Re: [computer-go] Designing faster, better influence functions

[Gunnar Farnebäck <gunnar@xxxxxxxxxxxxxx>]

Frank wrote:
> I was wondering, why do most influence functions (like Fotland's) use the
> Manhattan distance for the strength of the influence and not the Pythagorean
> distance?

I don't know. GNU Go has an influence function which for an isolated
stone of strength 100 looks like this, after rounding down to integer
values:

  0  0  0  0  0  0  0  0  0  0  0
  0  0  0  0  1  1  1  0  0  0  0
  0  0  0  1  2  3  2  1  0  0  0
  0  0  1  3  5 11  5  3  1  0  0
  0  1  2  5 16 33 16  5  2  1  0
  0  1  3 11 33  X 33 11  3  1  0
  0  1  2  5 16 33 16  5  2  1  0
  0  0  1  3  5 11  5  3  1  0  0
  0  0  0  1  2  3  2  1  0  0  0
  0  0  0  0  1  1  1  0  0  0  0
  0  0  0  0  0  0  0  0  0  0  0

> I can see that the argument is that the Manhattan distance is the number of
> stones needed to connect, but in Go, diagonally connected stones are pretty
> strong,

I agree.

> so one would expect that the Manhattan distance is mainly used
> because it speeds up the calculation perhaps?
  
Or because it's simpler to implement or because it's good enough.

It might interest you to search the image processing literature (or
Google) for "Euclidean distance transform" or some approximation like
the Chamfer distance.

/Gunnar
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