Fast approximate 4-D/3-D discrete radon transform for lightfield refocusing

Abstract

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 4-D lightfield into a 3-D volume of photographic planes as previously done by 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 3-D 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 a power of two is proposed.