Related papers: Can we Compute the Similarity Between Surfaces?
We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity and surface tension. The free…
We present a scalable approach for range and $k$ nearest neighbor queries under computationally expensive metrics, like the continuous Fr\'echet distance on trajectory data. Based on clustering for metric indexes, we obtain a dynamic tree…
We develop a finite element method for elliptic partial differential equations on so called composite surfaces that are built up out of a finite number of surfaces with boundaries that fit together nicely in the sense that the intersection…
Signed distance fields (SDFs) are a widely used implicit surface representation, with broad applications in computer graphics, computer vision, and applied mathematics. To reconstruct an explicit triangle mesh surface corresponding to an…
In this work, we study the computability of topological graphs, which are obtained by gluing arcs and rays together at their endpoints. We prove that every semicomputable graph in a computable metric space can be approximated, with…
We unveil an alluring alternative to parametric search that applies to both the non-geodesic and geodesic Fr\'echet optimization problems. This randomized approach is based on a variant of red-blue intersections and is appealing due to its…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
Common measures of neural representational (dis)similarity are designed to be insensitive to rotations and reflections of the neural activation space. Motivated by the premise that the tuning of individual units may be important, there has…
We apply verified numerics to the Nirenberg problem, proving that a genuine solution exists near two given computer-generated approximate solutions. This proves existence of a solution for a particular prescribed curvature that was…
In motion planning problems for autonomous robots, such as self-driving cars, the robot must ensure that its planned path is not in close proximity to obstacles in the environment. However, the problem of evaluating the proximity is…
The computation of geodesic distances is an important research topic in Geometry Processing and 3D Shape Analysis as it is a basic component of many methods used in these areas. In this work, we present a minimalistic parallel algorithm…
We embark in a program of studying the problem of better approximating surfaces by triangulations(triangular meshes) by considering the approximating triangulations as finite metric spaces and the target smooth surface as their…
Finding the graphs that are most similar to a query graph in a large database is a common task with various applications. A widely-used similarity measure is the graph edit distance, which provides an intuitive notion of similarity and…
We show how to represent a simple polygon $P$ by a grid (pixel-based) polygon $Q$ that is simple and whose Hausdorff or Fr\'echet distance to $P$ is small. For any simple polygon $P$, a grid polygon exists with constant Hausdorff distance…
Sphericity and roundness are fundamental measures used for assessing object uniformity in 2D and 3D images. However, using their strict definition makes computation costly. As both 2D and 3D microscopy imaging datasets grow larger, there is…
The fractal dimension of a surface allows its degree of roughness to be characterized quantitatively. However, limited effort is attempted to calculate the fractal dimension of surfaces computed from precisely known atomic coordinates from…
Let $\mathcal C$ be a real plane algebraic curve defined by the resultant of two polynomials (resp. by the discriminant of a polynomial). Geometrically such a curve is the projection of the intersection of the surfaces $P(x,y,z)=Q(x,y,z)=0$…
We propose $\kappa$-approximate nearest neighbor (ANN) data structures for $n$ polygonal curves under the Fr\'{e}chet distance in $\mathbb{R}^d$, where $\kappa \in \{1+\varepsilon,3+\varepsilon\}$ and $d \geq 2$. We assume that every input…
In this paper we consider an elementary, and largely unexplored, combinatorial problem in low-dimensional topology. Consider a real 2-dimensional compact surface $S$, and fix a number of points $F$ on its boundary. We ask: how many…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…