SGP03: Eurographics Symposium on Geometry Processing
https://diglib.eg.org:443/handle/10.2312/444
2019-10-14T00:47:40Z3D Reconstruction Using Labeled Image Regions
https://diglib.eg.org:443/handle/10.2312/SGP.SGP03.248-259
3D Reconstruction Using Labeled Image Regions
Ziegler, Remo; Matusik, Wojciech; Pfister, Hanspeter; McMillan, Leonard
Leif Kobbelt and Peter Schroeder and Hugues Hoppe
In this paper we present a novel algorithm for reconstructing 3D scenes from a set of images. The user defines a set of polygonal regions with corresponding labels in each image using familiar 2D photo-editing tools. Our reconstruction algorithm computes the 3D model with maximum volume that is consistent with the set of regions in the input images. The algorithm is fast, uses only 2D intersection operations, and directly computes a polygonal model. We implemented a user-assisted system for 3D scene reconstruction and show results on scenes that are difficult or impossible to reconstruct with other methods.
2003-01-01T00:00:00ZApproximate Implicitization Via Curve Fitting
https://diglib.eg.org:443/handle/10.2312/SGP.SGP03.240-247
Approximate Implicitization Via Curve Fitting
Wurm, E.; Jüttler, B.
Leif Kobbelt and Peter Schroeder and Hugues Hoppe
We discuss methods for fitting implicitly defined (e.g. piecewise algebraic) curves to scattered data, which may contain problematic regions, such as edges, cusps or vertices. As the main idea, we construct a bivariate function, whose zero contour approximates a given set of points, and whose gradient field simultaneously approximates an estimated normal field. The coefficients of the implicit representation are found by solving a system of linear equations. In order to allow for problematic input data, we introduce a criterion for detecting points close to possible singularities. Using this criterion we split the data into segments and develop methods for propagating the orientation of the normals globally. Furthermore we present a simple fallback strategy, that can be used when the process of orientation propagation fails. The method has been shown to work successfully
2003-01-01T00:00:00ZA Geometric Convection Approach of 3-D Reconstruction
https://diglib.eg.org:443/handle/10.2312/SGP.SGP03.218-229
A Geometric Convection Approach of 3-D Reconstruction
Chaine, Raphaëlle
Leif Kobbelt and Peter Schroeder and Hugues Hoppe
This paper introduces a fast and efficient algorithm for surface reconstruction. As many algorithms of this kind, it produces a piecewise linear approximation of a surface S from a finite, sufficiently dense, subset of its points. Originally, the starting point of this work does not come from the computational geometry field. It is inspired by an existing numerical scheme of surface convection developed by Zhao, Osher and Fedkiw. We have translated this scheme to make it depend on the geometry of the input data set only, and not on the precision of some grid around the surface. Our algorithm deforms a closed oriented pseudo-surface embedded in the 3D Delaunay triangulation of the sampled points, and the reconstructed surface consists of a set of oriented facets located in this 3D Delaunay triangulation. This paper provides an appropriate data structure to represent a pseudo-surface, together with operations that manage deformations and topological changes. The algorithm can handle surfaces with boundaries, surfaces of high genus and, unlike most of the other existing schemes, it does not involve a global heuristic. Its complexity is that of the 3D Delaunay triangulation of the points. We present some results of the method, which turns out to be efficient even on noisy input data.
2003-01-01T00:00:00ZApproximating and Intersecting Surfaces from Points
https://diglib.eg.org:443/handle/10.2312/SGP.SGP03.230-239
Approximating and Intersecting Surfaces from Points
Adamson, Anders; Alexa, Marc
Leif Kobbelt and Peter Schroeder and Hugues Hoppe
Point sets become an increasingly popular shape representation. Most shape processing and rendering tasks require the approximation of a continuous surface from the point data. We present a surface approximation that is motivated by an efficient iterative ray intersection computation. On each point on a ray, a local normal direction is estimated as the direction of smallest weighted co-variances of the points. The normal direction is used to build a local polynomial approximation to the surface, which is then intersected with the ray. The distance to the polynomials essentially defines a distance field, whose zero-set is computed by repeated ray intersection. Requiring the distance field to be smooth leads to an intuitive and natural sampling criterion, namely, that normals derived from the weighted co-variances are well defined in a tubular neighborhood of the surface. For certain, well-chosen weight functions we can show that well-sampled surfaces lead to smooth distance fields with non-zero gradients and, thus, the surface is a continuously differentiable manifold. We detail spatial data structures and efficient algorithms to compute ray-surface intersections for fast ray casting and ray tracing of the surface.
2003-01-01T00:00:00Z