Related papers: Sets Reconstructable with Medial Axis
With an increasing amount of observations on the dynamics of many complex systems, it is required to reveal the underlying mechanisms behind these complex dynamics, which is fundamentally important in many scientific fields such as climate,…
We prove that the medial axis of closed sets is Hausdorff stable in the following sense: Let $\mathcal{S} \subseteq \mathbb{R}^d$ be (fixed) closed set (that contains a bounding sphere). Consider the space of $C^{1,1}$ diffeomorphisms of…
We present a deep learning approach to reconstruct scene appearance from unstructured images captured under collocated point lighting. At the heart of Deep Reflectance Volumes is a novel volumetric scene representation consisting of…
It is known that, in finite dimensions, the support function of a compact convex set with non empty interior is differentiable excepting the origin if and only if the set is strictly convex. In this paper we realize a thorough study of the…
It is still a challenging task of today to recognize the type of a given algebraic surface which is described only by its implicit representation. In~this paper we will investigate in more detail the case of canal surfaces that are often…
A class of spherical functions is studied which can be viewed as the matrix generalization of Bessel functions. We derive a recursive structure for these functions. We show that they are only special cases of more general radial functions…
This article describes a natural piecewise Euclidean bi-simplicial cell structure for the space of $n$-element multisets in a fixed Euclidean rectangle. In particular, we highlight some connections with spaces of complex polynomials and…
"What cannot be measured cannot be improved" while likely never uttered by Lord Kelvin, summarizes effectively the driving force behind this work. This paper presents a detailed discussion of automated metrics for evaluating structured 3D…
We show that the closure of the value set of a real linear recurrence sequence is the union of a countable set and a finite collection of intervals. Conversely, any finite collection of closed intervals is the closure of the value set of…
We define and construct mixed Hodge structures on real schematic homotopy types of complex projective varieties, giving mixed Hodge structures on their homotopy groups and pro-algebraic fundamental groups. We also show that these split on…
Hyperspaces form a powerful tool in some branches of mathematics: lots of fractal and other geometric objects can be viewed as fixed points of some functions in suitable hyperspaces - as well as interesting classes of formal languages in…
In this paper, we present a simple yet effective formulation called Coverage Axis for 3D shape skeletonization. Inspired by the set cover problem, our key idea is to cover all the surface points using as few inside medial balls as possible.…
This paper systematically derives design dimensions for the structured evaluation of explainable artificial intelligence (XAI) approaches. These dimensions enable a descriptive characterization, facilitating comparisons between different…
A set of fundamental matrices relating pairs of cameras in some configuration can be represented as edges of a "viewing graph". Whether or not these fundamental matrices are generically sufficient to recover the global camera configuration…
We propose a method to recover the structure of a compound object from multiple silhouettes. Structure is expressed as a collection of 3D primitives chosen from a pre-defined library, each with an associated pose. This has several…
We provide algorithms to reconstruct rational ruled surfaces in three-dimensional projective space from the `apparent contour' of a single projection to the projective plane. We deal with the case of tangent developables and of general…
X-ray tomography has been studied in various fields. Although a great deal of effort has been directed at reconstructing the projection image set from a rigid-type specimen, little attention has been addressed to the reconstruction of…
Maximally embedding dimension (MED) numerical semigroups are a wide and interesting family, with some remarkable algebraic and combinatorial properties. Associated to any numerical semigroup one can construct a MED closure, as it is well…
The higher-order autocorrelations of integer-valued or rational-valued gridded data sets appear naturally in X-ray crystallography, and have applications in computer vision systems, correlation tomography, correlation spectroscopy, and…
We develop a `universal' support theory for derived categories of constructible (analytic or \'etale) sheaves, holonomic D-modules, mixed Hodge modules and others. As applications we classify such objects up to the tensor triangulated…