Related papers: Scenic Routes over Points in 2D Space
We introduce one dimensional sets to help describe and constrain the integral curves of an $n$ dimensional dynamical system. These curves provide more information about the system than the zero-dimensional sets (fixed points) do. In fact,…
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…
Detection of curvilinear structures in images has long been of interest. One of the most challenging aspects of this problem is inferring the graph representation of the curvilinear network. Most existing delineation approaches first…
Semantic 2D maps are commonly used by humans and machines for navigation purposes, whether it's walking or driving. However, these maps have limitations: they lack detail, often contain inaccuracies, and are difficult to create and…
Constructions and exploration of plane algebraic curves has received a new push with the development of automated methods, whose algorithms are continuously improved and implemented in various software packages. We use them to explore the…
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…
For intelligent robots to interact in meaningful ways with their environment, they must understand both the geometric and semantic properties of the scene surrounding them. The majority of research to date has addressed these mapping…
For any metric $d$ on $\mathbb{R}^2$, an ($\mathbb{R}^2,d$)-geometric graph is a graph whose vertices are points in $\mathbb{R}^2$, and two vertices are adjacent if and only if their distance is at most 1. If $d=\|.\|_{\infty}$, the metric…
We propose a new probabilistic programming language for the design and analysis of perception systems, especially those based on machine learning. Specifically, we consider the problems of training a perception system to handle rare events,…
Rich semantic information extraction plays a vital role on next-generation intelligent vehicles. Currently there is great amount of research focusing on fundamental applications such as 6D pose detection, road scene semantic segmentation,…
Scene graph is a structured representation of a scene that can clearly express the objects, attributes, and relationships between objects in the scene. As computer vision technology continues to develop, people are no longer satisfied with…
Scene graphs are a compact and explicit representation successfully used in a variety of 2D scene understanding tasks. This work proposes a method to incrementally build up semantic scene graphs from a 3D environment given a sequence of…
A geometric graph is a graph whose vertices are points in general position in the plane and its edges are straight line segments joining these points. In this paper we give an $O(n^2 \log n)$ algorithm to compute the number of pairs of…
There is extensive literature on perceiving road structures by fusing various sensor inputs such as lidar point clouds and camera images using deep neural nets. Leveraging the latest advance of neural architects (such as transformers) and…
Street-level visual appearances play an important role in studying social systems, such as understanding the built environment, driving routes, and associated social and economic factors. It has not been integrated into a typical…
Trajectories can be regarded as time-series of coordinates, typically arising from motile objects. Methods for trajectory classification are particularly important to detect different movement patterns, while methods for regression to…
3D scene flow estimation aims to estimate point-wise motions between two consecutive frames of point clouds. Superpoints, i.e., points with similar geometric features, are usually employed to capture similar motions of local regions in 3D…
We characterize the topological configurations of points and lines that may arise when placing n points on a circle and drawing the n perpendicular bisectors of the sides of the corresponding convex cyclic n-gon. We also provide exact and…
A comprehensive semantic understanding of a scene is important for many applications - but in what space should diverse semantic information (e.g., objects, scene categories, material types, texture, etc.) be grounded and what should be its…
Route choice is often modelled as a two-step procedure in which travellers choose their routes from small sets of promising candidates. Many methods developed to identify such choice sets rely on assumptions about the mechanisms behind the…