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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.

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  • $\begingroup$ AT least in V8.0 ClusteringComponents[]doesn't seem to accept a custom DistanceFunction. Just those listed in the help $\endgroup$ – Dr. belisarius Jan 25 '13 at 8:06
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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 use your own DistanceFunction in ClusteringComponents:

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 it with ImageData of a grayscale image. The following approach works: 

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

enter image description here enter image description here

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