Returning lists of pixels connected through their Moore neighborhoods

I have a binarized image in Mathematica 9, and I would like to generate a list of coordinates for clusters of pixels connected through their Moore neighborhoods, e.g. $((c_{1,1},c_{1,2},...),(c_{2,1},c_{2,2},...),...)$ where some $c_{n,k}$ is the coordinate for the $k$th pixel in the $N$th set of pixels connected through their Moore neighborhoods.

Is there a simple way to proceed with Mathematica 9's image analysis tool set?

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Have you tried MorphologicalComponents@Dilation[image, 1]? – Dr. belisarius Jun 25 '13 at 3:35
@belisarius MorphologicalComponents seems to work fairly well, but what exactly is this command doing? – Bob Jun 25 '13 at 4:47
Have you read this? (... and all the answers to that question, BTW) – Dr. belisarius Jun 25 '13 at 11:36

From Belisarius' comment:

MorphologicalComponents@Dilation[image, 1]


The documentation states:

MorphologicalComponents assigns sequential integers to different connected components.

and

MorphologicalComponents by default treats all eight pixels surrounding a given pixel as adjacent.

This is precisely the connectedness you were looking for.

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