Least Squares Fitting Method with a Circle
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Hi everyone,
Forgive me, I am no expert at MATLAB. I would appreciate it greatly if someone could explain to me the method of nonlinear least squares and how to fit it with a circle of random points. Here's what I have so far:
% radius information-------------------------------------------------------
r = 10; % constant radius
Rc = @(x,y,z) (x.^2 + y.^2 + z.^2).^(1/2); % radius as a function
n = rand(1000,3); % generate random points on nominal circle
xc = n(:,1);
yc = n(:,2); % separate into coordinates
zc = n(:,3);
%--------------------------------------------------------------------------
% angular information------------------------------------------------------
theta = linspace(0,2*pi,1000); % plot bounds
theta = theta';
%--------------------------------------------------------------------------
% generate random radii----------------------------------------------------
R = Rc(xc,yc,zc);
R(:,2) = R(:,1); % same radii in all directions
R(:,3) = R(:,1);
p = n + (r/100)*R; % generate plot points around the circle
figure(1)
polar(theta,Rc(xc,yc,zc))
%--------------------------------------------------------------------------
% Least Squares fitting----------------------------------------------------
e = dist(p,R');
perf = sse(e);
lsqrfit = lsqr(e,Rc(xc,yc,zc),[],1000);
%--------------------------------------------------------------------------
So from what I understand, the residuals (errors) need to be found and then the sum of squares of the residuals need to be found. After that I am not sure where to go. Thanks for all the help.
Ian
댓글 수: 2
Andrew Newell
2011년 7월 1일
I'm having trouble figuring out what this code is supposed to be doing. First, the data: are they random points on a circle, or scattered near a circle? Can the center and the radius of the circle vary? What is your fitting criterion? (I would think sum of squares of the distance from the circle would be best).
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bym
2011년 7월 2일
Maybe this will help, it is adapted from "measuring the radius of a roll of tape" demo in the image processing toolbox:
r = 5+.5*rand(100,1); %100 random radii
ang = linspace(0,2*pi,100)'; % angles
x = r.*cos(ang)+2; y = r.*sin(ang)+3; % x,y coordinates centered [2,3]
plot(x,y,'+')
axis equal; hold on;
c = [x y ones(length(x),1)]\-(x.^2+y.^2); %least squares fit
xhat = -c(1)/2;
yhat = -c(2)/2;
rhat = sqrt(xhat^2+yhat^2-c(3));
plot(rhat*cos(ang)+xhat,rhat*sin(ang)+yhat,...
'g','linewidth',2) %best fit circle
댓글 수: 4
Image Analyst
2020년 4월 11일
For a fixed radius, where would you want the center? At the mean of the point?
xCenter = mean(x);
yCenter = mean(y);
Rajdeep Chowdhury
2020년 4월 11일
I want a least square type fitting to obtain the center (x,y) when the radius is predefined.
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