How does DistanceFunction work with images in ClusteringComponents?

Question

Does anyone know the syntax to DistanceFunction? I am trying to define my own function to use with ClusteringComponents; e.g.,

ClusteringComponents[img, DistanceFunction -> (Norm[#1 - #2] &)]

Needless to say it does not work as shown (it overflows for some reason). I also tried using ImageData@img but that does not even terminate.

Answer 1

I tested ClusteringComponents with the examples provided in the Documentation Center (http://reference.wolfram.com/mathematica/ref/ClusteringComponents.html) of Mathematica. In Options > DistanceFunction there is an example provided how to apply your own DistanceFunction:

ClusteringComponents[{{1, 2}, 3, {10, 11}, {12, {13}}, 14}, 2, 1, 
     DistanceFunction -> (Abs[Length[#1] - Length[#2]] &)]

I tried to apply this to an image without any success. I only ended up with some very strange looking error messages. After a few more tests I found the following solution. First of all, ClusteringComponents seems to work with a selfmade DistanceFunction only if you provide the ImageData of a grayscale image. The following works:

Colorize@ClusteringComponents[ImageData[ColorConvert[img, "GrayScale"]], 3, 
  DistanceFunction -> (Norm[#1 - #2] &)]

I applied this to the following image

with the resulting image:

So at least it seems to work :) I really wonder what the implementation of ClusteringComponents looks like. To me this function is a little mystery now...