Selecting that pixel that minimizes the distance

Say I have the following two matrices:

    >> x = [1 4 3; 6 4 3; 6 9 3; 2 4 3; 5 4 0; 5 3 1; 6 4 7];
    >> y = [0 0 1; 1 1 0; 1 1 0; 0 1 1; 0.2 0.8 0.54; 1 1 1; 0 0 0];

Where you can think of `x` as some image, and `y` as the *degree of membership* of each element of `x` to some region of interest.

Say I set those elements in `x` that have degree of membership = 1 to `1` (*core*) and the other elements to `0` as follows:

    x = zeros(size(y));
    x(y==1) = 1;

In which case I will have the following output:

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

Now, for the elements of `0`, I substitute their values with the value of `y` in the corresponding location as follows:

    x(x==0)=y(x==0);

Now, I select those pixels that are considered `4-neighbours` of `core` but not in core as follows:

    four_neighbourhood_pixels = imdilate(core, strel('diamond', 1)) - core;

My question is: *how can we select a pixel `p` that belongs to `four_neighbourhood_pixels` that minimizes the distance between `x` & `core`*?

Provided that for distance I calculate it as follows:

    pdist([x,core],'minkowski');

Provided that `x` in the preceding command will be the matrix after substituting the `zeros` with the degree of membership values `y` i the corresponding location?

So, how can I select that pixel that belongs to ` four_neighbourhood_pixels` that minimizes the distance between `x` with the zeros substituted and `core`?

Thanks.

[Image Analyst]

Not sure I follow everything. Remind me what the original x was used for. It looks like you just ignore it because you reassign x to be all zeros. Is that true?

[med-sweng]

@Image Analyst. Thanks for your reply. You can assume that `x` is some image. I actually don't ignore `x`, but based on the membership values `y` modify the values of its elements. Does that make sense?

[Image Analyst]

No. If x is an image, then please explain what you are doing to x with this line:

x = zeros(size(y));

[med-sweng]

@Image Analyst. I used this line in order to set the elements of `x` that have a membership value of `1` to `1` and others to `0`. And, as a second step to set those zero valued elements to the value of their membership since I need the features for measutring the distance, where the membership value here represents the element's feature. For `x` then, not to confuse, let's say it is a simple matrix if you want...

[Image Analyst]

But you totally destroy your original x image when you do that.

[med-sweng]

@Image Analyst. I'm currently trying this in theory and will see the effect afterwards. But, now just in need to know how to write a matlab code that selects that pixel belonging to the 4-neighbourhood of `core` that minimizes the distance. Any ideas on how this statement an be written? Thanks