[37] | 1 | % NORMALISE2DPTS - normalises 2D homogeneous points |
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| 2 | % |
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| 3 | % Function translates and normalises a set of 2D homogeneous points |
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| 4 | % so that their centroid is at the origin and their mean distance from |
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| 5 | % the origin is sqrt(2). This process typically improves the |
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| 6 | % conditioning of any equations used to solve homographies, fundamental |
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| 7 | % matrices etc. |
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| 8 | % |
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| 9 | % Usage: [newpts, T] = normalise2dpts(pts) |
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| 10 | % |
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| 11 | % Argument: |
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| 12 | % pts - 3xN array of 2D homogeneous coordinates |
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| 13 | % |
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| 14 | % Returns: |
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| 15 | % newpts - 3xN array of transformed 2D homogeneous coordinates. The |
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| 16 | % scaling parameter is normalised to 1 unless the point is at |
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| 17 | % infinity. |
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| 18 | % T - The 3x3 transformation matrix, newpts = T*pts |
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| 19 | % |
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| 20 | % If there are some points at infinity the normalisation transform |
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| 21 | % is calculated using just the finite points. Being a scaling and |
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| 22 | % translating transform this will not affect the points at infinity. |
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| 23 | |
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| 24 | % Peter Kovesi |
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| 25 | % School of Computer Science & Software Engineering |
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| 26 | % The University of Western Australia |
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| 27 | % pk at csse uwa edu au |
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| 28 | % http://www.csse.uwa.edu.au/~pk |
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| 29 | % |
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| 30 | % May 2003 - Original version |
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| 31 | % February 2004 - Modified to deal with points at infinity. |
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| 32 | |
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| 33 | |
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| 34 | function [newpts, T] = normalise2dpts(pts) |
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| 35 | |
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| 36 | if size(pts,1) ~= 3 |
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| 37 | error('pts must be 3xN'); |
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| 38 | end |
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| 39 | |
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| 40 | % Find the indices of the points that are not at infinity |
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| 41 | finiteind = find(abs(pts(3,:)) > eps); |
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| 42 | |
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| 43 | if length(finiteind) ~= size(pts,2) |
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| 44 | warning('Some points are at infinity'); |
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| 45 | end |
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| 46 | |
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| 47 | % For the finite points ensure homogeneous coords have scale of 1 |
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| 48 | pts(1,finiteind) = pts(1,finiteind)./pts(3,finiteind); |
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| 49 | pts(2,finiteind) = pts(2,finiteind)./pts(3,finiteind); |
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| 50 | pts(3,finiteind) = 1; |
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| 51 | |
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| 52 | c = mean(pts(1:2,finiteind)')'; % Centroid of finite points |
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| 53 | newp(1,finiteind) = pts(1,finiteind)-c(1); % Shift origin to centroid. |
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| 54 | newp(2,finiteind) = pts(2,finiteind)-c(2); |
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| 55 | |
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| 56 | meandist = mean(sqrt(newp(1,finiteind).^2 + newp(2,finiteind).^2)); |
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| 57 | |
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| 58 | scale = sqrt(2)/meandist; |
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| 59 | |
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| 60 | T = [scale 0 -scale*c(1) |
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| 61 | 0 scale -scale*c(2) |
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| 62 | 0 0 1 ]; |
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| 63 | |
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| 64 | newpts = T*pts; |
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| 65 | |
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| 66 | |
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| 67 | |
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