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Explanations of an article

Hi guys,

Hopefully someone with a better brain than mine can explain the theory behind this paper. I have been staring at it all day and I can't get my head around it.

http://mesh.brown.edu/eps

There is a also this paper that goes into more detail but it's not that easy to understand https://www.cv-foundation.org/openaccess/content_cvpr_2015/papers/Moreno_Embedded_Phase_Shifting_2015_CVPR_paper.pdf

Ideally it would great if it could be explained with some real numbers and possibly an explanation on how it could be implemented in pseudo code.

Thanks in advance

JT