Related papers: Polygon Detection from a Set of Lines
To support exactly tracking a neutron moving along a given line segment through a CAD model with quadric surfaces, this paper considers the arithmetic precision required to compute the order of intersection points of two quadrics along the…
In this paper, we consider the problem of partitioning a polygon into a set of connected disjoint sub-polygons, each of which covers an area of a specific size. The work is motivated by terrain covering applications in robotics, where the…
A fundamental question for edge detection in noisy images is how faint can an edge be and still be detected. In this paper we offer a formalism to study this question and subsequently introduce computationally efficient multiscale edge…
There are many practical applications that require simplification of polylines. Some of the goals are to reduce the amount of information necessary to store, improve processing time, or simplify editing. The simplification is usually done…
Lane detection in driving scenes is an important module for autonomous vehicles and advanced driver assistance systems. In recent years, many sophisticated lane detection methods have been proposed. However, most methods focus on detecting…
An algorithm is demonstrated that finds an ordinary intersection in an arrangement of $n$ lines in $\mathbb{R}^2$, not all parallel and not all passing through a common point, in time $O(n \log{n})$. The algorithm is then extended to find…
Whether it is object detection, model reconstruction, laser odometry, or point cloud registration: Plane extraction is a vital component of many robotic systems. In this paper, we propose a strictly probabilistic method to detect finite…
While the contents of Euclid's Elements are well-known these days, some characters of the original text have been overlooked due to interpretation by modern mathematical languages. The lens of modern mathematics once anachronistically…
In this paper we propose an algorithm for the detection of edges in images that is based on topological asymptotic analysis. Motivated from the Mumford--Shah functional, we consider a variational functional that penalizes oscillations…
Based on cluster de-synchronization properties of phase oscillators, we introduce an efficient method for the detection and identification of modules in complex networks. The performance of the algorithm is tested on computer generated and…
This paper studies the problem of embedding very large information networks into low-dimensional vector spaces, which is useful in many tasks such as visualization, node classification, and link prediction. Most existing graph embedding…
The famous pancake theorem states that for every finite set $X$ in the plane, there exist two orthogonal lines that divide $X$ into four equal parts. We propose an algorithm whose running time is linear in the number of points in $X$ and…
Given a set of N points, we have discovered an algorithm that can separate these points from one another by n-dimensional planes. Each point is chosen at random and put into a set S and planes which separate them are determined and put into…
Linear diagrams are an effective way to visualize set-based data by representing elements as columns and sets as rows with one or more horizontal line segments, whose vertical overlaps with other rows indicate set intersections and their…
Hinging on ideas from physical-layer network coding, some promising proposals of coded random access systems seek to improve system performance (while preserving low complexity) by means of packet repetitions and decoding of linear…
3D shape representation and its processing have substantial effects on 3D shape recognition. The polygon mesh as a 3D shape representation has many advantages in computer graphics and geometry processing. However, there are still some…
We present a conceptually simple yet effective algorithm to detect wireframes in a given image. Compared to the previous methods which first predict an intermediate heat map and then extract straight lines with heuristic algorithms, our…
This paper describes an efficient approach to constructing a resultant polyline with a minimum number of segments and arcs. While fitting an arc can be done with complexity O(1) (see [1] and [2]), the main complexity is in checking that the…
Contour polygonal approximation is a simplified representation of a contour by line segments, so that the main characteristics of the contour remain in a small number of line segments. This paper presents a novel method for polygonal…
We define the \emph{visual complexity} of a plane graph drawing to be the number of basic geometric objects needed to represent all its edges. In particular, one object may represent multiple edges (e.g., one needs only one line segment to…