MATLAB: Is it possible to calculate the average Manhattan distance between a set of 2D points with one function

averagedistancedsearchnexclude current pointpdist2

Is there an easier way to calculate the average Manhattan distance between a set of points easier than I have it in my code? I have a matrix, which contains a set of 2D points (the columns corespond to the x and y coordinates).
%for the first point
[idx,~]=dsearchn(isec(2:end,:),isec(1,:));
sum=pdist2(isec(1,:), isec(idx+1,:), 'cityblock');
%for the rest of the points
for i=2:size(isec,1)-1
   others=[isec(1:i-1,:); isec(i+1:end,:)];
   [idx,~]=dsearchn(others,isec(i,:));
   man=pdist2(isec((i,:), others(idx,:), 'cityblock');
   sum=sum+man;
end
%for the last point
[idx,~]=dsearchn(isec(1:end-1,:),isec(end,:));
sum=sum+pdist2(isec(end,:), isec(idx,:), 'cityblock');
avg_dist=sum/size(isec,1);
As dsearch cannot calculate other distances than euclidean, I use it to find the index of the nearest point. After that I have to call the pdist2 function to measure the cityblock distance. What complicates things even more is the fact, that I have to exclude the current point (to which I'm trying to find the closest one); that's the purpos of my 'others' variable and the 2 pieces of code above and below the for-cycle.
To give a bit of context:
The goal is image segmentation. The points are actually line intersections in a grid. I want to calculate the average Manhattan distance in order to use the result as a treshhold to determine which points are roughly in the given row/column (unlike in the case of crosswords, sudokus, nonograms I'm not interested in the square areas between the lines, rather in the intersections).

Best Answer

I think this does what you want. You could probably make it more efficient recognizing the symmetry of the distance matrix, but just wanted to get the main idea across
% just some data to try, you'd put your here
x = [1 8 7 2 6 3]
y = [3 6 2 5 1 4]
numPoints = length(x)
% make array of Manhattan distances (L1 norm) between between each point to all other points
D = zeros(numPoints)
for j = 1:numPoints
    for k = 1:numPoints
        D(j,k) = norm([x(j),y(j)] -[x(k),y(k)],1);
    end
end
% set main diagonal to inf so it won't be included when looking for minimum
% distance
D = D + diag(inf(numPoints,1));
% find minimum distance for each row
dMin = min(D,[],2);
% find average minimum
dAvg = mean(dMin)
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