Algorithm to group sets of points together that follow a direction
Note: I am placing this question in both the MATLAB and Python tags as I am the most proficient in these languages. However, I welcome solutions in any language.
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Note 1: It has a number of settings -> which for other images may need to altered to get the result you want see % Settings - play around with these values
Note 2: It doesn't find all of the lines you want -> but its a starting point....
To call this function, invoke this in the command prompt:
>> [h, v] = testLines;We get:
>> celldisp(h) h{1} = 1 2 4 6 9 10 h{2} = 3 5 7 8 11 14 15 17 h{3} = 1 2 4 6 9 10 h{4} = 3 5 7 8 11 14 15 17 h{5} = 1 2 4 6 9 10 h{6} = 3 5 7 8 11 14 15 17 h{7} = 3 5 7 8 11 14 15 17 h{8} = 1 2 4 6 9 10 h{9} = 1 2 4 6 9 10 h{10} = 12 13 16 18 20 22 25 27 h{11} = 13 16 18 20 22 25 27 h{12} = 3 5 7 8 11 14 15 17 h{13} = 3 5 7 8 11 14 15 h{14} = 12 13 16 18 20 22 25 27 h{15} = 3 5 7 8 11 14 15 17 h{16} = 12 13 16 18 20 22 25 27 h{17} = 19 21 24 28 30 h{18} = 21 24 28 30 h{19} = 12 13 16 18 20 22 25 27 h{20} = 19 21 24 28 30 h{21} = 12 13 16 18 20 22 24 25 h{22} = 12 13 16 18 20 22 24 25 27 h{23} = 23 26 29 31 33 34 35 h{24} = 23 26 29 31 33 34 35 37 h{25} = 23 26 29 31 33 34 35 36 37 h{26} = 33 34 35 37 36 h{27} = 31 33 34 35 37 >> celldisp(v) v{1} = 33 28 18 8 1 v{2} = 34 30 20 11 2 v{3} = 26 19 12 3 v{4} = 35 22 14 4 v{5} = 29 21 13 5 v{6} = 25 15 6 v{7} = 31 24 16 7 v{8} = 37 32 27 17 9A figure is also generated that draws the lines through each proper set of points:
function [horiz_list, vert_list] = testLines global counter; global colours; close all; data = [ 475. , 605.75, 1.; 571. , 586.5 , 2.; 233. , 558.5 , 3.; 669.5 , 562.75, 4.; 291.25, 546.25, 5.; 759. , 536.25, 6.; 362.5 , 531.5 , 7.; 448. , 513.5 , 8.; 834.5 , 510. , 9.; 897.25, 486. , 10.; 545.5 , 491.25, 11.; 214.5 , 481.25, 12.; 271.25, 463. , 13.; 646.5 , 466.75, 14.; 739. , 442.75, 15.; 340.5 , 441.5 , 16.; 817.75, 421.5 , 17.; 423.75, 417.75, 18.; 202.5 , 406. , 19.; 519.25, 392.25, 20.; 257.5 , 382. , 21.; 619.25, 368.5 , 22.; 148. , 359.75, 23.; 324.5 , 356. , 24.; 713. , 347.75, 25.; 195. , 335. , 26.; 793.5 , 332.5 , 27.; 403.75, 328. , 28.; 249.25, 308. , 29.; 495.5 , 300.75, 30.; 314. , 279. , 31.; 764.25, 249.5 , 32.; 389.5 , 249.5 , 33.; 475. , 221.5 , 34.; 565.75, 199. , 35.; 802.75, 173.75, 36.; 733. , 176.25, 37.]; figure; hold on; axis ij; % Change due to Benoit_11 scatter(data(:,1), data(:,2),40, 'r.'); text(data(:,1)+10, data(:,2)+10, num2str(data(:,3))); text(data(:,1)+10, data(:,2)+10, num2str(data(:,3))); % Process your data as above then run the function below(note it has sub functions) counter = 0; colours = 'bgrcmy'; [horiz_list, vert_list] = findClosestPoints ( data(:,1), data(:,2) ); function [horiz_list, vert_list] = findClosestPoints ( x, y ) % calc length of points nX = length(x); % set up place holder flags modelledH = false(nX,1); modelledV = false(nX,1); horiz_list = {}; vert_list = {}; % loop for all points for p=1:nX % have we already modelled a horizontal line through these? % second last param - true - horizontal, false - vertical if modelledH(p)==false [modelledH, index] = ModelPoints ( p, x, y, modelledH, true, true ); horiz_list = [horiz_list index]; else [~, index] = ModelPoints ( p, x, y, modelledH, true, false ); horiz_list = [horiz_list index]; end % make a temp copy of the x and y and remove any of the points modelled % from the horizontal -> this is to avoid them being found in the % second call. tempX = x; tempY = y; tempX(index) = NaN; tempY(index) = NaN; tempX(p) = x(p); tempY(p) = y(p); % Have we found a vertial line? if modelledV(p)==false [modelledV, index] = ModelPoints ( p, tempX, tempY, modelledV, false, true ); vert_list = [vert_list index]; end end end function [modelled, index] = ModelPoints ( p, x, y, modelled, method, fullRun ) % p - row in your original data matrix % x - data(:,1) % y - data(:,2) % modelled - array of flags to whether rows have been modelled % method - horizontal or vertical (used to calc graadients) % fullRun - full calc or just to get indexes % this could be made better by storing the indexes of each horizontal in the method above % Settings - play around with these values gradDelta = 0.2; % find points where gradient is less than this value gradLimit = 0.45; % if mean gradient of line is above this ignore numberOfPointsToCheck = 7; % number of points to check when look along the line % to find other points (this reduces chance of it % finding other points far away % I optimised this for your example to be 7 % Try varying it and you will see how it effect the result. % Find the index of points which are inline. [index, grad] = CalcIndex ( x, y, p, gradDelta, method ); % check gradient of line if abs(mean(grad))>gradLimit index = []; return end % add point of interest to index index = [p index]; % loop through all points found above to find any other points which are in % line with these points (this allows for slight curvature combineIndex = []; for ii=2:length(index) % Find inedex of the points found above (find points on curve) [index2] = CalcIndex ( x, y, index(ii), gradDelta, method, numberOfPointsToCheck, grad(ii-1) ); % Check that the point on this line are on the original (i.e. inline -> not at large angle if any(ismember(index,index2)) % store points found combineIndex = unique([index2 combineIndex]); end end % copy to index index = combineIndex; if fullRun % do some plotting % TODO: here you would need to calculate your arrays to output. xx = x(index); [sX,sOrder] = sort(xx); % Check its found at least 3 points if length ( index(sOrder) ) > 2 % flag the modelled on the points found modelled(index(sOrder)) = true; % plot the data plot ( x(index(sOrder)), y(index(sOrder)), colours(mod(counter,numel(colours)) + 1)); counter = counter + 1; end index = index(sOrder); end end function [index, gradCheck] = CalcIndex ( x, y, p, gradLimit, method, nPoints2Consider, refGrad ) % x - data(:,1) % y - data(:,2) % p - point of interest % method (x/y) or (y\x) % nPoints2Consider - only look at N points (options) % refgrad - rather than looking for gradient of closest point -> use this % - reference gradient to find similar points (finds points on curve) nX = length(x); % calculate gradient for g=1:nX if method grad(g) = (x(g)-x(p))\(y(g)-y(p)); else grad(g) = (y(g)-y(p))\(x(g)-x(p)); end end % find distance to all other points delta = sqrt ( (x-x(p)).^2 + (y-y(p)).^2 ); % set its self = NaN delta(delta==min(delta)) = NaN; % find the closest points [m,order] = sort(delta); if nargin == 7 % for finding along curve % set any far away points to be NaN grad(order(nPoints2Consider+1:end)) = NaN; % find the closest points to the reference gradient within the allowable limit index = find(abs(grad-refGrad)
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