Bounding circle for objects in binary image?

Can anyone suggest a way to draw bounding circles around labeled objects in a binary image?

I have some irregularly shaped objects. Rather than finding the centroids of the objects themselves, I would like to find the centroids of the smallest circle that will enclose the objects. Contact between the bounding circle and the object should be maximized.

Thanks, Heidi

Answer 1

[Sean de Wolski]

Use the distance transform on the inverse of the image. The point that is the largest value on each object will be the centroid of the circle and its radius will be the value.

doc bwdist

[Teja Muppirala]

Neat idea, I wouldn't have thought of that.

[David Inglis]

This doesn't seem to be working for me. I have a binary image, and can draw a good bounding rectangle using region props, but the location and radii from bsdist never encompass the blob and seem weighted towards the centre of mass. You can see the contours from bwdist and the circle located at the centre with a radii of the max value. Any thoughts? Code below image.

clear all

exp=imread("test image.jpg");

exp=imresize(exp,0.5); % reduce image size by 2 for compute speed

n=4; %size of open and close

yellow=yellowballMask(exp,4); % find yellow ball pieces

blue=BlueBallMask(exp,2); % find blue ball pieces

K1=or(yellow,blue); % merge the two into a binary image

se = strel('disk',12);

K2 = imclose(K1,se); % try to close the gaps between blue and yellow

K3=~K2; % invert image for bwdist

D1 = bwdist(K3);

[val ind] = max(D1(:)); % determine location and value of maximum from bwdist

[I_row, I_col] = ind2sub(size(D1),ind); %convert to row and column

s=regionprops(K2,'BoundingBox'); % create rectangular bounding box

subplot(1,2,2)

imcontour(D1)

viscircles([I_col I_row],val);

rectangle('Position',s.BoundingBox,'EdgeColor','b')

title('bwdist Contours');

subplot(1,2,1)

imshow(exp); hold on

title('original iamge');

viscircles([I_col I_row],val);

[Image Analyst]

@David Inglis see my answer below and use the min bounding circle function in this:

https://www.mathworks.com/matlabcentral/fileexchange/34767-a-suite-of-minimal-bounding-objects?s_tid=srchtitle

Or use bwboundaries to get the actual outline of the blob.

% Plot the borders of all the blobs in the overlay above the original grayscale image 
% using the coordinates returned by bwboundaries().
% bwboundaries() returns a cell array, where each cell contains the row/column coordinates for an object in the image.
imshow(originalImage); % Optional : show the original image again.  Or you can leave the binary image showing if you want.
% Here is where we actually get the boundaries for each blob.
boundaries = bwboundaries(mask);
% boundaries is a cell array - one cell for each blob.
% In each cell is an N-by-2 list of coordinates in a (row, column) format.  Note: NOT (x,y).
% Column 1 is rows, or y.    Column 2 is columns, or x.
numberOfBoundaries = size(boundaries, 1); % Count the boundaries so we can use it in our for loop
% Here is where we actually plot the boundaries of each blob in the overlay.
hold on; % Don't let boundaries blow away the displayed image.
for k = 1 : numberOfBoundaries
    thisBoundary = boundaries{k}; % Get boundary for this specific blob.
    x = thisBoundary(:,2); % Column 2 is the columns, which is x.
    y = thisBoundary(:,1); % Column 1 is the rows, which is y.
    plot(x, y, 'r-', 'LineWidth', 2); % Plot boundary in red.
end
hold off;
caption = sprintf('%d Outlines, from bwboundaries()', numberOfBoundaries); 
fontSize = 15;
title(caption, 'FontSize', fontSize); 
axis('on', 'image'); % Make sure image is not artificially stretched because of screen's aspect ratio.

Answer 2

[Image Analyst]

See the min bounding circle here:

https://www.mathworks.com/matlabcentral/fileexchange/34767-a-suite-of-minimal-bounding-objects?s_tid=srchtitle

Just pass the coordinates of your blob mask into it. You can get the x,y of the binary image like this, assuming you have just one blob in the mask

[y, x] = find(mask);