Interesting paper. The idea is pretty simple and the algorithm does not seem to be difficult to implement.
I see one artifact with this approach however, given "Lenna" in greyscale:
(left: original, middle: this paper with τ = 0.5, right: imagemagick contrast +15)
Notice that the bow-shaped part enclosed by her hair at the bottom of the photo becomes much brighter than the body after contrast enhancement. This closed area becomes a separate hillock during sweeping and is stretched more than other parts due to a looser constraint (6). This becomes pretty noticeable with increasing τ. With that said this paper does a pretty good job at enhancing the texture of the hair.
I suppose this approach should work well on images with high contrast as it avoids over-saturating pixels, but then I have no idea how well it compares to other tools available in darktable/RawTherapee.