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1 function G = mk_2D_lattice(nrows, ncols, con)
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2 % MK_2D_LATTICE Return adjacency matrix for nearest neighbor connected 2D lattice
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3 % G = mk_2D_lattice(nrows, ncols, con)
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4 % G(k1, k2) = 1 iff k1=(i1,j1) is a neighbor of k2=(i2,j2)
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5 % (Two pixels are neighbors if their Euclidean distance is less than r.)
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6 % Default connectivity = 4.
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7 %
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8 % WE ASSUME NO WRAP AROUND.
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9 %
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10 % This is the neighborhood as a function of con:
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11 %
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12 % con=4,r=1 con=8,r=sqrt(2) con=12,r=2 con=24,r=sqrt(8)
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13 % nn 2nd order 4th order
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14 % x x x x x x
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15 % x x x x x x x x x x x x
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16 % x o x x o x x x o x x x x o x x
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17 % x x x x x x x x x x x x
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18 % x x x x x x
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19 %
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20 % Examples:
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21 % Consider a 3x4 grid
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22 % 1 4 7 10
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23 % 2 5 8 11
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24 % 3 6 9 12
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25 %
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26 % 4-connected:
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27 % G=mk_2D_lattice(3,4,4);
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28 % find(G(1,:)) = [2 4]
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29 % find(G(5,:)) = [2 4 6 8]
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30 %
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31 % 8-connected:
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32 % G=mk_2D_lattice(3,4,8);
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33 % find(G(1,:)) = [2 4 5]
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34 % find(G(5,:)) = [1 2 3 4 6 7 8 9]
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35
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36 % meshgrid trick due to Temu Gautama (temu@neuro.kuleuven.ac.be)
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37
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38 if nargin < 3, con = 4; end
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39
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40 switch con,
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41 case 4, r = 1;
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42 case 8, r = sqrt(2);
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43 case 12, r = 2;
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44 case 24, r = sqrt(8);
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45 otherwise, error(['unrecognized connectivity ' num2str(con)])
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46 end
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47
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48
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49 npixels = nrows*ncols;
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50
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51 [x y]=meshgrid(1:ncols, 1:nrows);
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52 M = [x(:) y(:)];
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53 M1 = repmat(reshape(M',[1 2 npixels]),[npixels 1 1]);
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54 M2 = repmat(M,[1 1 npixels]);
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55 %D = squeeze(sum(abs(M1-M2),2)); % Manhattan distance
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56 M3 = M1-M2;
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57 D = sqrt(squeeze(M3(:,1,:)) .^2 + squeeze(M3(:,2,:)) .^2); % Euclidean distance
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58 G = reshape(D <= r,npixels,npixels);
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59 G = setdiag(G, 0);
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