Related papers: Computing Hive Plots: A Combinatorial Framework
Starting from the (apparently) elementary problem of deciding how many different topological spaces can be obtained by gluing together in pairs the faces of an octahedron, we will describe the central role played by hyperbolic geometry…
This paper introduces a hierarchical framework that integrates graph search algorithms and model predictive control to facilitate efficient parking maneuvers for Autonomous Vehicles (AVs) in constrained environments. In the high-level…
Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…
Overplotting of data points is a common problem when visualizing large datasets in a scatterplot, particularly when mapping nominal dimensions to one of the scatterplot axes. Transparency, aggregation, and jittering have previously been…
This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…
Recently, Convolutional Neural Networks have shown promising results for 3D geometry prediction. They can make predictions from very little input data such as a single color image. A major limitation of such approaches is that they only…
A trivalent diagram is a connected, two-colored bipartite graph (parallel edges allowed but not loops) such that every black vertex is of degree 1 or 3 and every white vertex is of degree 1 or 2, with a cyclic order imposed on every set of…
We present an approach for analyzing grouping information contained within a neural network's activations, permitting extraction of spatial layout and semantic segmentation from the behavior of large pre-trained vision models. Unlike prior…
Convex optimization encompasses a wide range of optimization problems that contain many efficiently solvable subclasses. Interior point methods are currently the state-of-the-art approach for solving such problems, particularly effective…
In spectral clustering, one defines a similarity matrix for a collection of data points, transforms the matrix to get the Laplacian matrix, finds the eigenvectors of the Laplacian matrix, and obtains a partition of the data using the…
Shape graphs are complex geometrical structures commonly found in biological and anatomical systems. A shape graph is a collection of nodes, some connected by curvilinear edges with arbitrary shapes. Their high complexity stems from the…
A combinatorial tiling of the sphere is naturally given by an embedded graph. We study the case that each tile has exactly five edges, with the ultimate goal of classifying combinatorial tilings of the sphere by geometrically congruent…
A graph is a mathematical object consisting of a set of vertices and a set of edges connecting vertices. Graphs can be drawn on paper in various ways, but until recently all published methods of drawing graphs have had undesirable…
The paper presents two edge grouping algorithms for finding a closed contour starting from a particular edge point and enclosing a fixation point. Both algorithms search a shortest simple cycle in \textit{an angularly ordered graph} derived…
Orbit harmonics is a tool in combinatorial representation theory which promotes the (ungraded) action of a linear group $G$ on a finite set $X$ to a graded action of $G$ on a polynomial ring quotient by viewing $X$ as a $G$-stable point…
Reconfiguration schedules, i.e., sequences that gradually transform one solution of a problem to another while always maintaining feasibility, have been extensively studied. Most research has dealt with the decision problem of whether a…
We explore computational approaches for visual guidance to aid in creating aesthetically pleasing art and graphic design. Our work complements and builds on previous work that developed models for how humans look at images. Our approach…
Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…
Analyzing a visual scene by inferring the configuration of a generative model is widely considered the most flexible and generalizable approach to scene understanding. Yet, one major problem is the computational challenge of the inference…