Related papers: Sets Reconstructable with Medial Axis

The metric dimension of non-component graph, associated to a finite vector space, is determined. It is proved that the exchange property holds for resolving sets of the graph, except a special case. Some results are also related to an…

Segmenting arbitrary 3D objects into constituent parts that are structurally meaningful is a fundamental problem encountered in a wide range of computer graphics applications. Existing methods for 3D shape segmentation suffer from complex…

This paper considers the problem of unsupervised 3D object reconstruction from in-the-wild single-view images. Due to ambiguity and intrinsic ill-posedness, this problem is inherently difficult to solve and therefore requires strong…

Convolutional Neural Networks are a well-known staple of modern image classification. However, it can be difficult to assess the quality and robustness of such models. Deep models are known to perform well on a given training and estimation…

A matrix (and any associated linear system) will be referred to as structured if it has a small displacement rank. It is known that the inverse of a structured matrix is structured, which allows fast inversion (or solution), and reduced…

Complex networks datasets often come with the problem of missing information: interactions data that have not been measured or discovered, may be affected by errors, or are simply hidden because of privacy issues. This Element provides an…

Many concrete problems are formulated in terms of a finite set of points in $R^n$ which, via the ambient Euclidean metric, becomes a finite metric space. To obtain information from such a space, it is often useful to associate a graph to…

We introduce a notion of constructibility for \'etale sheaves with torsion coefficients over a suitable class of adic spaces. This notion is related to the classical notion of constructibility for schemes via the nearby cycles functor. We…

The fundamental groups of most (conjecturally, all) closed 3-manifolds with uniform geometries have finite complete rewriting systems. The fundamental groups of a large class of amalgams of circle bundles also have finite complete rewriting…

A set $A$ in a finite dimensional Euclidean space is \emph{monovex} if for every two points $x,y \in A$ there is a continuous path within the set that connects $x$ and $y$ and is monotone (nonincreasing or nondecreasing) in each coordinate.…

This paper studies the problem of reconstructing binary matrices that are only accessible through few evaluations of their discrete X-rays. Such question is prominently motivated by the demand in material science for developing a tool for…

This paper aims to establish a relation between the tangent cone of the medial axis of X at a given point a of R^n$ and the medial axis of the set of points in X realising the distance d(a,X). As a consequence, a lower bound for the…

We study the circumstances under which one can reconstruct a stack from its associated functor of isomorphism classes. This is possible surprisingly often: we show that many of the standard examples of moduli stacks are determined by their…

A metric graph is a 1-dimensional stratified metric space consisting of vertices and edges or loops glued together. Metric graphs can be naturally used to represent and model data that take the form of noisy filamentary structures, such as…

This paper concerns the reconstruction of possibly complex-valued coefficients in a second-order scalar elliptic equation posed on a bounded domain from knowledge of several solutions of that equation. We show that for a sufficiently large…

This article is devoted to the study of classical and new results concerning equidistant sets, both from the topological and metric point of view. We start with a review of the most interesting known facts about these sets in the euclidean…

Based on the concepts of isovists and medial axes, we developed a set of algorithms that can automatically generate axial lines for representing individual linearly stretched parts of open space of an urban environment. Open space is the…

Despite recent progress in our understanding of complex dynamic networks, it remains challenging to devisesufficiently accurate models to observe, control or predict the state of real systems in biology, economics or other fields. A largely…

This article is talking about the study constructive method of structural identification systems with chaotic dynamics. It is shown that the reconstructed attractors are a source of information not only about the dynamics but also on the…

Methods were developed in Ref. [1] for constructing reference metrics (and from them differentiable structures) on three-dimensional manifolds with topologies specified by suitable triangulations. This note generalizes those methods by…