Sampling great circles at their rate of innovation

In this work, we show that great circles, the intersection of a plane through the origin and a sphere centered at the origin, can be perfectly recovered at their rate of innovation. Specifically, we show that 4K(8K − 7) + 7 samples are sufficient to perfectly recover K great circles, given an approp...

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Bibliographic Details
Main Authors: Deslauriers-Gauthier, Samuel, Marziliano, Pina
Other Authors: Van De Ville, Dimitri
Format: Conference or Workshop Item
Language:English
Published: 2014
Subjects:
Online Access:https://hdl.handle.net/10356/100670
http://hdl.handle.net/10220/18606
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Institution: Nanyang Technological University
Language: English
Description
Summary:In this work, we show that great circles, the intersection of a plane through the origin and a sphere centered at the origin, can be perfectly recovered at their rate of innovation. Specifically, we show that 4K(8K − 7) + 7 samples are sufficient to perfectly recover K great circles, given an appropriate sampling scheme. Moreover, we argue that the number of samples can be reduced to 2K(4K − 1) while maintaining accurate results. This argument is supported by our numerical results. To improve the robustness to noise of our approach, we propose a modification that uses all the available information, instead of the critical amount. The increase in accuracy is demonstrated using numerical simulations.