Detecting coordinates of line edges

I have a matrix containing 1s and 0s. The elements of this matrix are pixels of an image, where 1&0 represents black and white. The 1s form non-intersecting line segmennts. I want to know pixel coordinates of line edges. Following is an example matrix-

binaryImage= [0 1 0 0;...
              0 0 1 0; ...
              0 0 0 1; ...
              0 0 0 0]

The desired output is-

[1, 2], [3, 4]

Note that there could be multiple line segments. Is Hough transform useful here?

Thanks

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Update: I am also attaching another example matrix and corrosponding `imagesc` for better visualization of problem.

[KALYAN ACHARJYA]

[2,3] also?

[Pankaj]

No, just the ends.

[sushanth govinahallisathyanarayana]

Yes, Hough might be useful, since you can describe a line with 2 points, however, you need an approximate idea of the scales at which you want to look, and how the lines may be oriented.

Answer 1

[Image Analyst]

Use bwmorph() to get an image of just the endpoints, then use find() to get the rows and columns:

endPointsImage = bwmorph(binaryImage, 'endpoints');
[rows, columns] = find(endPointsImage);

rows and columns will be a list of the rows and columns of each endpoints. They are synced up so for index N, rows(N) has the row of the Nth endpoint and columns(N) has the column of the Nth endpoint.

[Pankaj]

Image Analyst, I was really hoping for you to answer. I was looking for means to contact you. I am away from my computer. I will evaluate your answer as I reach home. 🙏

[KALYAN ACHARJYA]

yes sir

[Image Analyst]

OK, you can contact us here. I'm always here. Attach an actual image if you need more help.

[Pankaj]

Hello Image Analyst, your code gives me the desired output, thank you for that. Is it possible to get the endpoints in sets (two edges per line segment), like -

{[1 2], [3 4]}

{[x_21 y_21], [x_22 y_22]}

{[x_31 y_31], [x_32 y_32]}

[Image Analyst]

Yes. But you have to label the binary image so as to know which endpoint belongs to which blob. Keep in mind that is the blob is shaped like an X then it would have 4 endpoints, or 3 if it were shaped like a Y. So you could have different numbers of endpoints for each blob. So you'd do something like

[labeledImage, numRegions] = bwlabel(binaryImage);
endPointsImage = bwmorph(binaryImage, 'endpoints');
[rows, columns] = find(endPointsImage);
endpoints = cell(numRegions, 1; % At least 1 endpoint for each region
endpointsPerLabel = zeros(numRegions, 1);
for k = 1 : length(rows)
    blobLabel = labeledImage(rows(k), columns(k));
    endpointsPerLabel(blobLabel) = endpointsPerLabel(blobLabel) + 1;
    x = columns(k);
    y = rows(k);
    endpoints{blobLabel, endpointsPerLabel(blobLabel)} = [x, y];
end

If this doesn't work, re-read my last comment, especially the last sentence.

[Pankaj]

Thanks!! This is exactly what I wanted. I have also modified my question, slightly.

Answer 2

[KSSV]

A= [0 1 0 0;...
    0 0 1 0; ...
    0 0 0 1; ...
    0 0 0 0] ;
idx = find(A) ; 
[i,j] = ind2sub(size(A),idx) ;
[i j]

[Pankaj]

I need just the endpoints of the line segment.

[KSSV]

The above ives the locations of 1 in the matrix A.

[Image Analyst]

Pankaj, the code I gave you in my Answer gives the endpoints only. Did you overlook it?