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

### Aon (view profile)

on 14 Sep 2018
Latest activity Commented on by Image Analyst

on 16 Sep 2018

### jonas (view profile)

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)

jonas

### jonas (view profile)

on 15 Sep 2018
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

### Aon (view profile)

on 15 Sep 2018
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

### jonas (view profile)

on 15 Sep 2018
Yep, see the latest comment on the answer for two methods. Id try hist3 first

on 14 Sep 2018
Edited by jonas

### jonas (view profile)

on 15 Sep 2018

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')

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jonas

### jonas (view profile)

on 15 Sep 2018
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

### Aon (view profile)

on 16 Sep 2018
hist3 worked very well! Thank you very much for the help.
jonas

### jonas (view profile)

on 16 Sep 2018
Nice! My pleasure

on 15 Sep 2018

Aon

### Aon (view profile)

on 16 Sep 2018
hist3 helped me very well but I will read more about dbscan also. Thank you!
Image Analyst

### Image Analyst (view profile)

on 16 Sep 2018
Alternatively you could threshold the blurred image and use regionprops to find the weighted centroid of the region.