Algorithm Matlab：椭圆voronoi图的算法

是否有任何算法可以实现限制椭圆的Voronoi图？这个图表看起来像这里的图片

任何人都可以分享一些与之相关的链接、教程、代码等吗

---

提前谢谢。

我不知道你说的“省略号”是什么意思。但有一个实现的Voronoi图在C++中由斯蒂芬福斯恩/奥沙利文，

---

这里有一个算法，它使用和算法一起绘制椭圆的Voronoi图

%# 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

---

以防万一，这是Mathematica帮助系统中的一个示例：

(*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

---

这不是一个精确的计算，但对于实际应用来说已经足够公平了。

根据你最近提出的问题，我知道你一直在研究在RGB图像上绘制椭圆。您希望能够指定椭圆的位置、形状和颜色。您希望椭圆位于边界处，也希望椭圆位于边界处。现在，您希望以类似于Voronoi图的方式绘制分隔空间的线（但使用椭圆代替点）

如图所示，对于这个特殊问题，解决方案是将距离变换与分水岭算法结合使用

我想我继续上一个例子，并用乔纳斯的想法扩展它，以展示整个过程。希望你觉得有用

代码使用该函数计算组成椭圆的点的坐标，以及将图像的指定像素设置为某种选定颜色的函数

%# 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')

---

省略号代替了线所包围的“点”（x，y）。我可以对代码做些什么来控制线和省略号的颜色？@Ivy:

rgb=repmat（ws==0,1,1,3）；rgb（：，：，1）=rgb（：，：，1）| img；imshow（rgb）

如何在图像中同时显示椭圆和线条？因为imshow（dt）只显示椭圆，如果imshow（ws）只显示线。我尝试了rgb，“repmat”有一个错误：输入参数太多。我能做什么？@Ivy:对不起，打字错误。它应该是

rgb=repmat（ws==0[13]）：抱歉，我仍然不知道如何使用“imshow（？？）”显示图像。假设背景是黑色，椭圆的颜色是红色，线条的颜色是黄色。你能详细加上一些代码吗？非常感谢。我试着画实心椭圆，所以我拿出了线'mask=bwperim（L==I，8）；'这是为了得到椭圆的周长，但输出结果只有一个实心椭圆。为什么会发生这种情况？这是某种逻辑错误吗？@Ivy：如果你想画实心椭圆，你还应该在它后面立即删除线（加厚周长），这样你就只有：
mask=（L==i）是，删除两行后，更改'II=imoverlay（II，mask，clr（i，：）；'to’II=iOverlay（II，L，clr（i，：）；’也会起作用。顺便问一下，如果我的I是“I=0（500500,3）”，如何将背景色从黑色更改为（假设）青色[1 0 1]？我需要再次申请imoverlay吗？或者有一个快速的方法？@Ivy:准确地说，应该是：
II=imoverlay（II，L==i，clr（i，：）。现在，如果您从一个黑色图像开始
I（：）=0
，您可以使用
I=imoverlay（I，true（sz（1），sz（2）），[1 0 1]）
将其背景色更改为青色。我无法将头绕在零件周围检查重叠的椭圆，尤其是这一行，如果all（L（mask）==0）。这是什么意思？
(*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

%# 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')