Topology Preservation Within Digital Surfaces

International audienceGiven two connected subsets Y X of the set of the surfels of a connected digital surface, we propose three equivalent ways to express that Y is homotopic to X. The rst characterization is based on sequential deletion of simple surfels. This characterization enables us to deene thinning algorithms within a digital Jordan surface. The second characterization is based on the Euler characteristics of sets of surfels. This characterization enables us, given two connected sets Y X of surfels, to decide whether Y is nhomotopic to X. The third characterization is based on the (digital) fundamental group

Interactive Curvature Tensor Visualization on Digital Surfaces

International audienceInteractive visualization is a very convenient tool to explore complex scientific data or to try different parameter settings for a given processing algorithm. In this article, we present a tool to efficiently analyze the curvature tensor on the boundary of potentially large and dynamic digital objects (mean and Gaussian curvatures, principal curvatures , principal directions and normal vector field). More precisely, we combine a fully parallel pipeline on GPU to extract an adaptive triangu-lated isosurface of the digital object, with a curvature tensor estimation at each surface point based on integral invariants. Integral invariants being parametrized by a given ball radius, our proposal allows to explore interactively different radii and thus select the appropriate scale at which the computation is performed and visualized

Scale-space Feature Extraction on Digital Surfaces

International audienceA classical problem in many computer graphics applications consists in extracting significant zones or points on an object surface,like loci of tangent discontinuity (edges), maxima or minima of curvatures, inflection points, etc. These places have specific localgeometrical properties and often called generically features. An important problem is related to the scale, or range of scales,for which a feature is relevant. We propose a new robust method to detect features on digital data (surface of objects in Z^3 ),which exploits asymptotic properties of recent digital curvature estimators. In [1, 2], authors have proposed curvature estimators(mean, principal and Gaussian) on 2D and 3D digitized shapes and have demonstrated their multigrid convergence (for C^3 -smoothsurfaces). Since such approaches integrate local information within a ball around points of interest, the radius is a crucial parameter.In this article, we consider the radius as a scale-space parameter. By analyzing the behavior of such curvature estimators as the ballradius tends to zero, we propose a tool to efficiently characterize and extract several relevant features (edges, smooth and flat parts)on digital surfaces

Normals estimation for digital surfaces based on convolutions

International audienceIn this paper, we present a method that we call on-surface convolution which extends the classical notion of a 2D digital filter to the case of digital surfaces (following the cuberille model). We also define an averaging mask with local support which, when applied with the iterated convolution operator, behaves like an averaging with large support. The interesting property of the latter averaging is the way the resulting weights are distributed: given a digital surface obtained by discretization of a differentiable surface of R^3 , the masks isocurves are close to the Riemannian isodistance curves from the center of the mask. We eventually use the iterated averaging followed by convolutions with differentiation masks to estimate partial derivatives and then normal vectors over a surface. The number of iterations required to achieve a good estimate is determined experimentally on digitized spheres and tori. The precision of the normal estimation is also investigated according to the digitization step

Genus Computing for 3D digital objects: algorithm and implementation

This paper deals with computing topological invariants such as connected components, boundary surface genus, and homology groups. For each input data set, we have designed or implemented algorithms to calculate connected components, boundary surfaces and their genus, and homology groups. Due to the fact that genus calculation dominates the entire task for 3D object in 3D space, in this paper, we mainly discuss the calculation of the genus. The new algorithms designed in this paper will perform: (1) pathological cases detection and deletion, (2) raster space to point space (dual space) transformation, (3) the linear time algorithm for boundary point classification, and (4) genus calculation.Comment: 12 pages 7 figures. In Proceedings of the Workshop on Computational Topology in image context 2009, Aug. 26-28, Austria, Edited by W. Kropatsch, H. M. Abril and A. Ion, 200

SHREC’20 Track:Retrieval of digital surfaces with similar geometric reliefs

International audienceThis paper presents the methods that have participated in the SHREC'20 contest on retrieval of surface patches with similar geometric reliefs and 1 the analysis of their performance over the benchmark created for this challenge. The goal of the context is to verify the possibility of retrieving 3D models only based on the reliefs that are present on their surface and to compare methods that are suitable for this task. This problem is related to many real world applications, such as the classification of cultural heritage goods or the analysis of different materials. To address this challenge, it is necessary to characterize the local "geometric pattern" information, possibly forgetting model size and bending. Seven groups participated in this contest and twenty runs were submitted for evaluation. The performances of the methods reveal that good results are achieved with a number of techniques that use different approaches

Convolutions on digital surfaces: on the way iterated convolutions behave and preliminary results about curvature estimation

In [FoureyMalgouyres09] the authors present a generalized convolution operator for functions defined on digital surfaces. We provide here some extra material related to this notion. Some about the relative isotropy of the way a convolution kernel (or mask) grows when the convolution operator is iterated. We also provide preliminary results about a way to estimate curvatures on a digital surface, using the same convolution operator