Detection of line segments and length

I am trying to have MATLAB detect multiple line segments in a images and then tell the length (in pixels). I have tried the following code:

    I=imread('GFP1C2.tif');
canny=edge(I,'canny');
[H,T,R]=hough(canny);
imshow(H,[],'XData',T,'YData',R,'InitialMagnification','fit')
xlabel('\theta'),ylabel('\rho')
axis on, axis normal, hold on
P=houghpeaks (H,5,'threshold',ceil(0.8*max(H(:))));
x=T(P(:,2));y=R(P(:,1));
plot(x,y,'s','color','white');
lines=houghlines(BW,T,R,P,'FillGap',5,'MinLength',7);
figure,imshow(canny),hold on
max_len=0;
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');
    len=norm(lines(k).point1-lines(k).point2);
    if (len>max_len)
        max_len=len;
        xy_long=xy;
    end
end

This code will neither accurately detect the line segments nor will tell me the length of the segment. Help is appreciated; thanks!

[Anton Semechko]

Please post on here a sample image you want to process

[Anton Semechko]

Thanks, that helps.

Quality of the output generated Hough transform is only as good as the input. Are you satisfied with the edges found by the Canny edge detector?

[Victoria]

I feel that's probably the best that can be. It's the clearest I've been able to make it

[Victoria]

Perfect. Thank you so much!

[Image Analyst]

Anton, can you move this from a comment down to the official Answers section so Victoria can "Accept your answer" and give you credit (reputation points) for it? Thanks in advance.

[Anton Semechko]

I moved my comment to the Answers section, however, I don't think it addresses Victoria's problem of extracting individual filaments and measuring their length.

[Victoria]

I ran what you posted earlier:

    im=imread('GFP1C28cropped.tif');
figure
subtightplot(2,2,1), imshow(im)
subtightplot(2,2,3), imshow(edge(im,'canny'))
% Enhance fillaments with Frangi vesselness filter
opt.FrangiScaleRange=[1 3];
opt.FrangiScaleRatio=1;
opt.FrangiBetaOne=1;
opt.FrangiBetaTwo=20;
opt.BlackWhite=false;
[im_2,im_s]=FrangiFilter2D(double(im),opt);
I=edge(im_2,'canny');
figure,imshow(I);
[H,T,R]=hough(I);
imshow(H,[],'XData',T,'YData',R,'InitialMagnification','fit')
xlabel('\theta'),ylabel('\rho')
axis on, axis normal, hold on
P=houghpeaks (H,5,'threshold',ceil(0.8*max(H(:))));
x=T(P(:,2));y=R(P(:,1));
plot(x,y,'s','color','white');
lines = houghlines(I,T,R,P,'FillGap',5,'MinLength',7);
figure,imshow(I),hold on
max_len=0;
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');
    len=norm(lines(k).point1-lines(k).point2);
    if (len>max_len)
        max_len=len;
        xy_long=xy;
    end
end

The Hough Transform doesn't work again - it just borders the outside edges.

[Anton Semechko]

I think that a tractography-based approach will be more appropriate than Hough transform for the types of features you want to extract (i.e., curved filaments). Tractography [1] is typically used for reconstruction of white matter and muscle fiber architecture from diffusion tensor images. However, the same principles can be adapted to your data by replacing diffusion tensors with image structure tensors [2,3].

[1] Mori & van Zijl, 2002, 'Fiber tracking: Principles and strategies - a technical review'

[2] Weickert, 1999, 'Coherence-enhancing diffusion filtering'

[3] Weickert & Scharr, 2000, 'A scheme for coherence-enhancing diffusion filtering with optimized rotation invariance'

[Anton Semechko]

Hi, Victoria,

I was playing around with curvature filters and your image. What I found suggests that the filaments in your image do not have a coherent direction and thus cannot be easily segmented. Rather, the structure in your image is more like a matrix composed of interweaving fibers:

In view of this, how would you define the beginning and end of a single "line segment"?

[Victoria]

I guess that's one of my biggest problems as well. But thank you for the help!

Answer 1

[Anton Semechko]

It doesn't look very clear to me, and is maybe the reason why the Hough transform isn't generating the output you want. For example, have you considered enhancing the filaments in your image prior to edge detection?

% Sample image
im=imread('https://www.mathworks.com/matlabcentral/answers/uploaded_files/123386/GFP1C28cropped.jpg');
figure
subtightplot(2,2,1), imshow(im)
subtightplot(2,2,3), imshow(edge(im,'canny'))

% Enhance fillaments with Frangi vesselness filter
opt.FrangiScaleRange=[1 3];
opt.FrangiScaleRatio=1;
opt.FrangiBetaOne=1;
opt.FrangiBetaTwo=20;
opt.BlackWhite=false;
[im_2,im_s]=FrangiFilter2D(double(im),opt);

subtightplot(2,2,2), imshow(im_2)
subtightplot(2,2,4), imshow(edge(im_2,'canny'))

Notice how much less cluttered is the edges image after enhancement. Try experimenting with different filter settings to see what works best for you.

Functions used in this demo can be downloaded from here and here.