I have a Healpy map of a scalar field, i.e. a map produced with the Python implementation of the Healpix discretisation scheme. I want to calculate the Minkowski Functionals of this field from this map.
Reading some literature I understood that one first sets a threshold value of the field and transforms the pixels in the map in 1 and 0 values if they pass or not the threshold.
How can one then proceed to calculate Area, Volume and Euler characteristics? I guess the first step is to identify the 4 nearest neighbours for each pixel of the map and then study the possible configurations of 4-pixels blocks that one obtains, but
1) it is not clear to me how to relate the configurations to the actual values of the functionals
2) how to identify and make sense of the nearest enighbours is actually not that simple in Healpy, given the very special ordering of pixels that characterises Healpix.
Any insight would be very much appreciated