点云曲线拟合

Question

I have a 2D cloud of points, i imported them into matlab and i want to have a smoothing spline function that passes through them. I tried with the "curve fitting" app and the "smoothing spline" option but in the extremes the function seems to not follow much the cloud and anyway in the middle of the cloud does not pass trough the points but goes up or down the points. I tried "basic fitting" option after i plotted the cloud but no improvements as you can see:

The idea of what i wanted is this:

Of course i modified the image with Gimp (i am using linux) and the red line is a hand made one...so not so smooth as it would be. Note i have magnified the image. I was asking to myself if it was possible to have a variable grade fitting along all the cloud. Anyway i don't know how to do it and any suggestion is appreciated.

The "smoothing spline" (in the "curve fitting tool") seems to be more equal to an interpolation than to a spline

Answer 1

You could use the function spline instead of the graphical tool. For example:

x = 1:100; % x-axis values for data
y = conv(randn(1,100),ones(1,10),'same'); % example smooth random data

xx = 1:.1:100; % x-axis values for plotting the spline
yy = spline(x,y,xx);
plot(x,y,'.',xx,yy)

See the doc of spline for more information.