Matlab: Crow Chart Algorithm for Ellipses

Question

Are there any algorithms for implementing the Voronoi diagram that bounds ellipses? The chart will look like the images here are the voronoi ellipse chart

Can anyone share some links, tutorials, codes, etc. with him

Thanks in advance.

Answer 1

Here's an algorithm that uses distance conversion along with watershed 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)

Answer 2

Just in case, this is an example from the Mathematica help system:

(*Generate ellipses*)
p= Rasterize@Graphics@Table[
          Rotate[
              Disk[RandomReal[10, 2],          (*Rnd position*)
                   RandomReal[{.3, 1.5}, 2]],  (*Rnd radii*)
          RandomReal[Pi]], {i, 10}]            (*Rnd rotation*)

(*Compute Voronoi*)

LaplacianGaussianFilter[DistanceTransform[p], 2] // ImageAdjust

, .

Answer 3

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calculateEllipse , , imoverlay .

%# color image (canvas to draw on)
I = imread('pears.png');
sz = size(I);

%# random ellipses
num = 20;
centers = bsxfun(@times, rand(num,2), sz([2 1]));   %# center x/y-coords
radii = bsxfun(@times, rand(num,2), [300 50])+10;   %# major/minor axis length
angles = rand(num,1) .* 360;                        %# angle of rotation
ex = cell(num,1);                                   %# vertices x-coords
ey = cell(num,1);                                   %# vertices y-coords

%# label image, used to hold rasterized ellipses
L = zeros(sz(1),sz(2));

%# randomly place ellipses one-at-a-time, skip if overlaps previous ones
flag = false(num,1);
for i=1:num
    %# ellipse we would like to draw directly on image matrix
    [ex{i},ey{i}] = calculateEllipse(centers(i,1),centers(i,2), ...
        radii(i,1),radii(i,2), angles(i), 100);

    %# create mask for image pixels inside the ellipse polygon
    mask = poly2mask(ex{i},ey{i}, sz(1),sz(2));

    %# check if there is no existing overlapping ellipse
    if all( L(mask)==0 )
        %# use the mask to place the ellipse in the label image
        L(mask) = sum(flag)+1;    %# assign value using an increasing counter
        flag(i) = true;
    end
end

%# filter ellipses to only those that made through the overlap test
num = sum(flag);
centers = centers(flag,:);
radii = radii(flag,:);
angles = angles(flag);
ex = ex(flag);
ey = ey(flag);

%# rasterized voroni diagram of the ellipses [Jonas]
E = (L ~= 0);                             %# ellipses as binary image
WS = watershed( bwdist(E) );              %# distance transform + watershed
WS = (WS == 0);                           %# WS==0 corresponds voronoi diagram
WS = bwmorph(WS, 'thicken',1);            %# thicken the lines

%# set pixels corresponding to voronoi diagram to white
II = I;
II = imoverlay(II, WS, [1 1 1]);          %# you can customize the color here

%# set pixels corresponding to ellipses using specified colors
clr = hsv(num);                           %# color of each ellipse
for i=1:num
    mask = bwperim(L==i,8);               %# get perimeter of the ellipse mask
    mask = bwmorph(mask, 'thicken',1);    %# thicken the ellipse perimeter
    II = imoverlay(II, mask, clr(i,:));   %# set those pixels with RGB color
end

%# show final rasterized image (image + ellipses + voronoi diagram)
figure, imshow(II, 'InitialMagnification',100, 'Border','tight')

Answer 4

, "" . voronoi ++ Stephan Fortune/Shane O'Sullivan,

http://www.skynet.ie/~sos/mapviewer/voronoi.php