What do you call an iterated flood fill algorithm?

I have an algorithm that I'm using for my work, but I need a name for it. I am curious if name exists in the literature for an algorithm of this type.

The algorithm takes a pixelated height map and a starting point s, and returns a modified pixelated height map. For each pixel p in the returned height map, p is the value of lowest height you must pass through to get from s to p.

Example, consider the "peak" image in Matlab: imagesc(peak) .

And use the pixel (20,20) as the seed, then this modified height map I am describing looks like this: .

I had called this a flood fill algorithm, until my colleagues pointed out that flood fills are typically binary maps. So, Ive taken to calling this a "graduated flood fill" algorithm.

We have not found this operation defined in the literature. Any suggestions?

In Matlab, this algorithm is called Morphological Reconstruction. The matlab command to implement the algorithm is called: imreconstruct.

The specific steps are:

tmp = peaks
apt = zeros(size(tmp));
apt(20,20) = tmp(20,20);
imagesc(imreconstruct(apt, tmp))

which generates this image, as requested.