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I am very very new to Topological Data Analysis (TDA) and I am trying to apply the method described in this paper. I understood everything but stuck on methodology section (3.2) where he described:

use R package "TDA" [FKLM14] to compute the 0- and 1-dimentional superlevel set pesistent homology barcodes of the surface...

where TDA package link is here.

Now what I am confused is, because most of PH or TDA is done on "clouds of data points" such as a circle etc, idk how that would be translated into an image which is a 2D matrix (with each entry being a pixel). When we use clouds of data, those data are only given in (x,y) coordinates, not with intensities (or we can think as z coordinate)...

So the question is... how do we convert these intensities into simplexes?

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