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

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Ankit Bhandari
on 6 Aug 2017

Answered: jacob faerman
on 15 Jan 2018

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### Accepted Answer

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
on 7 Aug 2017

### More Answers (4)

KSSV
on 6 Aug 2017

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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))

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.

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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')

##### 0 Comments

jacob faerman
on 15 Jan 2018

The median filter worked nicely for me, and filter2 does not need the image processing toolbox.

##### 0 Comments

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