Sampling great circles at their rate of innovation

Samuel Deslauriers-Gauthier; Pina Marziliano

doi:10.1117/12.2023863

26 September 2013 Sampling great circles at their rate of innovation

Samuel Deslauriers-Gauthier, Pina Marziliano

Proceedings Volume 8858, Wavelets and Sparsity XV; 88580V (2013) https://doi.org/10.1117/12.2023863
Event: SPIE Optical Engineering + Applications, 2013, San Diego, California, United States

Abstract

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.

Citation Download Citation

Samuel Deslauriers-Gauthier and Pina Marziliano "Sampling great circles at their rate of innovation", Proc. SPIE 8858, Wavelets and Sparsity XV, 88580V (26 September 2013); https://doi.org/10.1117/12.2023863

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available