Related papers: Enumerating fundamental normal surfaces: Algorithm…
Machine learning and deep learning have been used extensively to classify physical surfaces through images and time-series contact data. However, these methods rely on human expertise and entail the time-consuming processes of data and…
We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive…
Most existing approaches for point cloud normal estimation aim to locally fit a geometric surface and calculate the normal from the fitted surface. Recently, learning-based methods have adopted a routine of predicting point-wise weights to…
Generative models that produce point clouds have emerged as a powerful tool to represent 3D surfaces, and the best current ones rely on learning an ensemble of parametric representations. Unfortunately, they offer no control over the…
Point normal, as an intrinsic geometric property of 3D objects, not only serves conventional geometric tasks such as surface consolidation and reconstruction, but also facilitates cutting-edge learning-based techniques for shape analysis…
We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure is generic (with…
In this article we discuss applications of neural networks to recognising knots and, in particular, to the unknotting problem. One of motivations for this study is to understand how neural networks work on the example of a problem for which…
Maps are arguably one of the most fundamental concepts used to define and operate on manifold surfaces in differentiable geometry. Accordingly, in geometry processing, maps are ubiquitous and are used in many core applications, such as…
Learning to reconstruct depths in a single image by watching unlabeled videos via deep convolutional network (DCN) is attracting significant attention in recent years. In this paper, we introduce a surface normal representation for…
This paper extends a recently proposed robust computational framework for constructing the boundary representation (brep) of the volume swept by a given smooth solid moving along a one parameter family $h$ of rigid motions. Our extension…
The goal of this study is to provide a method for computing the following: Given a network of curves in 3d (satisfying a condition at the intersection points), compute efficiently a smooth surface such that the curves are geodesics on it.…
In this work, we study the perception problem for sampled surfaces (possibly with boundary) using tools from computational topology, specifically, how to identify their underlying topology starting from point-cloud samples in space, such as…
In the past few years, convolutional neural nets (CNN) have shown incredible promise for learning visual representations. In this paper, we use CNNs for the task of predicting surface normals from a single image. But what is the right…
This article consists of two parts. The first part is a survey on the normal reduction numbers of normal surface singularities. It includes results on elliptic singularities, cone-like singularities and homogeneous hypersurface…
A new type of knot energy is presented via real life experiments involving a thin resilient metallic tube. Knotted in different ways, the device mechanically acquires a uniquely determined (up to isometry) normal form at least when the…
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…
The substantial increase in data volume and complexity expected from future experiments will require significant investment to prepare experimental algorithms. These algorithms include physics object reconstruction, calibrations, and…
Using tools from topology and functional analysis, we provide a framework where artificial neural networks, and their architectures, can be formally described. We define the notion of machine in a general topological context and show how…
This is a survey on the use of low-degree polynomials to predict and explain the apparent statistical-computational tradeoffs in a variety of average-case computational problems. In a nutshell, this framework measures the complexity of a…
These notes are an introduction to knot theory from the perspective of surfaces. The notes cover fundamental concepts such as isotopies, Reidemeister moves, torus knots, and (orientable, connected) surfaces with one boundary component. They…