A non-iterative method for robustly computing the intersections between a line and a curve or surface

The need to compute the intersections between a line and a high-order curve or surface arises in a large number of finite element applications. Such intersection problems are easy to formulate but hard to solve robustly. We introduce a non-iterative method for computing intersections by solving a matrix singular value decomposition (SVD) and an eigenvalue problem. That is, all intersection points and their parametric coordinates are determined in one-shot using only standard linear algebra techniques available in most software libraries. As a result, the introduced technique is far more robust than the widely used Newton-Raphson iteration or its variants. The maximum size of the considered matrices depends on the polynomial degree $q$ of the shape functions and is $2q \times 3q$ for curves and $6 q^2 \times 8 q^2$ for surfaces. The method has its origin in algebraic geometry and has here been considerably simplified with a view to widely used high-order finite elements. In addition, the method is derived from a purely linear algebra perspective without resorting to algebraic geometry terminology. A complete implementation is available from http://bitbucket.org/nitro-project/

Deep Learning for Vanishing Point Detection Using an Inverse Gnomonic Projection

We present a novel approach for vanishing point detection from uncalibrated monocular images. In contrast to state-of-the-art, we make no a priori assumptions about the observed scene. Our method is based on a convolutional neural network (CNN) which does not use natural images, but a Gaussian sphere representation arising from an inverse gnomonic projection of lines detected in an image. This allows us to rely on synthetic data for training, eliminating the need for labelled images. Our method achieves competitive performance on three horizon estimation benchmark datasets. We further highlight some additional use cases for which our vanishing point detection algorithm can be used.Comment: Accepted for publication at German Conference on Pattern Recognition (GCPR) 2017. This research was supported by German Research Foundation DFG within Priority Research Programme 1894 "Volunteered Geographic Information: Interpretation, Visualisation and Social Computing

Algebraic Smooth Occluding Contours

Computing occluding contours is a key building block of non-photorealistic rendering, but producing contours with consistent visibility has been notoriously challenging. This paper describes the first general-purpose smooth surface construction for which the occluding contours can be computed in closed form. For a given input mesh and camera viewpoint, we produce a $G^1$ piecewise-quadratic surface approximating the mesh. We show how the image-space occluding contours of this representation may then be described as piecewise rational curves. We show that this method produces smooth contours with consistent visibility much more efficiently than the state-of-the-art.Comment: 10 pages, 11 figure

Interrogation of spline surfaces with application to isogeometric design and analysis of lattice-skin structures

A novel surface interrogation technique is proposed to compute the intersection of curves with spline surfaces in isogeometric analysis. The intersection points are determined in one-shot without resorting to a Newton-Raphson iteration or successive refinement. Surface-curve intersection is required in a wide range of applications, including contact, immersed boundary methods and lattice-skin structures, and requires usually the solution of a system of nonlinear equations. It is assumed that the surface is given in form of a spline, such as a NURBS, T-spline or Catmull-Clark subdivision surface, and is convertible into a collection of B\'ezier patches. First, a hierarchical bounding volume tree is used to efficiently identify the B\'ezier patches with a convex-hull intersecting the convex-hull of a given curve segment. For ease of implementation convex-hulls are approximated with k-dops (discrete orientation polytopes). Subsequently, the intersections of the identified B\'ezier patches with the curve segment are determined with a matrix-based implicit representation leading to the computation of a sequence of small singular value decompositions (SVDs). As an application of the developed interrogation technique the isogeometric design and analysis of lattice-skin structures is investigated. The skin is a spline surface that is usually created in a computer-aided design (CAD) system and the periodic lattice to be fitted consists of unit cells, each containing a small number of struts. The lattice-skin structure is generated by projecting selected lattice nodes onto the surface after determining the intersection of unit cell edges with the surface. For mechanical analysis, the skin is modelled as a Kirchhoff-Love thin-shell and the lattice as a pin-jointed truss. The two types of structures are coupled with a standard Lagrange multiplier approach

Loopy Cuts: Surface-Field Aware Block Decomposition for Hex-Meshing.

We present a new fully automatic block-decomposition hexahedral meshing algorithm capable of producing high quality meshes that strictly preserve feature curve networks on the input surface and align with an input surface cross-field. We produce all-hex meshes on the vast majority of inputs, and introduce localized non-hex elements only when the surface feature network necessitates those. The input to our framework is a closed surface with a collection of geometric or user-demarcated feature curves and a feature-aligned surface cross-field. Its output is a compact set of blocks whose edges interpolate these features and are loosely aligned with this cross-field. We obtain this block decomposition by cutting the input model using a collection of simple cutting surfaces bounded by closed surface loops. The set of cutting loops spans the input feature curves, ensuring feature preservation, and is obtained using a field-space sampling process. The computed loops are uniformly distributed across the surface, cross orthogonally, and are loosely aligned with the cross-field directions, inducing the desired block decomposition. We validate our method by applying it to a large range of complex inputs and comparing our results to those produced by state-of-the-art alternatives. Contrary to prior approaches, our framework consistently produces high-quality field aligned meshes while strictly preserving geometric or user-specified surface features

Computer-implemented system and method for automated and highly accurate plaque analysis, reporting, and visualization

A computer-implemented system and method of intra-oral analysis for measuring plaque removal is disclosed. The system includes hardware for real-time image acquisition and software to store the acquired images on a patient-by-patient basis. The system implements algorithms to segment teeth of interest from surrounding gum, and uses a real-time image-based morphing procedure to automatically overlay a grid onto each segmented tooth. Pattern recognition methods are used to classify plaque from surrounding gum and enamel, while ignoring glare effects due to the reflection of camera light and ambient light from enamel regions. The system integrates these components into a single software suite with an easy-to-use graphical user interface (GUI) that allows users to do an end-to-end run of a patient record, including tooth segmentation of all teeth, grid morphing of each segmented tooth, and plaque classification of each tooth image