Circle detection from gray level image in MATLAB

Question

I have the image shown below. My aim is to detect the circle which shown in the second image. I used [centers,radii] = imfindcircles(IM,[100 300]); but it found nothing.

Is there any other way to detect the circle? How can I do that?

Original image:

The circle:I drew it with paint.

Solution 1

Here is an alternative solution to imfindcircles. Basically threshold the image, dilate it with a disk structuring element and then, after finding the edges, apply a Hough transform to detect the circle using the circle_hough algorithm available form the file exchange here.

Here is the code:

clear
clc
close all

A = imread('CircleIm.jpg');

%// Some pre-processing. Treshold image and dilate it.
B = im2bw(A,.85);

se = strel('disk',2);

C = imdilate(B,se);

D = bwareaopen(C,10000);

%// Here imfill is not necessary but you might find it useful in other situations.
E = imfill(D,'holes');

%// Detect edges
F = edge(E);

%// circle_hough from the File Exchange.

%// This code is based on Andrey's answer here:
%https://dsp.stackexchange.com/questions/5930/find-circle-in-noisy-data.

%// Generate range of radii.
 radii = 200:10:250;

h = circle_hough(F, radii,'same');
[~,maxIndex] = max(h(:));
[i,j,k] = ind2sub(size(h), maxIndex);
radius = radii(k);
center.x = j;
center.y = i;

%// Generate circle to overlay
N = 200;

theta=linspace(0,2*pi,N);
rho=ones(1,N)*radius;

%Cartesian coordinates
[X,Y] = pol2cart(theta,rho); 

figure;

subplot(2,2,1)
imshow(B);
title('Thresholded image  (B)','FontSize',16)

subplot(2,2,2)
imshow(E);
title('Filled image (E)','FontSize',16)

subplot(2,2,3)
imshow(F);hold on

plot(center.x-X,center.y-Y,'r-','linewidth',2);

title('Edge image + circle (F)','FontSize',16)

subplot(2,2,4)
imshow(A);hold on
plot(center.x-X,center.y-Y,'r-','linewidth',2);
title('Original image + circle (A)','FontSize',16)

Which gives the following:

You can play around with the parameters passed to threshold or to dilate as well to see how it affects the outcome.

Hope that helps!

Solution 2

Here is another approach to solve this problem. It´s not based on Hough Transform, as imfindcircles and previous answer are.

Basically:

1. Segment the image (threshold is estimated using Otsu´s method)
2. Find connected components and leave just 2% of them, starting from those whose area is bigger
3. Dilate the image with a circle (disk) of small radius
4. Find connected components again and take the component with biggest area as the circle

HT sometimes is slow, depending on input data size and resolution. It may be useful to compare the execution time of both approaches (HT, non HT).

The proposed method may also be able to detect objects of another shape (non circular).

function[circle] = ipl_find_circle(I)

% NOTE: I is assumed to be a grayscale image

% Step 1: Segment image using Otsu´s method
t = graythresh(I); 
BW = im2bw(I, t); 

% Step 2: Leave just "big" components on binary image
[L, num] = bwlabel(BW); 
stats = regionprops(L, 'Area', 'PixelIdxList');
area_vector = [stats(:).Area];
area_vector = sort(area_vector);
threshold_pos = floor(num * 0.98);
threshold = area_vector(threshold_pos);

for i=1:num
    if(stats(i).Area < threshold)
        BW(stats(i).PixelIdxList) = false;
    end
end

% Step 3: Dilate image with a circle of small radius
str = strel('disk', 5); 
BW = imdilate(BW, str); 

% Step 4: Take component with biggest area as the circle
L = bwlabel(BW); 
stats = regionprops(L, 'Area', 'BoundingBox', 'Centroid', 'EquivDiameter');
area_vector = [stats(:).Area];
[max_value, max_idx] = max(area_vector);
soi = stats(max_idx);

% Set output variable
circle = imcrop(I, soi.BoundingBox);

% Display results
radius = soi.EquivDiameter/2;
N = 1000;
theta = linspace(0, 2*pi, N);
rho = ones(1, N) * radius;
[X,Y] = pol2cart(theta, rho);
X = soi.Centroid(1) - X;
Y = soi.Centroid(2) - Y;

figure; 
subplot(1,2,1);
imshow(I);
hold on;
plot(X, Y, '-r', 'LineWidth', 2);
title('Original graycale image + circle', 'FontSize', 12)

subplot(1,2,2);
imshow(circle);
title('Circle region', 'FontSize', 12);

end