How do I fit a curve ?

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SATISH SONWANE
SATISH SONWANE 2022-12-8
评论： SATISH SONWANE 2022-12-17
Hi, I have been trying t fit a curve to the attached data. I tried fitPolynomialRANSAC but didn't get intended result. The data and the output are attached. Here is the code I used.
load data.mat
figure
plot(idx(:,1),idx(:,2),'*');
set(gca,'XAxisLocation','top','YAxisLocation','left','ydir','reverse');
x = idx(:,1);
y = idx(:,2);
N = 2; % second-degree polynomial
maxDistance = 5; % maximum allowed distance for a point to be inlier
[P, inlierIdx] = fitPolynomialRANSAC([x y],N,maxDistance);
yRecoveredCurve = polyval(P,x);
figure
plot(x(inlierIdx),y(inlierIdx),'.',x(~inlierIdx),y(~inlierIdx),'r+')
set(gca,'XAxisLocation','top','YAxisLocation','left','ydir','reverse');
hold on
plot(x,yRecoveredCurve,'-g','LineWidth',1)
hold off
Any help is greatly appreciated.
Edit: Requirement is that the curve should closely follow the point.
  1 个评论
SATISH SONWANE
SATISH SONWANE 2022-12-8
Tried following code too. Got a little better result.
load data.mat
x = idx(:,1);
y = idx(:,2);
p=polyfit(x,y,4);
f = polyval(p,x);
plot(x,y,'o',x,f,'-')

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采纳的回答

Mathieu NOE
Mathieu NOE 2022-12-8
hello
a cardioid equation may be the solution but I have serious doubts you can fit a polynomial for this shape
as I am lazy and it's already late here , I didn't included any fitting optimisation (if that may work)
load data.mat
y = idx(:,1);
m = max(y);
y = (y-m/2)./(m/2);
x = idx(:,2);
n = max(x);
x = x./n;
% cardioid function
t = linspace(-pi,pi,100);
yc = 0.5*t .* sin( pi * .9*sin(t)./t);
xc = 0.45*abs(t) .* cos(pi * sin(t)./t);
xc = 0.05 +xc - min(xc); % shift x so that min value is zero
figure(1),plot(x,y,'r*',xc,yc,'k','linewidth',2)
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SATISH SONWANE
SATISH SONWANE 2022-12-12
编辑：SATISH SONWANE 2022-12-12
Thank you @Image Analyst. Tried with the toolbox first and then came here. I got a new insight from @Mathieu NOE's answer though. Like for example I could fit a Sigmoid function to symmetric 'S' shaped datapoints, Gompertz function to a non-symmetrical S-shaped datapoints etc.
I will now experiment with different curve equations to get the desired shape of the curve in the toolbox. Thanks again.
Edit: Please comment if I am going in the wrong direction.
SATISH SONWANE
SATISH SONWANE 2022-12-17
Found this great link. Anyone who is viewing this, please check this link by @John D'Errico.

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