Related papers: Discretized Approaches to Schematization
Surface parameterization is a fundamental concept in fields such as differential geometry and computer graphics. It involves mapping a surface in three-dimensional space onto a two-dimensional parameter space. This process allows for the…
We introduce pointwise map smoothness via the Dirichlet energy into the functional map pipeline, and propose an algorithm for optimizing it efficiently, which leads to high-quality results in challenging settings. Specifically, we first…
Cost-based image patch matching is at the core of various techniques in computer vision, photogrammetry and remote sensing. When the subpixel disparity between the reference patch in the source and target images is required, either the cost…
Retraction maps have been generalized to discretization maps in (Barbero Li\~n\'an and and Mart\'{\i}n de Diego, 2022). Discretization maps are used to systematically derive numerical integrators that preserve the symplectic structure, as…
This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…
Simplification is one of the fundamental operations used in geoinformation science (GIS) to reduce size or representation complexity of geometric objects. Although different simplification methods can be applied depending on one's purpose,…
We consider the problem of efficiently computing a discrete Morse complex on simplicial complexes of arbitrary dimension and very large size. Based on a common graph-based formalism, we analyze existing data structures for simplicial…
A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G corresponds a circle. If two vertices are connected by an edge in G, the corresponding circles…
Semidefinite programming (SDP) is a powerful tool for tackling a wide range of computationally hard problems such as clustering. Despite the high accuracy, semidefinite programs are often too slow in practice with poor scalability on large…
A simple model of a frustrated disordered system is presented. Apart from the (very different) physical interpretation, the model shares many features with that of Sherrington-Kirkpatrick for spin glasses, but, as a consequence of its…
Surface parameterizations have been widely used in computer graphics and geometry processing. In particular, as simply-connected open surfaces are conformally equivalent to the unit disk, it is desirable to compute the disk conformal…
The notion of graph covers is a discretization of covering spaces introduced and deeply studied in topology. In discrete mathematics and theoretical computer science, they have attained a lot of attention from both the structural and…
How much cutting is needed to simplify the topology of a surface? We provide bounds for several instances of this question, for the minimum length of topologically non-trivial closed curves, pants decompositions, and cut graphs with a given…
Symmetric edge polytopes are lattice polytopes associated with finite simple graphs that are of interest in both theory and applications. We investigate the facet structure of symmetric edge polytopes for various models of random graphs.…
We numerically benchmark methods for computing harmonic maps into the unit sphere, with particular focus on harmonic maps with singularities. For the discretization we compare two different approaches, both based on Lagrange finite…
A spectrahedron is the feasible set of a semidefinite program, SDP, i.e., the intersection of an affine set with the positive semidefinite cone. While strict feasibility is a generic property for random problems, there are many classes of…
We study minimal harmonic maps $g: {\mathbb{C}} \to SO(3) \backslash SL(3,{\mathbb{R}})$, parameterized by polynomial cubic differentials $P$ in the plane. The asymptotic structure of such a $g$ is determined by a convex polygon $Y(P)$ in…
Stochastic Neighbor Embedding (SNE) methods minimize the divergence between the similarity matrix of a high-dimensional data set and its counterpart from a low-dimensional embedding, leading to widely applied tools for data visualization.…
In contrast to comparing faces via single exemplars, matching sets of face images increases robustness and discrimination performance. Recent image set matching approaches typically measure similarities between subspaces or manifolds, while…
3D printing of surfaces has become an established method for prototyping and visualisation. However, surfaces often contain certain degenerations, such as self-intersecting faces or non-manifold parts, which pose problems in obtaining a 3D…