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Is there any way I can make the attached contour plots more smooth ?

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I have attached two contour plots for pressure field outside an ellipse. The contour plots I got are jagged, may be due to the numerical integration I am using to calculate the pressure fields.The two plots are with Gaussian points 15000 and 5000 respectively. It is observable that with more Gaussian points, the contour plots are becoming smooth, but it is also taking time. Is there any other way to get smooth contour lines.

Accepted Answer

John D'Errico
John D'Errico on 6 Aug 2017
Sorry. If you try to resize a matrix (using interpolation) that is not itself sufficiently smooth that the original matrix yields non-smooth contours, you will get more finely interpolated noise! Interp2 is a waste of time here.
If you have a noisy matrix, then BEFORE you compute contours, you MUST smooth it FIRST if you want smooth contours. That smoothing may be done by removing the noise before you create the matrix, thus noise reduction prior to creating the matrix of data. Or you can do smoothing by applying a smoothing tool to your matrix, after creation.
You are doing some form of numerical integration that creates a noisy result. So a higher precision numerical integration is an option. Noise in the integration, as well as your comments, suggests you might be doing a Monte Carlo integration. I can't help if you don't say.
If you must do post smoothing on the matrix, then the classic solution is simply to apply a Gaussian blur to the matrix. You can do that using conv2. Or it should be possible to use methods like Savitsky-Golay, in two dimensions.
  4 Comments
Image Analyst
Image Analyst on 7 Aug 2017
I agree with John. Smoothing array before finding contours is a good solution, otherwise Savitzky-Golay filter to smooth a jaggedy outline on a non-smoothed array. It's easy enough to try them both and see which you like better. For what it's worth, see my attached Savitzky-Golay outline smoothing demo.

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More Answers (4)

KSSV
KSSV on 6 Aug 2017
You should be plotting the contours from a matrix say Z..you can increase the dimensions of this matrix using imresize. If you have spatial data matrices X and Y also, you may go for interpolation using interp2.

Chad Greene
Chad Greene on 6 Aug 2017
I like KSSV's option of using imresize, because it performs antialiasing before interpolation. To scale by 1/5,
sc = 1/5; % scaling factor
contour(imresize(X,sc),imresize(Y,sc),imresize(Z,sc))
Alternatively, you can do a 2D gaussian lowpass filter pretty easily with filt2. Syntax would be
res = ?;
lambda = ?;
Zf = filt2(Z,res,lambda,'lp');
contour(X,Y,Zf)
where you'll have to enter res, which is the pixel size in x,y; and you'll have to enter lambda, the approximate lowpass wavelength.

Teja Muppirala
Teja Muppirala on 7 Aug 2017
Edited: Teja Muppirala on 7 Aug 2017
Maybe a median filter? However ORDFILT2 needs the Image Processing Toolbox.
Z = peaks(501); % Sample data
Z = Z +0.1*randn(size(Z));
Z(abs(Z)<0.5) = 0;
subplot(211);
contourf(Z);
title('original')
subplot(212);
rad = 5; %Filter radius
[x,y] = meshgrid(-rad:rad);
filtArea = x.^2+y.^2 <= rad.^2; % Use a round filter
Zfilt = ordfilt2(Z,ceil(nnz(filtArea)/2),filtArea);
contourf(Zfilt);
title('filtered')

jacob faerman
jacob faerman on 15 Jan 2018
The median filter worked nicely for me, and filter2 does not need the image processing toolbox.

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