applying curve fitting for a 2D curve from a perimeter of an object

Hello,

I have been working in an interesting project in Matlab. We have to classify 2D objects in images based on a prediction model we are building. So far we can get the boundaries of each object from the image.

Now what we want is to apply curve fitting to the boundaries, so that to have a function that best describes the data points. I have been trying with the Matlab cftool, but I didn't find any method that works well. The data are the coordinates of the object boundaries and I tried several methods including Fourier, Gaussian, Polynomial, etc.

Do you think there is a more effective way to achieve this? We just want a function that describes the data points with the less possible error. One sample with the data points looks like the attached image.

Thanks in advance,

Dimos