Crop the largest square inside a circle object - Matlab - image

Question

I am trying to find a way to crop from a circle object (Image A) the largest square that can fit inside it.
Can someone please explain/show me how to find the biggest square fit parameters of the white space inside the circle (Image I) and based on them crop the square in the original image (Image A).
Script:
A = imread('E:/CirTest/Test.jpg');
%imshow(A)
level = graythresh(A);
BW = im2bw(A,level);
%imshow(BW)
I = imfill(BW, 'holes');
imshow(I)
d = imdistline;
[centers, radii, metric] = imfindcircles(A,[1 500]);
imageCrop=imcrop(A, [BoxBottomX BoxBottomY NewX NewY]);

Answer 1

I have a solution for you but it requires a bit of extra work. What I would do first is use imfill but directly on the grayscale image. This way, noisy pixels in uniform areas get inpainted with the same intensities so that thresholding is easier. You can still use graythresh or Otsu's thresholding and do this on the inpainted image.
Here's some code to get you started:
figure; % Open up a new figure
% Read in image and convert to grayscale
A = rgb2gray(imread('http://i.stack.imgur.com/vNECg.jpg'));
subplot(1,3,1); imshow(A);
title('Original Image');
% Find the optimum threshold via Otsu
level = graythresh(A);
% Inpaint noisy areas
I = imfill(A, 'holes');
subplot(1,3,2); imshow(I);
title('Inpainted image');
% Threshold the image
BW = im2bw(I, level);
subplot(1,3,3); imshow(BW);
title('Thresholded Image');
The above code does the three operations that I mentioned, and we see this figure:
Notice that the thresholded image has border pixels that need to be removed so we can concentrate on the circular object. You can use the imclearborder function to remove the border pixels. When we do that:
% Clear off the border pixels and leave only the circular object
BW2 = imclearborder(BW);
figure; imshow(BW2);
... we now get this image:
Unfortunately, there are some noisy pixels, but we can very easily use morphology, specifically the opening operation with a small circular disk structuring element to remove these noisy pixels. Using strel with the appropriate structuring element in addition to imopen should help do the trick:
% Clear out noisy pixels
SE = strel('disk', 3, 0);
out = imopen(BW2, SE);
figure; imshow(out);
We now get:
This mask contains the locations of the circular object we now need to use to crop our original image. The last part is to determine the row and column locations using this mask to locate the top left and bottom right corner of the original image and we thus crop it:
% Find row and column locations of circular object
[row,col] = find(out);
% Find top left and bottom right corners
top_row = min(row);
top_col = min(col);
bottom_row = max(row);
bottom_col = max(col);
% Crop the image
crop = A(top_row:bottom_row, top_col:bottom_col);
% Show the cropped image
figure; imshow(crop);
We now get:
It's not perfect, but it will of course get you started. If you want to copy and paste this in its entirety and run this on your computer, here we are:
figure; % Open up a new figure
% Read in image and convert to grayscale
A = rgb2gray(imread('http://i.stack.imgur.com/vNECg.jpg'));
subplot(2,3,1); imshow(A);
title('Original Image');
% Find the optimum threshold via Otsu
level = graythresh(A);
% Inpaint noisy areas
I = imfill(A, 'holes');
subplot(2,3,2); imshow(I);
title('Inpainted image');
% Threshold the image
BW = im2bw(I, level);
subplot(2,3,3); imshow(BW);
title('Thresholded Image');
% Clear off the border pixels and leave only the circular object
BW2 = imclearborder(BW);
subplot(2,3,4); imshow(BW2);
title('Cleared Border Pixels');
% Clear out noisy pixels
SE = strel('disk', 3, 0);
out = imopen(BW2, SE);
% Show the final mask
subplot(2,3,5); imshow(out);
title('Final Mask');
% Find row and column locations of circular object
[row,col] = find(out);
% Find top left and bottom right corners
top_row = min(row);
top_col = min(col);
bottom_row = max(row);
bottom_col = max(col);
% Crop the image
crop = A(top_row:bottom_row, top_col:bottom_col);
% Show the cropped image
subplot(2,3,6);
imshow(crop);
title('Cropped Image');
... and our final figure is:

Answer 2

You can use bwdist with L_inf distance (aka 'chessboard') to get the axis-aligned distance to the edges of the region, thus concluding the dimensions of the largest bounded box:
bw = imread('http://i.stack.imgur.com/7yCaD.png');
lb = bwlabel(bw);
reg = lb==2; %// pick largest area
d = bwdist(~reg,'chessboard'); %// compute the axis aligned distance from boundary inward
r = max(d(:)); %// find the largest distance to boundary
[cy cx] = find(d==r,1); %// find the location most distant
boundedBox = [cx-r, cy-r, 2*r, 2*r];
And the result is
figure;
imshow(bw,'border','tight');
hold on;
rectangle('Position', boundedBox, 'EdgeColor','r');
Once you have the bounding box, you can use imcrop to crop the original image
imageCrop = imcrop(A, boundedBox);
Alternatively, you can
imageCrop = A(cy + (-r:r-1), cx + (-r:r-1) );