Hi. I have a graph theory question:
I would like to make a definition of a particular patch of cortex, that has a centroid at position (x,y,z) and has a total area of A.
I thought that this was going to be somewhat hard, but I soon learned that it is very hard.
First, I found some code for the Dijkstra algorithm, which can quickly tell me what is the minimum number of jumps needed from one vertex to another. IF the freesurfer surface triangles were all of EXACTLY the same euclidean distances on each side, then this alone could solve my problem. I could simply take all vertices which have a jump distance less than some number.
However, because the side lengths of the triangles in a freesurfer surface are NOT the same, I need to get more sophisticated.
Ideally, what I would like is the following: If I were an ant, walking along on the surface of the folded brain, I could walk from the centroid in any direction for a certain distance, and still be within my "patch." Knowing that distance (radius), I could just use pi*r^2 and call that the area of the patch.
But how do I find this idealized patch in real life?
Thanks Daniel Goldenholz