Question

Are there any algorithms to implement Voronoi diagram that bounds the ellipses? The diagram would look like the pictures here voronoi diagram of ellipses

Can anyone share some links,tutorials,codes etc related to it?

Thanks in advance.

Answer 1

Here’s an algorithm that uses the distance transform together with the watershed algorithm to draw a Voronoi diagram for ellipses.

%# first, define some ellipses (for simplicity, I use 0/90 orientation)
ellipses = [10,20,5,10;30,10,10,7;40,40,8,3];

%# put the ellipses into an image (few pixels, therefore pixelated)
img = false(50);
[xx,yy]=ndgrid(1:50,1:50);
for e = 1:size(ellipses,1),img = img | (xx-ellipses(e,1)).^2/ellipses(e,3)^2 + (yy-ellipses(e,2)).^2/ellipses(e,4)^2 <= 1;end

%# perform the distance transform
dt = bwdist(img);

%# apply the watershed algorithm. 
%# ws==0 are the lines for the Voronoi diagram
ws = watershed(dt);

%# create a RGB image and display
%# note: for yellow lines, replace the last
%# "ws==0" by "zeros(size(ws))", so that you
%# only put ws into the red and green channel (=yellow)
rgb = cat(3,ws==0,ws==0,ws==0)); 
%# add the ellipses into the red channel
rgb(:,:,1) = rgb(:,:,1) | img;
imshow(rgb)