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Fitting smooth closed spline to scattered 2D points

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David
David on 21 Jun 2015
Answered: Praful Agrawal on 29 Sep 2018
Hi everyone,
I have a set of points scattered in a 2D plane. The points are scattered in a somwhat circular/elipptical way, but I would like to fit some arbitrarily (but smoothed) shaped spline. The points are distributed like:
To enable closing of a spline, the last and first data points are the same.
As said I would like to fit a closed smoothed spline to this curve. I've tried the cscvn-option giving me the below, but I would like something a bit more smoothened out (cscvn forces the spline to go exactly through each and every point):
Reading up in the help, csaps seem to enable smoothing (to be fair, I'm not really sure how), but if trying this on my data I get a smoothed non-closed curve like below:
The last option I've looked at is creating a new parameter to which I fit both my (x,y)-data (as suggested in an earlier thread: http://www.mathworks.com/matlabcentral/newsreader/view_thread/33868 ), but this actually gives me an even more jagged curve:
However I might be applying the parametrization in an incorrect way...
So, to my question. Does anyone have a good way of creating a closed smoothed spline to my data? Any suggestion or help would be very much appreciated. (P.S: I'm trying to create an automatized code, so I'm preferably looking for executable code than GUI in the curve fitting toolbox (but I understand that they are somewhat connected...)).
Thanks for the help!
/David

Accepted Answer

Image Analyst
Image Analyst on 21 Jun 2015
If you don't want or require the curve to go through every point exactly, you can use a Savitzky-Golay filter on the parameterized data.
% Now smooth with a Savitzky-Golay sliding polynomial filter
windowWidth = 35
polynomialOrder = 2
smoothX = sgolayfilt(x, polynomialOrder, windowWidth);
smoothY = sgolayfilt(y, polynomialOrder, windowWidth);
  8 Comments
David
David on 22 Jun 2015
Hi again, thanks for coming with new suggestions.
No I'm not that familiar with active contours. I did some tries but seem not to find the right way of getting a smoother boundary. According to the help of activecontour(), an example command would be:
bw = activecontour(I, mask, 200, 'edge','SmoothFactor',1.5);
but when I try to perform the same (see code below) I get an error prompt:
if true
BW = poly2mask(xy(1,:),xy(2,:),120,120);
mask = zeros(size(BW));
mask(10:end-10,10:end-10) = 1;
bw = activecontour(BW,mask,'SmoothFactor',1.5);
Error message:
Error using activecontour>parse_inputs (line 287)
Too many input arguments were passed to activecontour.
So it seems like 'SmoothFactor' cannot be passed to the activecontour. Has this been changed in a new Matlab version (I'm running R2014a)? Or am I running the commands incorrectly?
Lastly: if I manage to get a smoothed contour map (i.e. binary image), can I then retrieve the edge points (i.e. going back to some spline/polygon shape) again?
Again, thanks for all the help.

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More Answers (1)

Praful Agrawal
Praful Agrawal on 29 Sep 2018
the original task can be achieved by converting the piecewise polynomial fit to bspline fit using fn2fm function:
X - set of points
pp = cscvn(X); bsp = fn2fm(pp, 'B-');

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