Easy 'n fast smoothing for 1-D to N-D data

SMOOTHN allows automatized and robust smoothing in arbitrary dimension w/wo missing values

Description

SMOOTHN provides a fast, unsupervised and robust discretized spline smoother for data of arbitrary dimension.

SMOOTHN(Y) automatically smoothes the uniformly-sampled array Y. Y can be any N-D multicomponent noisy array (e.g. time series, images, 3D data, 3D vector fields, tensors...).
 
To smooth a vector field or multi-component data, Y must be a cell array. For example, if you need to smooth a 3-D vectorial flow (Vx,Vy,Vz), use Y = {Vx,Vy,Vz}. The output Z is also a cell array which contains the smoothed components.

SMOOTHN can deal with missing (NaN) values (see screenshot and examples).

SMOOTHN(...,'robust') carries out a robust smoothing that minimizes the influence of outlying data (see screenshot and examples).

SMOOTHN is made automated by the minimization of the generalized cross-validation score.

Enter "help smoothn" in the Matlab command window for complete instructions and 1-D to 3-D examples.

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For details about the algorithm, refer to:
Garcia D. Robust smoothing of gridded data in one and higher dimensions with missing values.
Comput Statist Data Anal, 2010;54:1167-1178
http://www.biomecardio.com/pageshtm/publi/csda10.pdf

For velocity vector fields, also refer to:
Garcia D. A fast all-in-one method for automated post-processing of PIV data.
Exp Fluids, 2011;50:1247-1259.
http://www.biomecardio.com/pageshtm/publi/expfluids10.pdf
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Acknowledgements

This file inspired Quick Spline Smoothing For 1 D Data and Pi Vlab Time Resolved Particle Image Velocimetry (Piv) Tool.

• MATLAB release: MATLAB 7.10 (R2010a)

[Martin Lechner]

Super tool for smoothing!

[Ben]

Thanks for sharing!! This is really a nice pice of code.

[Michael]

What is with the "DCTN and iDCTN are required"? I was able to access them outside the MatLab browser, but not from within it.

[none]

 

[Jakub Wosyka]

Hello Damien,
very useful and nice function.
I tried to add the non-uniform grid (x values) according to your article but then it only interpolates the data. When I raise the value of smooting parameter, new the function will fall to zero (zero mean). (...probably my fault...). Do you plan to extend this nice function for non-uniform grids? Thank you

[Erdal Bizkevelci]

 

[Erik]

Really nice method!

I does seem to me though that there is a bug when using this in combination with your pppiv-function.

In the function RobustWeights, there is a line:
MAD = median(abs(r(I)-median(r(I))));

However, the values of r are complex when using it together with pppiv. That causes the median function to sort the values by the real component and then take the middle value. I think you probably want to add
r = abs(r);
before taking the median to sort the residuals by magnitude instead. Is that correct?

[Richard]

Well done! well documented. very easy to use.
Richard

[Balengi]

I like this function very much...I do have a question though. I am smoothing a 50x50x3 n-d array but after smoothing my 3-d object is much flatter than the original. it almost seems distorted...has this ever happened to you before?

[Juha-Matti Alakoskela]

 

[Warwick]

Very good!. Minor effort to obtain dctn and idctn but this is an easy way to smooth out "zigzag" contours (much better than going with INTERP2( Array, ntimes)).
thank you.

[Damien Garcia]

to Matthew: you should have read the File description:
MATLAB release: MATLAB 7.5 (R2007b)
BSXFUN is nonexistent in versions prior to 7.4!
Regards. DG

[Matthew Souders]

Code does not work out of the box for MATLAB 7.1 - at least I was unable to get it to function. Attempted a test case and got this error:

??? Undefined function or method 'bsxfun' for input argument of type 'function_handle'.

Error in ==> smoothn at line 266
Lambda = bsxfun(@plus,Lambda...

If some special set-up is required to make this code run successfully, this needs to be carefully documented.

[Mark Shore]

 

[Mark Shore]

Definitely very interesting looking. Well referenced with a range of 1, 2 and 3D examples, which work quite well. I'll rate this once I've had a chance to look at it in more detail.

However the author should correct the required products listing since the image processing toolbox is NOT a requirement per se. All of the provided test examples work perfectly without it. A call to bwdist to replace NaNs in supplied data defaults gracefully to another option if the image processing toolbox is not installed. And rgb2gray and imnoise are required only to _create_ the example of the noisy Saturn image given above, not to denoise it.

It would also be convenient for the author to include his subroutines dctn.m and idctn.m in the FEX file if possible, rather than requiring a separate download from an external web site.

[Rob Campbell]

This is nice!

[Jan Simon]

H1 line, really descriptive help, examples, date and author mentioned, comments in the code, referenced method, and finally it works well.

[Xianmin]

Good job!

[Carlos Adrian Vargas Aguilera]

Welcome back!