How do I fit a curve ?

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.

[SATISH SONWANE]

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,'-') 

Answer 1

[Mathieu NOE]

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)

[SATISH SONWANE]

Thanks you for the answer @Mathieu NOE. May be I could have framed my question better. I needed a generalised way to fit curve to such shapes. The shape could be an 'S' in the next round. It may not even be uniform on the upper and bottom side. Like that.

[Image Analyst]

@SATISH SONWANE if you need a more generalized and flexible way to find the best fit curve, maybe you should get the Curve Fitting Toolbox.

[SATISH SONWANE]

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]

Found this great link. Anyone who is viewing this, please check this link by @John D'Errico.