Identify all co-linear line segments (in matlab)

Question

I have posted a related but not the same question here https://stackoverflow.com/questions/8279698/measuring-length-of-dna-fibers-from-an-image-of-single-molecules

Background: I have many images that look like this:

I would like to identify all line segments that are co-linear and then measure the length of these segments. In the image above there are 3 pairs of segments that are on an imaginary line with a negative slope. The line segment that is the longest does not have a pair so it would not be considered i.e. there must be atleast 2 segments that are colinear.

I get the following:

I  = imread('http://dl.dropbox.com/u/18072545/c_39_green.tif'); 
BW = edge(I,'canny');
[H,T,R] = hough(BW);
NUMPEAKS=15;
PEAKTHRESHOLD= 80; 
SUPPRESSNHBR=[40 40];
P  = houghpeaks(H,NUMPEAKS,'threshold',PEAKTHRESHOLD,'NHoodSize',SUPPRESSNHBR); 
MINLENGTH_OF_SEGMENT=50;
GAPLENGTH_TO_MERGE=30;
lines = houghlines(BW,T,R,P,'FillGap',GAPLENGTH_TO_MERGE,'MinLength',MINLENGTH_OF_SEGMENT);
max_len = 0;
figure, imshow(I), hold on
for k = 1:length(lines)
  xy = [lines(k).point1; lines(k).point2];
  plot(xy(:,1),xy(:,2),'LineWidth',2,'Color','green');
  plot(xy(1,1),xy(1,2),'x','LineWidth',2,'Color','yellow');
  plot(xy(2,1),xy(2,2),'x','LineWidth',2,'Color','red');
end

I had to play around with the parameters in order to get a reasonable performance (though I am unable to find a parameter that will capture the starting bit of the segment that is at the bottom). However, I am unable to avoid finding multiple segments that are overlapping.

Can someone please help me 1. Prevent identification of overlapping segments. 2. Identify all the lines that are co-linear

Many thanks!

Answer 1

This code finds co-linear groups of lines.

theta = zeros(length(lines),1);
rho   = zeros(length(lines),1);
for k = 1:length(lines)
  xy = [lines(k).point1; lines(k).point2];
  plot(xy(:,1),xy(:,2),'LineWidth',1,'Color','green');
  plot(xy(1,1),xy(1,2),'x','LineWidth',1,'Color','yellow');
  plot(xy(2,1),xy(2,2),'x','LineWidth',1,'Color','red');
  %text(xy(1,1),xy(1,2),['    ' num2str(k)],'fontsize',10,'color',[1 1 1]);
  theta(k) = lines(k).theta;
  rho(k) = lines(k).rho;
end

theta_tolerance = 2;
theta2 = abs(bsxfun(@minus, theta, theta')) <= theta_tolerance;
theta2(1:size(theta2,2)+1:numel(theta2)) = 0; % zero diagonal
rho_tolerance = 1;
rho2 = abs(bsxfun(@minus, rho, rho')) <= rho_tolerance;
rho2(1:size(rho2,2)+1:numel(rho2)) = 0; % zero diagonal
rhotheta2 = sparse(rho2 & theta2);
[nc, C] = graphconncomp(rhotheta2);


paired = ismember(C,find(hist(C,1:max(C))>1)); % paired lines
colors=get(gcf,'DefaultAxesColorOrder');
for line=find(paired)
    xy = [lines(line).point1; lines(line).point2];
    plot(xy(:,1),xy(:,2),':','LineWidth',4,'Color',colors(C(line),:));
    text(xy(1,1),xy(1,2),num2str(C(line)),'fontsize',20,'Color',colors(C(line),:));
end

It doesn't take care of overlapping. It is not clear how want to treat a case with 3 co-linear segments, where the first segment and the second segment intersect? Do you need to consider both the set containing the first and the third and the set containing the second and the third segment?