
Generalized Shortest Pathbased Superpixels for Accurate Segmentation of Spherical Images
Most of existing superpixel methods are designed to segment standard pla...
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Conformal Geometry, Euclidean Space and Geometric Algebra
Projective geometry provides the preferred framework for most implementa...
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A new upper bound for spherical codes
We introduce a new linear programming method for bounding the maximum nu...
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Sifting Convolution on the Sphere
A novel spherical convolution is defined through the sifting property of...
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A Single Image based Head Pose Estimation Method with Spherical Parameterization
Head pose estimation plays a vital role in various applications, e.g., d...
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Rendering NonEuclidean Geometry in RealTime Using Spherical and Hyperbolic Trigonometry
This paper introduces a method of calculating and rendering shapes in a ...
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Areapreserving parameterizations for spherical ellipses
We present new methods for uniformly sampling the solid angle subtended ...
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Optimal AnyAngle Pathfinding on a Sphere
Pathfinding in Euclidean space is a common problem faced in robotics and computer games. For longdistance navigation on the surface of the earth or in outer space however, approximating the geometry as Euclidean can be insufficient for realworld applications such as the navigation of spacecraft, aeroplanes, drones and ships. This article describes an anyangle pathfinding algorithm for calculating the shortest path between point pairs over the surface of a sphere. Introducing several novel adaptations, it is shown that Anya as described by (Harabor Grastien, 2013) for Euclidean space can be extended to Spherical geometry. There, where the shortestdistance line between coordinates is defined instead by a greatcircle path, the optimal solution is typically a curved line in Euclidean space. In addition the turning points for optimal paths in Spherical geometry are not necessarily corner points as they are in Euclidean space, as will be shown, making further substantial adaptations to Anya necessary. Spherical Anya returns the optimal path on the sphere, given these different properties of world maps defined in Spherical geometry. It preserves all primary benefits of Anya in Euclidean geometry, namely the Spherical Anya algorithm always returns an optimal path on a sphere and does so entirely online, without any preprocessing or large memory overheads. Performance benchmarks are provided for several game maps including Starcraft and Warcraft III as well as for sea navigation on Earth using the NOAA bathymetric dataset. Always returning the shorter path compared with the Euclidean approximation yielded by Anya, Spherical Anya is additionally shown to be faster than Anya for the majority of routes, due to the wider field of vision provided by cone projections in Spherical geometry.
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