How to transform different shapes to circles in Matlab - matlab

Question

I have this image:
that has different shapes, and I want to transform each shape in a circle. And each circle must have different radius, depending on the size of the shape. How can I do that? With Morphology Operations or there are any function on Matlab that does that?
I used the function Regionprops to detect every individual shape, then I can do operations on each region separately.

Answer 1

I would use bwlabel to first label all of the components. Then I would use regionprops to find the bounding box of each component. You can then use the rectangle with a Curvature value of [1 1] to plot an ellipse at each bounding box.
%// Load the image and convert to 0's and 1's
img = imread('http://i.stack.imgur.com/9wRYK.png');
img = double(img(:,:,1) > 0);
%// Label the image
L = bwlabel(img);
%// Compute region properties
P = regionprops(L);
imshow(img)
for k = 1:numel(P)
%// Get the bounding box
bb = P(k).BoundingBox;
%// Plot an ellipse around each object
hold on
rectangle('Position', bb, ...
'Curvature', [1 1], ...
'EdgeColor', 'r', ...
'LineWidth', 2);
end
If you actually want circles, you will need to decide how exactly you define a circle from a rectangle. For this, I just used the maximum of the width and height for the diameter.
t = linspace(0, 2*pi, 100);
cost = cos(t);
sint = sin(t);
for k = 1:numel(P)
bb = P(k).BoundingBox;
%// Compute the radius and center of the circle
center = [bb(1)+0.5*bb(3), bb(2)+0.5*bb(4)];
radius = max(bb(3:4)) / 2;
%// Plot each circle
plot(center(1) + radius * cost, ...
center(2) + radius * sint, ...
'Color', 'r');
end
Now if you actually want to modify the image data itself rather than simply displaying it, you can use a meshgrid of all of the pixel centers to test whether a given pixel is within a circle or not.
%// Create a new image the size of the old one
newImage = zeros(size(img));
%// Determine the x/y coordinates for each pixel
[xx,yy] = meshgrid(1:size(newImage, 2), 1:size(newImage, 1));
xy = [xx(:), yy(:)];
for k = 1:numel(P)
bb = P(k).BoundingBox;
%// Compute the circle that fits each bounding box
center = [bb(1)+0.5*bb(3), bb(2)+0.5*bb(4)];
radius = max(bb(3:4)) / 2;
%// Now check if each pixel is within this circle
incircle = sum(bsxfun(#minus, xy, center).^2, 2) <= radius^2;
%// Change the values of newImage
newImage(incircle) = k;
end
%// Create a binary mask of all points that were within any circle
mask = newImage > 0;