find an equation for the set of coordinates

I have the above plot with a different set of coordinates for each object(labeled by different colors). I was wondering if there was a way to find an approximate equation for each object in matlab.

I was thinking about smoothing out the "rougher" parts to make it easier but I'm not sure how to go about doing that. any ideas?

thanks

Answer 1

[Image Analyst]

How about just taking the average of the coordinates

windowWidth = 5;
newx = conv(x, ones(1, windowWidth)/windowWidth, 'same');
newy = conv(y, ones(1, windowWidth)/windowWidth, 'same');

[Duncan]

and then using polyfit?

[Image Analyst]

Huh? Why? conv2() is already like doing a polyfit of order 1 (a line). If you want higher order for less smoothing, use a Savitzky-Golay filter, sgolayfilt() in the Signal Processing Toolbox.

Perhaps increasing sampling and getting a smoother curve via splines would interest you. See attached demo.

[Duncan]

hi sorry, i noticed you put conv() in the e.g. and then said that conv2() is a polyfit of order 1.

[Image Analyst]

Sorry - I usually use conv2(), which is for 2D arrays (images). For a 1-D signal, you'd use conv().

Answer 2

[Ahmet Cecen]

I would use cftool, easier to play around with different fits, and not confined to polynomials.