Subdivision surface fitting to a dense mesh using ridges and umbilics

Fitting a sparse surface to approximate vast dense data is of interest for many applications: reverse engineering, recognition and compression, etc. The present work provides an approach to fit a Loop subdivision surface to a dense triangular mesh of arbitrary topology, whilst preserving and aligning the original features. The natural ridge-joined connectivity of umbilics and ridge-crossings is used as the connectivity of the control mesh for subdivision, so that the edges follow salient features on the surface. Furthermore, the chosen features and connectivity characterise the overall shape of the original mesh, since ridges capture extreme principal curvatures and ridges start and end at umbilics. A metric of Hausdorff distance including curvature vectors is proposed and implemented in a distance transform algorithm to construct the connectivity. Ridge-colour matching is introduced as a criterion for edge flipping to improve feature alignment. Several examples are provided to demonstrate the feature-preserving capability of the proposed approach

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

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

A triangulation-invariant method for anisotropic geodesic map computation on surface meshes

pre-printThis paper addresses the problem of computing the geodesic distance map from a given set of source vertices to all other vertices on a surface mesh using an anisotropic distance metric. Formulating this problem as an equivalent control theoretic problem with Hamilton-Jacobi-Bellman partial differential equations, we present a framework for computing an anisotropic geodesic map using a curvature-based speed function. An ordered upwind method (OUM)-based solver for these equations is available for unstructured planar meshes. We adopt this OUM-based solver for surface meshes and present a triangulation-invariant method for the solver. Our basic idea is to explore proximity among the vertices on a surface while locally following the characteristic direction at each vertex. We also propose two speed functions based on classical curvature tensors and show that the resulting anisotropic geodesic maps reflect surface geometry well through several experiments, including isocontour generation, offset curve computation, medial axis extraction, and ridge/valley curve extraction. Our approach facilitates surface analysis and processing by defining speed functions in an application-dependent manner

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

3D minutiae extraction in 3D fingerprint scans.

Traditionally, fingerprint image acquisition was based on contact. However the conventional touch-based fingerprint acquisition introduces some problems such as distortions and deformations to the fingerprint image. The most recent technology for fingerprint acquisition is touchless or 3D live scans introducing higher quality fingerprint scans. However, there is a need to develop new algorithms to match 3D fingerprints. In this dissertation, a novel methodology is proposed to extract minutiae in the 3D fingerprint scans. The output can be used for 3D fingerprint matching. The proposed method is based on curvature analysis of the surface. The method used to extract minutiae includes the following steps: smoothing; computing the principal curvature; ridges and ravines detection and tracing; cleaning and connecting ridges and ravines; and minutiae detection. First, the ridges and ravines are detected using curvature tensors. Then, ridges and ravines are traced. Post-processing is performed to obtain clean and connected ridges and ravines based on fingerprint pattern. Finally, minutiae are detected using a graph theory concept. A quality map is also introduced for 3D fingerprint scans. Since a degraded area may occur during the scanning process, especially at the edge of the fingerprint, it is critical to be able to determine these areas. Spurious minutiae can be filtered out after applying the quality map. The algorithm is applied to the 3D fingerprint database and the result is very encouraging. To the best of our knowledge, this is the first minutiae extraction methodology proposed for 3D fingerprint scans

Feature preserving variational smoothing of terrain data

Journal ArticleIn this paper, we present a novel two-step, variational and feature preserving smoothing method for terrain data. The first step computes the field of 3D normal vectors from the height map and smoothes them by minimizing a robust penalty function of curvature. This penalty function favors piecewise planar surfaces; therefore, it is better suited for processing terrain data then previous methods which operate on intensity images. We formulate the total curvature of a height map as a function of its normals. Then, the gradient descent minimization is implemented with a second-order partial differential equation (PDE) on the field of normals. For the second step, we define another penalty function that measures the mismatch between the the 3D normals of a height map model and the field of smoothed normals from the first step. Then, starting with the original height map as the initialization, we fit a non-parametric terrain model to the smoothed normals minimizing this penalty function. This gradient descent minimization is also implemented with a second-order PDE. We demonstrate the effectiveness of our approach with a ridge/gully detection application