Home » Source Code » fisheye corrction » fitellipse.m

fitellipse.m ( File view )

  • By zhengzou 2014-05-09
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			function [Ru,uCentre vCentre] = fitellipse(X,Y)

% FITELLIPSE  Least-squares fit of ellipse to 2D points.
%        A = FITELLIPSE(X,Y) returns the parameters of the best-fit
%        ellipse to 2D points (X,Y).
%        The returned vector A contains the center, radii, and orientation
%        of the ellipse, stored as (Cx, Cy, Rx, Ry, theta_radians)
%
% Authors: Andrew Fitzgibbon, Maurizio Pilu, Bob Fisher
% Reference: "Direct Least Squares Fitting of Ellipses", IEEE T-PAMI, 1999
%
% This is a more bulletproof version than that in the paper, incorporating
% scaling to reduce roundoff error, correction of behaviour when the input
% data are on a perfect hyperbola, and returns the geometric parameters
% of the ellipse, rather than the coefficients of the quadratic form.
%
%  Example:  Run fitellipse without any arguments to get a demo
% if nargin == 0
%   % Create an ellipse
%   t = linspace(0,2);
% 
%   Rx = 300
%   Ry = 200
%   Cx = 250
%   Cy = 150
%   Rotation = .4 % Radians
% 
%   x = Rx * cos(t);
%   y = Ry * sin(t);
%   nx = x*cos(Rotation)-y*sin(Rotation) + Cx;
%   ny = x*sin(Rotation)+y*cos(Rotation) + Cy;
%   % Draw it
% %   plot(nx,ny,'o');
%   % Fit it
%   fitellipse(nx,ny)
%   % Note it returns (Rotation - pi/2) and swapped radii, this is fine.
%   return
% end

% normalize data
mx = mean(X);
my = mean(Y);
sx = (max(X)-min(X))/2;
sy = (max(Y)-min(Y))/2;

x = (X-mx)/sx;
y = (Y-my)/sy;

% Force to column vectors
x = x(:);
y = y(:);

% Build design matrix
D = [ x.*x  x.*y  y.*y  x  y  ones(size(x)) ];

% Build scatter matrix
S = D'*D;

% Build 6x6 constraint matrix
C(6,6) = 0; C(1,3) = -2; C(2,2) = 1; C(3,1) = -2;

% Solve eigensystem
[gevec, geval] = eig(S,C);

% Find the negative eigenvalue
I = find(real(diag(geval)) < 1e-8 & ~isinf(diag(geval)));

% Extract eigenvector corresponding to negative eigenvalue
A = real(gevec(:,I));

% unnormalize
par = [
  A(1)*sy*sy,   ...
      A(2)*sx*sy,   ...
      A(3)*sx*sx,   ...
      -2*A(1)*sy*sy*mx - A(2)*sx*sy*my + A(4)*sx*sy*sy,   ...
      -A(2)*sx*sy*mx - 2*A(3)*sx*sx*
...
...
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060-1.fig270.39 kB01-08-12|10:26
060.bmp406.05 kB18-07-12|09:51
060.fig261.75 kB01-08-12|09:39
080.bmp406.05 kB18-07-12|09:51
090l.bmp406.05 kB18-07-12|09:51
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090r.fig277.17 kB01-08-12|09:34
90.bmp406.05 kB20-07-12|16:14
circ.m533.00 B30-07-12|15:32
correct_image_061g.bmp3.82 MB01-08-12|19:52
fitellipse.m3.13 kB28-07-12|22:38
markpoint.m621.00 B01-08-12|09:57
rec.asv3.29 kB04-08-12|10:40
rec.m3.32 kB04-08-12|11:16
rec2.asv2.02 kB01-08-12|15:54
rec2.m2.02 kB01-08-12|15:55
shiyan5.m3.69 kB27-07-12|15:30
test.asv1.59 kB01-08-12|11:04
test.m1.63 kB01-08-12|16:43
test2.asv3.92 kB01-08-12|10:09
Thumbs.db36.00 kB18-07-12|09:51
trapezial_correction-wrong.m1.50 kB02-08-12|16:59
trapezial_correction.asv3.23 kB02-08-12|17:23
trapezial_correction.m1.66 kB04-08-12|10:09
Untitled.m1.45 kB26-07-12|20:43
Untitled3.m3.98 kB25-07-12|15:44
Untitled5.m3.75 kB23-07-12|08:58
Untitled6.m3.82 kB23-07-12|15:35
截图.jpg125.80 kB29-07-12|20:25
校正0.00 B09-04-13|09:07
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fitellipse.m (3.14 MB)

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