An Upper Bound on the Average Size of Silhouettes

It is a widely observed phenomenon in computer graphics that the size of the silhouette of a polyhedron is much smaller than the size of the whole polyhedron. This paper provides, for the first time, theoretical evidence supporting this for a large class of objects, namely for polyhedra that approximate surfaces in some reasonable way; the surfaces may be non-convex and non-differentiable and they may have boundaries. We prove that such polyhedra have silhouettes of expected size $O(\sqrt{n})$ where the average is taken over all points of view and n is the complexity of the polyhedron

On the complements of 3-dimensional convex polyhedra as polynomial images of R3{\mathbb R}^3

We prove that the complement ${\mathcal S}:={\mathbb R}^3\setminus{\mathcal K}$ of a 3-dimensional convex polyhedron ${\mathcal K}\subset{\mathbb R}^3$ and its closure $\overline{{\mathcal S}}$ are polynomial images of ${\mathbb R}^3$. The former techniques cannot be extended in general to represent such semialgebraic sets ${\mathcal S}$ and $\overline{{\mathcal S}}$ as polynomial images of ${\mathbb R}^n$ if $n\geq4$.Comment: 12 pages, 1 figur

Feature and viewpoint selection for industrial car assembly

Abstract. Quality assurance programs of today’s car manufacturers show increasing demand for automated visual inspection tasks. A typical example is just-in-time checking of assemblies along production lines. Since high throughput must be achieved, object recognition and pose estimation heavily rely on offline preprocessing stages of available CAD data. In this paper, we propose a complete, universal framework for CAD model feature extraction and entropy index based viewpoint selection that is developed in cooperation with a major german car manufacturer

Efficient view point selection for silhouettes of convex polyhedra

AbstractSilhouettes of polyhedra are an important primitive in application areas such as machine vision and computer graphics. In this paper, we study how to select view points of convex polyhedra such that the silhouette satisfies certain properties. Specifically, we give algorithms to find all projections of a convex polyhedron such that a given set of edges, faces and/or vertices appear on the silhouette.We present an algorithm to solve this problem in O(k2) time for k edges. For orthogonal projections, we give an improved algorithm that is fully adaptive in the number l of connected components formed by the edges, and has a time complexity of O(klogk+kl). We then generalize this algorithm to edges and/or faces appearing on the silhouette

Perimeter detection in sketched drawings of polyhedral shapes

Ponència presentada al STAG17: Smart tools and Applications in Graphics, celebrat a Catania (Itàlia) 11-12 setembre 2017This paper describes a new “envelope” approach for detecting object perimeters in line-drawings vectorised from sketches of polyhedral objects. Existing approaches for extracting contours from digital images are unsuitable for Sketch-Based Modelling, as they calculate where the contour is, but not which elements of the line-drawing belong to it. In our approach, the perimeter is described in terms of lines and junctions (including intersections and T-junctions) of the original line drawing

ADAM: a general method for using various data types in asteroid reconstruction

We introduce ADAM, the All-Data Asteroid Modelling algorithm. ADAM is simple and universal since it handles all disk-resolved data types (adaptive optics or other images, interferometry, and range-Doppler radar data) in a uniform manner via the 2D Fourier transform, enabling fast convergence in model optimization. The resolved data can be combined with disk-integrated data (photometry). In the reconstruction process, the difference between each data type is only a few code lines defining the particular generalized projection from 3D onto a 2D image plane. Occultation timings can be included as sparse silhouettes, and thermal infrared data are efficiently handled with an approximate algorithm that is sufficient in practice due to the dominance of the high-contrast (boundary) pixels over the low-contrast (interior) ones. This is of particular importance to the raw ALMA data that can be directly handled by ADAM without having to construct the standard image. We study the reliability of the inversion by using the independent shape supports of function series and control-point surfaces. When other data are lacking, one can carry out fast nonconvex lightcurve-only inversion, but any shape models resulting from it should only be taken as illustrative global-scale ones.Comment: 11 pages, submitted to A&