function?[apar1par2par3par4par5par6]?=?fitellipse（XY）

%?FITELLIPSE?Least-squares?fit?of?ellipse?to?2D?points.
%????????A?=?FITELLIPSE（XY）?returns?the?parameters?of?the?best-fit
%????????ellipse?to?2D?points?（XY）.
%????????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（02）;

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（nxny‘o‘）;
%?Fit?it
fitellipse（nxny）
%?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（66）?=?0;?C（13）?=?-2;?C（22）?=?1;?C（31）?=?-2;

%?Solve?eigensystem
[gevec?geval]?=?eig（SC）;

%?Find?the?negative?eigenvalue
%?[NegRNegC]=find（geval<0&~isinf（geval））;
%?A=gevec（:NegC）;
I?=?find（real（diag（geval））?
%?Extract?eigenvector?corresponding?to?negative?eigenvalue
A?=?real（gevec（:I））;
%??m=（A‘*S*A）;
%??A=A*sqrt（geval（I）/m）;

%?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*my?+?A（5）*sx*sx*sy???...
??????A（1）*sy*sy*mx*mx?+?A（2）*sx*sy*mx*my?+?A（3）*sx*sx*my*my???...
??????-?A（4）*sx*sy*sy*mx?-?A（5）*sx*sx*sy*my???...
??????+?A（6）*sx*sx*sy*sy???...
??????]‘;

%?Convert?to?geometric?radii?and?centers

thetarad?=?0.5*atan2（par（2）par（1）?-?par（3））;
cost?=?cos（thetarad）;
sint?=?sin（thetarad）;
sin_squared?=?sint.*sint;
cos_squared?=?cost.*cost;
cos_sin?=?sint?.*?cost;

Ao?=?par（6）;
Au?=???par（4）?.*?cost?+?par（5）?.*?sint;
Av?=?-?par（4）?.*?sint?+?par（5）?.*?cost;
Auu?=?par（1）?.*?cos_squared?+?par（3）?.*?sin_squared?+?par（2）?.*?cos_sin;
Avv?=?par（1）?.*?sin_squared?+?par（3）?.*?cos_squared?-?par（2）?.*?cos_sin;

%?ROTATED?=?[Ao?Au?Av?Auu?Avv]

tuCentre?=?-?Au./（2.*Auu）;
tvCentre?=?-?Av./（2.*Avv）;
wCentre?=?Ao?-?Auu.*tuCentre.*tuCentre?-?Avv.*tvCentre.*tvCentre;

uCentre?=?tuCentre

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2012-06-21?14:25??ransac擬合代碼\
?????目錄???????????0??2012-08-17?14:33??ransac擬合代碼\橢圓擬合程序\
?????文件????????3553??2010-11-26?18:29??ransac擬合代碼\橢圓擬合程序\fitellipse.m
?????文件????????4958??2010-11-26?19:35??ransac擬合代碼\橢圓擬合程序\fitellipse1.m
?????文件????????1904??2010-11-26?18:34??ransac擬合代碼\橢圓擬合程序\fitellipse2.m
?????目錄???????????0??2012-08-27?14:03??ransac擬合代碼\直線擬合程序\
?????文件?????5019478??2011-12-28?17:07??ransac擬合代碼\直線擬合程序\image4.bmp
?????文件????????1408??2012-05-04?16:44??ransac擬合代碼\直線擬合程序\ransac.asv
?????文件????????1426??2012-08-09?16:00??ransac擬合代碼\直線擬合程序\ransac.m
?????文件??????302586??2012-05-04?16:40??ransac擬合代碼\直線擬合程序\硅臂直線.bmp
?????文件??????852282??2012-05-04?17:13??ransac擬合代碼\直線擬合程序\硅臂直線2.bmp