. We examine different feature line methods. For this, we provide the differential geometry behind these concepts and adapt this mathematical field to the discrete differential geometry. All discrete differential geometry terms are explained for triangulated surface meshes. These utilities serve as basis for the feature line methods. We provide the reader with all knowledge to re-implement every feature line method. Furthermore, we summarize the methods and suggest a guideline for which kind of surface which feature line algorithm is best suited. Our work is motivated by, but not restricted to, medical and biological surface models.Comment: 33 page

3D Reconstruction Using High Resolution Implicit Surface Representations and Memory Management Strategies

La disponibilité de capteurs de numérisation 3D rapides et précis a permis de capturer de très grands ensembles de points à la surface de différents objets qui véhiculent la géométrie des objets. La métrologie appliquée consiste en l'application de mesures dans différents domaines tels que le contrôle qualité, l'inspection, la conception de produits et la rétroingénierie. Une fois que le nuage de points 3D non organisés couvrant toute la surface de l'objet a été capturé, un modèle de la surface doit être construit si des mesures métrologiques doivent être effectuées sur l'objet. Dans la reconstruction 3D en temps réel, à l'aide de scanners 3D portables, une représentation de surface implicite très efficace est le cadre de champ vectoriel, qui suppose que la surface est approchée par un plan dans chaque voxel. Le champ vectoriel contient la normale à la surface et la matrice de covariance des points tombant à l'intérieur d'un voxel. L'approche globale proposée dans ce projet est basée sur le cadre Vector Field. Le principal problème abordé dans ce projet est la résolution de l'incrément de consommation de mémoire et la précision du modèle reconstruit dans le champ vectoriel. Ce tte approche effectue une sélection objective de la taille optimale des voxels dans le cadre de champ vectoriel pour maintenir la consommation de mémoire aussi faible que possible et toujours obtenir un modèle précis de la surface. De plus, un ajustement d e surface d'ordre élevé est utilisé pour augmenter la précision du modèle. Étant donné que notre approche ne nécessite aucune paramétrisation ni calcul complexe, et qu'au lieu de travailler avec chaque point, nous travaillons avec des voxels dans le champ vectoriel, cela réduit la complexité du calcul.The availability of fast and accurate 3D scanning sensors has made it possible to capture very large sets of points at the surface of different objects that convey the geometry of the objects. A pplied metrology consists in the application of measurements in different fields such as quality control, inspection, product design and reverse engineering. Once the cloud of unorganized 3D points covering the entire surface of the object has been capture d, a model of the surface must be built if metrologic measurements are to be performed on the object. In realtime 3D reconstruction, using handheld 3D scanners a very efficient implicit surface representation is the Vector Field framework, which assumes that the surface is approximated by a plane in each voxel. The vector field contains the normal to the surface and the covariance matrix of the points falling inside a voxel. The proposed global approach in this project is based on the Vector Field framew ork. The main problem addressed in this project is solving the memory consumption increment and the accuracy of the reconstructed model in the vector field. This approach performs an objective selection of the optimal voxels size in the vector field frame work to keep the memory consumption as low as possible and still achieve an accurate model of the surface. Moreover, a highorder surface fitting is used to increase the accuracy of the model. Since our approach do not require any parametrization and compl ex calculation, and instead of working with each point we are working with voxels in the vector field, then it reduces the computational complexity

Comparing Features of Three-Dimensional Object Models Using Registration Based on Surface Curvature Signatures

This dissertation presents a technique for comparing local shape properties for similar three-dimensional objects represented by meshes. Our novel shape representation, the curvature map, describes shape as a function of surface curvature in the region around a point. A multi-pass approach is applied to the curvature map to detect features at different scales. The feature detection step does not require user input or parameter tuning. We use features ordered by strength, the similarity of pairs of features, and pruning based on geometric consistency to efficiently determine key corresponding locations on the objects. For genus zero objects, the corresponding locations are used to generate a consistent spherical parameterization that defines the point-to-point correspondence used for the final shape comparison

Modeling, assessment, and design of porous cells based on schwartz primitive surface for bone scaffolds

The design of bone scafolds for tissue regeneration is a topic of great interest, which involves diferent issues related to geometry of architectures, mechanical behavior, and biological requirements, whose optimal combination determines the success of an implant. Additive manufacturing (AM) has widened the capability to produce structures with complex geometries, which should potentially satisfy the diferent requirements. These architectures can be obtained by means of refned methods and have to be assessed in terms of geometrical and mechanical properties. In this paper a triply periodic minimal surface (TPMS), the Schwarz's Primitive surface (P-surface), has been considered as scafold unit cell and conveniently parameterized in order to investigate the efect of modulation of analytical parameters on the P-cell geometry and on its properties. Several are the cell properties, which can afect the scafold performance. Due to the important biofunctional role that the surface curvature plays in mechanisms of cellular proliferation and diferentiation, in this paper, in addition to properties considering the cell geometry in its whole (such as volume fraction or pore size), new properties were proposed. Tese properties involve, particularly, the evaluation of local geometrical-diferential properties of the P-surface. Te results of this P-cell comprehensive characterization are very useful for the design of customized bone scafolds able to satisfy both biological and mechanical requirements. A numerical structural evaluation, by means of fnite element method (FEM), was performed in order to assess the stifness of solid P-cells as a function of the changes of the analytical parameters of outer surface and the thickness of cell. Finally, the relationship between stifness and porosity has been analyzed, given the relevance that this property has for bone scafolds design

Weighted Mean Curvature

In image processing tasks, spatial priors are essential for robust computations, regularization, algorithmic design and Bayesian inference. In this paper, we introduce weighted mean curvature (WMC) as a novel image prior and present an efficient computation scheme for its discretization in practical image processing applications. We first demonstrate the favorable properties of WMC, such as sampling invariance, scale invariance, and contrast invariance with Gaussian noise model; and we show the relation of WMC to area regularization. We further propose an efficient computation scheme for discretized WMC, which is demonstrated herein to process over 33.2 giga-pixels/second on GPU. This scheme yields itself to a convolutional neural network representation. Finally, WMC is evaluated on synthetic and real images, showing its superiority quantitatively to total-variation and mean curvature.Comment: 12 page

Fitting of Analytic Surfaces to Noisy Point Clouds

Fitting -continuous or superior surfaces to a set of points sampled on a 2-manifold is central to reverse engi- neering, computer aided geometric modeling, entertaining, modeling of art heritage, etc -- This article addresses the fit- ting of analytic (ellipsoid, cones, cylinders) surfaces in general position in -- Currently, the state of the art presents limitations in 1) automatically finding an initial guess for the analytic surface F sought, and 2) economically estimat- ing the geometric distance between a point of and the analytic surface SF -- These issues are central in estimating an analytic surface which minimizes its accumulated distances to the point set -- In response to this situation, this article presents and tests novel user-independent strategies for addressing aspects 1) and 2) above, for cylinders, cones and ellipsoids -- A conjecture for the calculation of the distance point-ellipsoid is also proposed -- Our strategies produce good initial guesses for F and fast fitting error estimation for F, leading to an agile and robust optimization algorithm -- Ongoing work addresses the fitting of free-form parametric surfaces to

Edge Aware Anisotropic Diffusion for 3D Scalar Data

Fig. 1: The left half of the figure demonstrates the consistency in smoothing of our method compared to the existing method. The right half of the figure demonstrates the de-noising capabilities of our method. All the images from (a-c) were obtained byrenderingan iso-surface of 153. (a) Diffused with an existing diffusion model proposed by Krissian et al. [20] with k = 40, and100 iterations (b) The original Sheep’s heart data. (c) Diffused with our method with σ = 1 and the same number of iterations. The yellow circle indicates aregionwheretheiso-surfacehasbothhighandmediumrangegradient magnitude, and the blue circle marks a region where the gradient magnitude is much lower. Note the inconsistent smoothing in (a) inside the yellow circle. (d) The tooth data contaminated with Poisson noise (SNR=12.8) (e)Theoriginaltoothdata(f)Diffusedwithourmethod(SNR=25.76) withσ = 1 and 25 iterations. We used the exact same transfer function to render all the images in(d-f). Abstract—Inthispaperwepresentanovelanisotropicdiffusionmodel targeted for 3D scalar field data. Our model preserves material boundaries as well as fine tubular structures while noise is smoothed out. One of the major novelties is the use of the directional second derivative to define material boundaries instead of the gradient magnitude for thresholding. This results in a diffusion model that has much lower sensitivity to the diffusion parameter and smoothes material boundaries consistently compared to gradient magnitude based techniques. We empirically analyze the stability and convergence of the proposed diffusion and demonstrate its de-noising capabilities for both analytic and real data. We also discuss applications in the context of volume rendering