相关论文: Computational Geometry Column 45

We consider practical aspects of reconstructing planar curves with prescribed Euclidean or affine curvatures. These curvatures are invariant under the special Euclidean group and the equi-affine groups, respectively, and play an important…

In this paper, we propose several mathematical models for 3D surface reconstruction and volume estimation from a set of scattered cloud data. Three meshless methods including the interpolation-based method by RBF, PDE-based approach by…

The structure of the reconstruction algorithm OPED permits a natural way to generate additional data, while still preserving the essential feature of the algorithm. This provides a method for image reconstruction for limited angel problems.…

3D recovery from multi-stereo and stereo images, as an important application of the image-based perspective geometry, serves many applications in computer vision, remote sensing and Geomatics. In this chapter, the authors utilize the…

We present an approach for the planar surface reconstruction of a scene from images with limited overlap. This reconstruction task is challenging since it requires jointly reasoning about single image 3D reconstruction, correspondence…

SUMMARY Geophysical imaging using the inversion procedure is a powerful tool for the exploration of the Earth's subsurface. However, the interpretation of inverted images can sometimes be difficult, due to the inherent limitations of…

We present a new algorithm for computing the endomorphism ring of an ordinary abelian surface over a finite field which is subexponential and generalizes an algorithm of Bisson and Sutherland for elliptic curves. The correctness of this…

An efficient algorithm for computing the branching structure of a compact Riemann surface defined via an algebraic curve is presented. Generators of the fundamental group of the base of the ramified covering punctured at the discriminant…

Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…

We propose a novel way of computing surface folding maps via solving a linear PDE. This framework is a generalization to the existing quasiconformal methods and allows manipulation of the geometry of folding. Moreover, the crucial quantity…

In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the…

A variational approach to the reconstruction of a shape (2D simple manifolds) as triangulated surface from given level set using shape gradients is presented. It involves an energy functional that depends on the local shape characteristics…

Establishing structure-property linkages in polycrystalline materials requires representative two- (2D) and three- (3D) dimensional microstructural inputs for full-field simulations. A core objective of microstructure characterization and…

Orbital tomography has recently been established as a technique to reconstruct molecular orbitals directly from photoemission data using iterative phase retrieval algorithms. In this work, we present a detailed description of steps for…

Generic 3D reconstruction from a single image is a difficult problem. A lot of data loss occurs in the projection. A domain based approach to reconstruction where we solve a smaller set of problems for a particular use case lead to greater…

A two-dimensional tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A Non Uniform Rational Basis Splines (NURBS) curve is used as computational representation of the boundary. This…

Many man-made objects are characterised by a shape that is symmetric along one or more planar directions. Estimating the location and orientation of such symmetry planes can aid many tasks such as estimating the overall orientation of an…

A pants decomposition of an orientable surface S is a collection of simple cycles that partition S into pants, i.e., surfaces of genus zero with three boundary cycles. Given a set P of n points in the plane, we consider the problem of…

Implicit shape representation, such as SDFs, is a popular approach to recover the surface of a 3D shape as the level sets of a scalar field. Several methods approximate SDFs using machine learning strategies that exploit the knowledge that…

An example of potential density of rational points on the second punctual Hilbert scheme of certain K3 surfaces is treated in detail. This is an amplification of some remarks made by O'Grady and Oguiso.