How can I fit a circle to a region of pixels?

I have a series of 2D CT slices of trabecular bone. I have binarized them and detected the boundaries of the bone, and now I would like to do a bit more processing. I am trying to fit the largest possible circle into each slice in the black pixel regions. I've included an image so you can see what I mean.

I've tried something like this:

stats = regionprops('table',bw,'Centroid','EquivDiam');

where bw is my binary image without the boundaries drawn in.

Any help would be great! I'm struggling to find other examples which match mine.

Thanks in advance!

Answer 1

[Massimo Zanetti]

You can manage by exploiting the "shape measurements" and other properties that function regionprops allows you to use:

https://it.mathworks.com/help/images/ref/regionprops.html

[Kelsey Hilton]

Hi Massimo,

Thanks for your answer. I have tried using that option but it only seems to find a circle right in the centre of the image rather than fitting a circle to the largest black pixel area.

Maybe I am just using it incorrectly? I am not sure how to specify that it only selects a black area.

[Kelsey Hilton]

I've attached an example of what I get if I use that option. Maybe it'll help.

[Massimo Zanetti]

You are considering "on" pixels the white ones. Try negate the input of bwconncomp. For example instead of using:

C = bwconncomp(BW)

use

C = bwconncomp(~BW)

This way you will consider the black areas.

Answer 2

[Bert]

I'm not familiar with this toolbox. But have you tried simply scanning all point? you could do something like this:

% create indexes
ix = repmat([1:size(bw,2)],size(bw,1),1);
iy = repmat([1:size(bw,1)]',1,size(bw,1));
% all in vector
bw = bw(:);
ix = ix(:);
iy = iy(:);
% init loop
center = [];
radius = 0;
% indexes of all black points, possibally the center
I = 1:length(bw);
I = I(bw==0);
for i = I
    % all distances from thi point to white ones
    distances = sqrt( (ix(i)-ix(bw==1)).^2 + (iy(i)-iy(bw==1)).^2 );
    % smallest distance
    distance = min(distances);
    if distance>radius % this point has the biggest minimal distance to a white one yet
        radius = distance;
        center = [iy(i) ix(i)];
    end
end

Answer 3

[Gianluca Iori]

dear Kelsey, the problem is called "Maximum Inscribed Circle". Solution is provided here: https://de.mathworks.com/matlabcentral/fileexchange/30805-maximum-inscribed-circle-using-distance-transform