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function G = mk_2D_lattice(nrows, ncols, con)
% MK_2D_LATTICE Return adjacency matrix for nearest neighbor connected 2D lattice
% G = mk_2D_lattice(nrows, ncols, con)
% G(k1, k2) = 1 iff k1=(i1,j1) is a neighbor of k2=(i2,j2)
% (Two pixels are neighbors if their Euclidean distance is less than r.)
% Default connectivity = 4.
%
% WE ASSUME NO WRAP AROUND.
%
% This is the neighborhood as a function of con:
%
% con=4,r=1 con=8,r=sqrt(2) con=12,r=2 con=24,r=sqrt(8)
% nn 2nd order 4th order
% x x x x x x
% x x x x x x x x x x x x
% x o x x o x x x o x x x x o x x
% x x x x x x x x x x x x
% x x x x x x
%
% Examples:
% Consider a 3x4 grid
% 1 4 7 10
% 2 5 8 11
% 3 6 9 12
%
% 4-connected:
% G=mk_2D_lattice(3,4,4);
% find(G(1,:)) = [2 4]
% find(G(5,:)) = [2 4 6 8]
%
% 8-connected:
% G=mk_2D_lattice(3,4,8);
% find(G(1,:)) = [2 4 5]
% find(G(5,:)) = [1 2 3 4 6 7 8 9]
% meshgrid trick due to Temu Gautama (temu@neuro.kuleuven.ac.be)
if nargin < 3, con = 4; end
switch con,
case 4, r = 1;
case 8, r = sqrt(2);
case 12, r = 2;
case 24, r = sqrt(8);
otherwise, error(['unrecognized connectivity ' num2str(con)])
end
npixels = nrows*ncols;
[x y]=meshgrid(1:ncols, 1:nrows);
M = [x(:) y(:)];
M1 = repmat(reshape(M',[1 2 npixels]),[npixels 1 1]);
M2 = repmat(M,[1 1 npixels]);
%D = squeeze(sum(abs(M1-M2),2)); % Manhattan distance
M3 = M1-M2;
D = sqrt(squeeze(M3(:,1,:)) .^2 + squeeze(M3(:,2,:)) .^2); % Euclidean distance
G = reshape(D <= r,npixels,npixels);
G = setdiag(G, 0);
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