Related papers: Fast and Accurate Intersections on a Sphere
The task of approximating points with circular arcs is performed in many applications, such as polyline compression, noise filtering, and feature recognition. However, the development of algorithms that perform a significant amount of…
We present improved algorithms for fast calculation of the inverse square root for single-precision floating-point numbers. The algorithms are much more accurate than the famous fast inverse square root algorithm and have the same or…
Collision-free motion planning in complex outdoor environments relies heavily on perceiving the surroundings through exteroceptive sensors. A widely used approach represents the environment as a voxelized Euclidean distance field, where…
Numerical integration on spheres, including the computation of the areas of spherical triangles, is a core computation in geomathematics. The commonly used techniques sometimes suffer from instabilities and significant loss of accuracy. We…
We present a general perturbative effective field theory (EFT) description of galaxy shape correlations, which are commonly known as intrinsic alignments. This rigorous approach extends current analytical modelling strategies in that it…
Under conditions that prevent tangential intersection, we prove quadratic convergence of a projection algorithm for the feasibility problem of finding a point in the intersection of a smooth curve and line in $\mathbb{R}^2$. This nonconvex…
The operations of data set, such as intersection, union and complement, are the fundamental calculation in mathematics. It's very significant that designing fast algorithm for set operation. In this paper, the quantum algorithm for…
Image stitching aims to construct a wide field of view with high spatial resolution, which cannot be achieved in a single exposure. Typically, conventional image stitching techniques, other than deep learning, require complex computation…
This article presents an easy distance field-based collision detection scheme to detect collisions of an object with its environment. Through the clever use of back-face culling and z-buffering, the solution is precise and very easy to…
We study the problem of fitting circles (or circular arcs) to data points observed with errors in both variables. A detailed error analysis for all popular circle fitting methods -- geometric fit, Kasa fit, Pratt fit, and Taubin fit -- is…
In computer vision, the estimation of the fundamental matrix is a basic problem that has been extensively studied. The accuracy of the estimation imposes a significant influence on subsequent tasks such as the camera trajectory…
Effective field theories (EFTs) organize the description of complex systems into an infinite sequence of decreasing importance. Predictions are made with a finite number of terms, which induces a truncation error that is often left…
Matching two images while estimating their relative geometry is a key step in many computer vision applications. For decades, a well-established pipeline, consisting of SIFT, RANSAC, and 8-point algorithm, has been used for this task.…
We study how the supporting hyperplanes produced by the projection process can complement the method of alternating projections and its variants for the convex set intersection problem. For the problem of finding the closest point in the…
The Fast Fourier Transform (FFT) over a finite field $\mathbb{F}_q$ computes evaluations of a given polynomial of degree less than $n$ at a specifically chosen set of $n$ distinct evaluation points in $\mathbb{F}_q$. If $q$ or $q-1$ is a…
Interacting with the environment, such as object detection and tracking, is a crucial ability of mobile robots. Besides high accuracy, efficiency in terms of processing effort and energy consumption are also desirable. To satisfy both…
Fusion-based place recognition is an emerging technique jointly utilizing multi-modal perception data, to recognize previously visited places in GPS-denied scenarios for robots and autonomous vehicles. Recent fusion-based place recognition…
This paper presents a set of simple and intuitive robot collision detection algorithms that show substantial scaling improvements for high geometric complexity and large numbers of collision queries by leveraging hardware-accelerated ray…
We introduce Integral Curve Coordinates, which identify each point in a bounded domain with a parameter along an integral curve of the gradient of a function $f$ on that domain; suitable functions have exactly one critical point, a maximum,…
Graph similarity computation is one of the core operations in many graph-based applications, such as graph similarity search, graph database analysis, graph clustering, etc. Since computing the exact distance/similarity between two graphs…