Binary Element Distance Function (similar to graycomatrix)

I would like a function that takes a binary image, and outputs the minimum distance between connected elements of different sizes.

Example:

BW =

     1     1     0     1     0
     0     0     0     1     0
     0     0     0     0     0
     1     1     0     0     0
     1     0     0     0     1

MinimumDistanceMatrix =

     0     2     2     0     0     0
     2     1     1     0     0     0
     2     1     0     0     0     0
     0     0     0     0     0     0
     0     0     0     0     0     0
     0     0     0     0     0     0

This output is similar to the graycomatrix output matrix, suchthat value (1,1) represents the minimum distace between any 2 elements of size 1 and 1. And (2,1) represents the minimum distace between any 2 elements of size 2 and 1.

Note: The result will always be a symmetric matrix because the minimum distance from 2 elements of size i and j will be identical to the minimum distance from 2 elements of size j and i.

I have started going down the path of using bwlabel on the initial binary image to get a matrix of each unique elements.

LabeledBW =

     1     1     0     3     0
     0     0     0     3     0
     0     0     0     0     0
     2     2     0     0     0
     2     0     0     0     4

Then selecting each element and changing each value of the element to be the size of the element.

BWElementSize =

     2     2     0     2     0
     0     0     0     2     0
     0     0     0     0     0
     3     3     0     0     0
     3     0     0     0     1

But form here the only way I have thought of to get to the result I want is to use the graycomatrix function in a rediculous set of loops which will be sure to be very slow and I want to avoid coding.

So if anyone has any sugestions I would love to hear them. I feel like I am headed down the wrong path with the loops and there must be a better way to do this.

Thanks, Barrett