Improve Ellipse Fit around a Binary Image

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N.B.
N.B. 2013-5-21
评论： Priya Natarajan 2013-12-20
Hello all,
The attached image shows a binary edge detection of a bean (shown in white.) In red is an ellipse for which I have attempted to fit to this bean.
My goal is to more precisely fit this ellipse to the bean, instead of the ellipse poorly encompassing the bean. How can I do this? Are there any lines that I can edit to improve this?
The code for which I am applying the ellipse is as follows (where the variable, isolatedBean is used as the binary image input):
s = regionprops (isolatedBean, 'Orientation', 'MajorAxisLength','MinorAxisLength', 'Eccentricity', 'Centroid');
hold on
phi = linspace(0,2*pi,50);
cosphi = cos(phi);
sinphi = sin(phi);
for k = 1:length(s)
xbar = s(k).Centroid(1);
ybar = s(k).Centroid(2);
a = s(k).MajorAxisLength/2;
b = s(k).MinorAxisLength/2;
theta = pi*s(k).Orientation/180;
R = [ cos(theta) sin(theta)
-sin(theta) cos(theta)];
xy = [a*cosphi; b*sinphi];
xy = R*xy;
x = xy(1,:) + xbar;
y = xy(2,:) + ybar;
plot(x,y,'r','LineWidth',2);
end
Thanks for your help!

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回答（2 个）

Image Analyst
Image Analyst 2013-5-21
编辑：Image Analyst 2013-5-22
Why not just take the convex hull?
If you really want an true ellipse fit, it's not so easy. But there is a paper on it:
"Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola"
by Sung Joon Ahn*, Wolfgang Rauh, Hans-JuK rgen Warnecke,
Fraunhofer Institute for Manufacturing Engineering and Automation (IPA), Nobelstr. 12, 70569 Stuttgart, Germany Fraunhofer Society, Leonrodstr. 54, 80636 Munich, Germany Received 16 June 2000; accepted 12 September 2000
Pattern Recognition 34 (2001) 2283}2303
http://www.sciencedirect.com/science/article/pii/S0031320300001527
and a FAQ entry: http://matlab.wikia.com/wiki/FAQ#Can_you_program_up_the_algorithm_in_this_article_for_me_and_explain_it_to_me.3F
  1 个评论
N.B.
N.B. 2013-5-21
My end goal is to graph the different radii of each bean. Can I extract radius data from the bwconvhull function?

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Matt Kindig
Matt Kindig 2013-5-21
编辑：Matt Kindig 2013-5-21
To build on Image Analyst's point, you can do something like this.
outline = bwmorph( isolatedBean, 'skel'); %convert to thin borderline
[r,c]=find(outline); %find locations where outline=1 (i.e. outline of bean)
I would then use one of the ellipse fitting functions on the File Exchange, such as http://www.mathworks.com/matlabcentral/fileexchange/15125-fitellipse-m to actually fit the ellipse.

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