Related papers: Sets Reconstructable with Medial Axis
We prove that the k-medial axis of an arbitrary closed set in Rn is n-k+1-rectifiable (and hence of dimension at most n-k+1). This result gives a first stratification for medial axis of any closed set, which has been widely studied and used…
Shape reconstruction from imaging volumes is a recurring need in medical image analysis. Common workflows start with a segmentation step, followed by careful post-processing and,finally, ad hoc meshing algorithms. As this sequence can be…
In binary images, the distance transformation (DT) and the geometrical skeleton extraction are classic tools for shape analysis. In this paper, we present time optimal algorithms to solve the reverse Euclidean distance transformation and…
The deck of a topological space $X$ is the set $\mathcal{D}(X)=\{[X \setminus \{x\}] \colon x \in X\}$, where $[Z]$ denotes the homeomorphism class of $Z$. A space $X$ is topologically reconstructible if whenever…
The Medial Axis Transform (MAT) is a complete shape descriptor capable of reconstructing the geometry of the original domain. A high-quality MAT should not only facilitate high-fidelity reconstruction but also capture structural features --…
We propose a novel framework for computing the medial axis transform of 3D shapes while preserving their medial features via restricted power diagram (RPD). Medial features, including external features such as the sharp edges and corners of…
We prove that a large family of graphs which are decomposable with respect to the modular decomposition can be reconstructed from their collection of vertex-deleted subgraphs.
Unsigned distance fields (UDFs) offer broader modeling capabilities than signed distance fields (SDFs), enabling the representation of shapes with open boundaries, non-manifold structures or mixed curve and surface parts. However,…
The erosion of a set in Euclidean space by a radius r>0 is the subset of X consisting of points at distance >/-r from the complement of X. A set is resilient to erosion if it is similar to its erosion by some positive radius. We give a…
We investigate the notion of the medial axis for pseudo-Euclidean spaces. For most of the article, we follow the path of Birbrair and Denkowski's article "Medial Axis and Singularities", checking its feasibility in the new context.
Defining the $m$-th stratum of a closed subset of an $n$ dimensional Euclidean space to consist of those points, where it can be touched by a ball from at least $n-m$ linearly independent directions, we establish that the $m$-th stratum is…
Resistive-capacitive (RC) networks are used to model various processes in engineering, physics or biology. We consider the problem of recovering the network connection structure from measured input-output data. We address this problem as a…
The medial axis $M_X$ of a closed set $X\subset \mathbb{R}^n$ is the set of points from the ambient space that admit more than one closest point in $X$. We study the problem of reaching the singularities, i.e. of characterising the points…
The aim of this paper is to study the Lipschitz normally embedded property for a set and its medial axis. We consider if and when a non-LNE set implies non-LNE medial axis and converse. We present an example a of Lipschitz normally set that…
This paper investigates topological reconstruction, related to the reconstruction conjecture in graph theory. We ask whether the homeomorphism types of subspaces of a space $X$ which are obtained by deleting singletons determine $X$…
We extend Ahlbrandt and Ziegler's reconstruction results to the metric setting: we show that separably categorical metric structures are determined, up to bi-interpretability, by their automorphism groups.
The matching polynomial of a graph is the generating function of the numbers of its matchings with respect to their cardinality. A graph polynomial is polynomial reconstructible, if its value for a graph can be determined from its values…
Network reconstruction consists in retrieving the hidden interaction structure of a system from observations. Many reconstruction algorithms have been proposed, although less research has been devoted to describe their theoretical…
The deck, $\mathcal{D}(X)$, of a topological space $X$ is the set $\mathcal{D}(X)=\{[X \setminus \{x\}]\colon x \in X\}$, where $[Y]$ denotes the homeomorphism class of $Y$. A space $X$ is (topologically) reconstructible if whenever…
The surface reconstruction problem from sets of planar parallel slices representing cross sections through 3D objects is presented. The final result of surface reconstruction is always based on the correct estimation of the structure of the…