How to detect the 6 circles and the center points?

I = imread("myimage.jpg"); %original file
imshow(I)
imhist(I)
I = im2gray(I); %coverting to grayscale
Ia = imadjust(I); %histogram stretching
imshow(Ia)
imhist(Ia)
avg = fspecial("average",[50 50]) %average filtering
Iavg = imfilter(Ia,avg);
If = medfilt2(Iavg,[60 60]); %median filtering
imshow(If)

Ibw = imbinarize(If);
imshow(Ibw)

edges = edge(Ibw);
imshow(edges)

From the original image "myimage.jpg" I want to detect the 6 circles and the center point and center line for those cirlces. I tried basic averaging and median filters to make the image smooth and the curves smooth (images attached). After that I tried using hough transform to detect the circles but it did not give me the results.

Is there any function or method that could solve this issue.

[Image Analyst]

I don't see 6 circles. I see a big fuzzy asterisk.

Can you annotate an image and show us exactly where the circles are?

[Husain Signalwala]

@Image Analyst I want to locate these lines indicated in the figures and the circles(attached). It is not necessary that the centerlines coincide at one point. Any way I can locate these?

Thanks.

Answer 1

[Image Analyst]

Try using radon

However it's a judgment call as to how far out you want to go to define the boundary of the circle.

[Husain Signalwala]

@Image Analyst do you suggest performing any other operation or filter before using radon? I want to get the center lines annotated in the image. That is important.

Thankyou

[Image Analyst]

Perhaps this

kernel = ones(61)
img = imfilter(double(grayImage), kernel);
subplot(2, 2, 4);
imshow(img, []);

[Husain Signalwala]

I = imread("myimage.jpg");
imshow(I)
I = im2gray(I);
I = rescale(I);
imshow(I)
I = imadjust(I);

kernel = ones(61);
If = imfilter(double(I),kernel);

imshow(If,[])

BW = edge(If);
imshow(BW)

theta = 0:179;
[R,xp] = radon(BW,theta);

figure
imagesc(theta,xp,R)
colormap("hot")
xlabel("\theta (degrees)")
ylabel("x^{\prime} (pixels from center)")
title("R_{\theta} (x^{\prime})")
colorbar

R_sort = sort(unique(R),"descend");

[row_peak,col_peak] = find(ismember(R,R_sort(1:6)));
xp_peak_offset = xp(row_peak)
theta_peak = theta(col_peak)

@Image Analyst

This is my code until now.

The theta_peak values are [0 2 90 90 90 90], which I think does not give me the solution. Can you just recheck the code? I have applied edges too before applying radon.

I am just a beginner, sorry if there are any dumb mistakes.

[Husain Signalwala]

@Image Analyst Hello Sir,

By using this code, this is the closest I could come to finding the centerlines. The results are not accurate. From the theta_peak values I had chosen 6 values on assumptions. Can you suggest me something to get a bit more accurate results? Also using radon, all the centerlines meet the centerpoint of the image. This is not true. It is not necessary they all pas through a single point.

I = imread("myimage.jpg");
imshow(I)
I = im2gray(I);
I = rescale(I);
imshow(I)
I = imadjust(I);


BW = edge(I);
imshow(BW)
theta = 0:179;
[R,xp] = radon(BW,theta); %

figure
imagesc(theta,xp,R)
colormap("hot")
xlabel("\theta (degrees)")
ylabel("x^{\prime} (pixels from center)")
title("R_{\theta} (x^{\prime})")
colorbar

R_sort = sort(unique(R),"descend");
[row_peak,col_peak] = find(ismember(R,R_sort(1:12)));
xp_peak_offset = xp(row_peak)
theta_peak = theta(col_peak)

centerX = ceil(size(I,2)/2)
centerY = ceil(size(I,1)/2)

figure
imshow(I)
hold on
scatter(centerX,centerY,50,"bx",LineWidth=2)

axis on
plot(centerX + xp_peak_offset(1,:),tan,"bx",LineWidth=2) %using tan

[x1,y1] = pol2cart(deg2rad(42),600);
plot([centerX-x1 centerX+x1],[centerY+y1 centerY-y1],"r--",LineWidth=2)

plot (961,290,"bx",LineWidth=2)
[x2,y2] = pol2cart(deg2rad(46),500);
plot([centerX-x2 centerX+x2],[centerY+y2 centerY-y2],"r--",LineWidth=2)

[x3,y3] = pol2cart(deg2rad(100),500);
plot([centerX-x3 centerX+x3],[centerY+y3 centerY-y3],"r--",LineWidth=2)

[x4,y4] = pol2cart(deg2rad(106),500);
plot([centerX-x4 centerX+x4],[centerY+y4 centerY-y4],"r--",LineWidth=2)

[x5,y5] = pol2cart(deg2rad(157),500);
plot([centerX-x5 centerX+x5],[centerY+y5 centerY-y5],"r--",LineWidth=2)

[x6,y6] = pol2cart(deg2rad(166),500);
plot([centerX-x6 centerX+x6],[centerY+y6 centerY-y6],"r--",LineWidth=2)

Waiting for your valuable suggestion/inputs.

Thankyou.