Art’s hidden topology: A window into human perception
Fig 2
Exploring topology and persistence through filtration.
Visualisation of a pixel-based structure with varying brightness levels, demonstrating the use of grey intensity (on a scale from 0 to 1) as a filtration parameter. At a grey intensity of 0.1, the structure is divided into two distinct parts, outlined by a red contour) with two ‘holes’ of grey intensities 0.3 and 0.5. This results in Betti numbers and
. As the filter transparency (greyness) increases, changes in the visibility of pixels at grey level 0.3, the two distinct shapes are still present, although one of the holes in the bigger part (with intensity r = 0.3) disappears, changing the Betti numbers to
and
. At the intensity r = 0.4, the two shapes merged into one part with one hole (
and
). If we further increase filter intensity to r = 0.5 all pixels will become visible yielding Betti numbers
and
.