How to find the point where most lines intersect in a binary image?

In a multi-line binary image with different slopes and center points. How do you find the coordinate where most lines intersect? (it should be close where the red arrow points)

Thanks in advance

[Image Analyst]

Do you have the lines equations, or endpoints? If not, how did you get this image? Can you get a listing of (x,y) crossing points?

[Aon]

I have the endpoints of the lines. Yes I have an array with the crossing points generated by the InterX function.

Can I find the cluster with only the array?

[jonas]

So basically you have a set of points where the lines meet? That would be relevant information to include in the original submission... or perhaps you tried this after posting the Q.

[Aon]

Yes with the help of InterX function I now have an array with the intersectpoints. Is it possible to find the cluster with only the array?

[jonas]

Yep, see the latest comment on the answer for two methods. Id try hist3 first

Answer 1

[jonas]

A good solution would be to identify each line by e.g. Hough transform, determine each intersection (e.g. InterX ) and then find the cluster with the highest density of intersections using e.g hist3.

In this case, it seems the point of interest is also the point with the highest density of white pixels, so you could apply some smoothing filter and then find the highest value in the matrix. Here's an example using a very simple 10x10 pixel average.

w=ones(10,10);
A=conv2(I,w/numel(w),'same') 
imagesc(A)
colormap(gca,'jet')

[Aon]

Thanks for the answer! I have tried the InterX function and it works very well.

I would like to find the cluster with only the help of the intersect points array. So plotting of the lines and intersect is not needed.

Do you know how to do this?

Thanks again

[jonas]

Nice! You could put the intersections in a binary matrix, smooth it and find the highest value in the resulting matrix, just like I did in the original answer.

Better yet, use hist3 to find the bin with highest density of points. Something like

[count,bin]=hist3([x,y],'cdatamode','auto');
[idx,idy]=find(count==max(count(:)));
xmax=bin{1}(idx);
ymax=bin{2}(idy);

and adjust the bin size to get the desired resolution.

[Aon]

hist3 worked very well! Thank you very much for the help.

[jonas]

Nice! My pleasure

[Felix Onofrei sunt]

Aon, could you tell me how did you use the interX function to get the intersection of every line, not only two? I am trying to use this function for geographical track lines. Basically i want the same thing, and then to find the cluster. Thanks in advance!

Answer 2

[Image Analyst]

Have you considered dbscan?

https://en.wikipedia.org/wiki/DBSCAN

MATLAB Code for it:

https://www.mathworks.com/matlabcentral/fileexchange/?utf8=%E2%9C%93&term=dbscan

[Aon]

hist3 helped me very well but I will read more about dbscan also. Thank you!

[Image Analyst]

Alternatively you could threshold the blurred image and use regionprops to find the weighted centroid of the region.