Fast approximate 4D:3D discrete radon transform, from light field to focal stack with O(N4) sums

José G. Marichal-Hernández; Jonas P. Lüke; Fernando L. Rosa; José M. Rodríguez-Ramos

doi:10.1117/12.872359

2 February 2011 Fast approximate 4D:3D discrete Radon transform, from light field to focal stack with O(N⁴) sums

José G. Marichal-Hernández, Jonas P. Lüke, Fernando L. Rosa, José M. Rodríguez-Ramos

Proceedings Volume 7871, Real-Time Image and Video Processing 2011; 78710G (2011) https://doi.org/10.1117/12.872359
Event: IS&T/SPIE Electronic Imaging, 2011, San Francisco Airport, California, United States

Abstract

In this work we develop a new algorithm, that extends the bidimensional Fast Digital Radon transform from Götz and Druckmüller (1996), to digitally simulate the refocusing of a 4D light field into a 3D volume of photographic planes, as previously done by Ren Ng et al. (2005), but with the minimum number of operations. This new algorithm does not require multiplications, just sums, and its computational complexity is O(N⁴) to achieve a volume consisting of 2N photographic planes focused at different depths, from a N⁴ plenoptic image. This reduced complexity allows for the acquisition and processing of a plenoptic sequence with the purpose of estimating 3D shape at video rate. Examples are given of implementations on GPU and CPU platforms. Finally, a modified version of the algorithm to deal with domains of sizes different than power of two, is proposed.

Citation Download Citation

José G. Marichal-Hernández, Jonas P. Lüke, Fernando L. Rosa, and José M. Rodríguez-Ramos "Fast approximate 4D:3D discrete Radon transform, from light field to focal stack with O(N⁴) sums", Proc. SPIE 7871, Real-Time Image and Video Processing 2011, 78710G (2 February 2011); https://doi.org/10.1117/12.872359

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