# Sort or place several points into the nearst point in an unknown a x b grid, and get each point's (i,j) index in the grid.

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raym am 23 Jul. 2023
Kommentiert: raym am 23 Jul. 2023
Hi I encountered a problem when I try to allocate K points into a horzontal/vertical grid of unkonwn size.
Suppose there are variable number (k) points, each have a coordination recorded in a Kx2 matrix M.
M(:,1) is the x coordinates for all these k points, and M(:,2) is the y coordinates for all these k points.
These points could be roughly fitted into unknown a x unknown b grid with the minimum of offset for each point..
Is there a way to get the number a and b, and get the index (i,j) for each ppint so that each point could be fitted to the nearest grid point.
The grid is always in perfect horzontal/vertical direction without skew.
Thanks.
% demo for M
M = [ -539.7520 572.6035
-365.0520 573.6035
-190.3520 572.6035
-15.6520 574.6035
159.0480 571.6035
333.7480 572.6035
-536.8940 -292.9921
-362.1940 -296.9921
-187.4940 -293.9921
-12.7940 -296.9921
161.9060 -296.9921
336.6060 -296.9921
-536.8940 -122.2920
-362.1940 -124.2920
-187.4940 -122.2920
-12.7940 -121.2920
161.9060 -122.2920
336.6060 -122.2920
-536.8940 223.7002
-362.1940 224.7002
-187.4940 222.7002
-12.7940 221.7002
161.9060 224.7002
336.6060 224.7002
-536.8940 399.0250
-362.1940 398.0250
-187.4940 399.0250
-12.7940 397.0250
161.9060 397.0250
336.6060 399.0250
-536.8940 51.2372
-362.1940 51.2372
-187.4940 56.2372
-12.7940 53.2372
161.9060 51.2372
336.6060 51.2372
-536.8940 752.0284
-362.1940 750.0284
-187.4940 752.0284
-12.7940 751.0284
161.9060 752.0284
336.6060 752.0284
-536.8940 927.7109
-362.1940 925.7109
-187.4940 927.7109
-12.7940 926.7109
161.9060 927.7109
336.6060 927.7109];
aLeftMost = min(M(:,1));
aTopMost = min(M(:,2));
aLeftTopCornerDist = arrayfun(@(x) abs(M(x,1)-aLeftMost) + abs(M(x,2)-aTopMost),1:size(M,1));
aLeftTopCornerHit = find(aLeftTopCornerDist==min(aLeftTopCornerDist));
aRightBotCornerHit = find(aLeftTopCornerDist==max(aLeftTopCornerDist));
eva = evalclusters(aLeftTopDistAss(:,1),'kmeans','CalinskiHarabasz','KList',1:20);
eva.OptimalK % often does not get the real optimal rows or columns
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### Akzeptierte Antwort

Image Analyst am 23 Jul. 2023
You might want to use pdist2 to get an array of distances from every point to every other point. Then take the histogram and look for peaks. The "unit" distances should be one peak, then the diagonal distances would be the next peak, then you'd have additional peaks for distances at multiples of those distances.
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raym am 23 Jul. 2023
Works very well.
Below is my raw code:
D = pdist2(aLeftTopDistAss,aLeftTopDistAss);
a = hist(D(:),1000);
aUnitHit = find(a~=0,2);
aUnitDist = (max(D(:))-min(D(:)))*aUnitHit(2)/1000;
nHorSplits = round((aRightMost-aLeftMost)/aUnitDist)+1;
nVerSplits = round((aBotMost-aTopMost)/aUnitDist)+1;
end;assert(nHorSplits*nVerSplits==nImage,'Error:');end
for i =1:nImage
aLeftTopDistAss(i,3) = round((aLeftTopDistAss(i,1) - aLeftMost)/aUnitDist)+1;
aLeftTopDistAss(i,4) = round((aLeftTopDistAss(i,2) - aTopMost)/aUnitDist)+1;
end

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