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

An investigation on methods for axis detection of high-density generic axially symmetric mechanical surfaces for automatic geometric inspection

none2noThe detection of the symmetry axis from discrete axially symmetric surfaces is an interesting topic, which is transversal to various fields: from geometric inspection to reverse engineering, archeology, etc. In the literature, several approaches have been proposed for estimating the axis from high-density triangular models of surfaces acquired by three-dimensional (3D) scanning. The axis evaluation from discrete models is, in fact, a very complex task to accomplish, due to several factors that inevitably influence the quality of the estimation and the accuracy of the measurements and evaluations depending on it. The underlying principle of each one of these approaches takes advantage of a specific property of axially symmetric surfaces. No investigations, however, have been carried out so far in order to support in the selection of the most suitable algorithms for applications aimed at automatic geometric inspection. In this regard, ISO standards currently do not provide indications on how to perform the axis detection in the case of generic axially symmetric surfaces, limiting themselves to addressing the issue only in the case of cylindrical or conical surfaces. This paper first provides an overview of the approaches that can be used for geometric inspection purposes; then, it applies them to various case studies involving one or more generic axially symmetric surfaces, functionally important and for which the axis must be detected since necessary for geometric inspection. The aim is to compare, therefore, the performances of the various methodologies by trying to highlight the circumstances in which these ones may fail. Since this investigation requires a reference (i.e. the knowledge of the true axis), the methodologies have been applied to discrete models suitably extracted from CAD surfaces.openE Guardiani; A MorabitoGuardiani, E; Morabito,

Piecewise smooth reconstruction of normal vector field on digital data

International audienceWe propose a novel method to regularize a normal vector field defined on a digital surface (boundary of a set of voxels). When the digital surface is a digitization of a piecewise smooth manifold, our method localizes sharp features (edges) while regularizing the input normal vector field at the same time. It relies on the optimisation of a variant of the Ambrosio-Tortorelli functional, originally defined for denoising and contour extraction in image processing [AT90]. We reformulate this functional to digital surface processing thanks to discrete calculus operators. Experiments show that the output normal field is very robust to digitization artifacts or noise, and also fairly independent of the sampling resolution. The method allows the user to choose independently the amount of smoothing and the length of the set of discontinuities. Sharp and vanishing features are correctly delineated even on extremely damaged data. Finally, our method can be used to enhance considerably the output of state-of- the-art normal field estimators like Voronoi Covariance Measure [MOG11] or Randomized Hough Transform [BM12]

04131 Abstracts Collection -- Geometric Properties from Incomplete Data

From 21.03.04 to 26.03.04, the Dagstuhl Seminar 04131 ``Geometric Properties from Incomplete Data\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Multi-Sample Consensus Driven Unsupervised Normal Estimation for 3D Point Clouds

Deep normal estimators have made great strides on synthetic benchmarks. Unfortunately, their performance dramatically drops on the real scan data since they are supervised only on synthetic datasets. The point-wise annotation of ground truth normals is vulnerable to inefficiency and inaccuracies, which totally makes it impossible to build perfect real datasets for supervised deep learning. To overcome the challenge, we propose a multi-sample consensus paradigm for unsupervised normal estimation. The paradigm consists of multi-candidate sampling, candidate rejection, and mode determination. The latter two are driven by neighbor point consensus and candidate consensus respectively. Two primary implementations of the paradigm, MSUNE and MSUNE-Net, are proposed. MSUNE minimizes a candidate consensus loss in mode determination. As a robust optimization method, it outperforms the cutting-edge supervised deep learning methods on real data at the cost of longer runtime for sampling enough candidate normals for each query point. MSUNE-Net, the first unsupervised deep normal estimator as far as we know, significantly promotes the multi-sample consensus further. It transfers the three online stages of MSUNE to offline training. Thereby its inference time is 100 times faster. Besides that, more accurate inference is achieved, since the candidates of query points from similar patches can form a sufficiently large candidate set implicitly in MSUNE-Net. Comprehensive experiments demonstrate that the two proposed unsupervised methods are noticeably superior to some supervised deep normal estimators on the most common synthetic dataset. More importantly, they show better generalization ability and outperform all the SOTA conventional and deep methods on three real datasets: NYUV2, KITTI, and a dataset from PCV [1]