SPLINEFIT

Fit a spline to noisy data.

Description

Direct spline interpolation of noisy data may result in a curve with
unwanted oscillations. This is particularly bad if the slope of the
curve is important.

A better approach is to reduce the degrees of freedom for the spline
and use the method of least squares to fit the spline to the noisy data.
The deegres of freedom are connected to the number of breaks (knots),
so the smoothing effect is controlled by the selection of breaks.

SPLINEFIT:
- A curve fitting tool based on B-splines
- Splines on ppform (piecewise polynomial)
- Any spline order (cubic splines by default)
- Periodic boundary conditions
- Linear constraints on function values and derivatives
- Robust fitting scheme
- Operates on ND arrays in the same way as SPLINE
- Nonuniform distributions of breaks

M-FILES ALSO INCLUDED:
examples - Examples for splinefit
ppdiff - Differentiate piecewise polynomial
ppint - Integrate piecewise polynomial

• MATLAB release: MATLAB 7.10 (2010a)

[Trevor Rayment]

this is a useful piece of code. It does exactly what it says it does. Much appreciated.

[M C]

 

[David Villeneuve]

Thanks, this provides a simple method to put a smooth line through noisy data. You control the tightness by the number of break points.

[P.S. Ramesh]

I am trying to generate a smooth curve through noisy data that is periodic at the ends. Can I use this code or is there a version that enforces periodicty

[Jonas Lundgren]

Sorry, SPFIT don't support periodicity.

[Husam Aldahiyat]

Good I guess.

[Chaos]

for images, it's too slow, use better steepest descent. this figure isn't 'noisy' at all. try to pluck an image out of the 'dirt' where the SN is about 12dB

[Jonas Lundgren]

That's true Chaos. This code was not intended for image processing and the figure shouldn't contain any image noise. How did you do to apply the code to a noisy image?

[Amit Ailiani]

A very useful code for cubic spline interpolation. Can you please give me the details of the method or any reference to read?

[Maryam Ra]

A very useful code in Matlab. I am wondering if anyone knows how to call this function from VC++?

[David]

Works very good to fit noisy 1D data, saved me a lot of effort, thank you!

[Steffen Huber]

Thank you very much - this code saved me a lot of time. Can you please send me references to the implemented method?

[Arthur Hebert]

Easy to use, does what it says, saves me a ton of work. Thanks.

[Ambrogio Manzino]

If point distribution is not homogeneous, probably the software have some problem in L.S. parametres solution.
How cai I use the software in a multiresolution field data?

[Jonas Lundgren]

Non-uniform distributions of breaks/knots is ok. No problem.

[Vinesh Rajpaul]

 

[Vinesh Rajpaul]

Useful...however, support for data containing NaNs would be helpful (spline interpolation using built-in MATLAB functions works fine for data containing NaNs)

[Sami Aldalahmeh]

That's a very useful code. Can you please provide some references for the robust spline fit and the periodic condition options?

[Jonas Lundgren]

Sami, the robust fitting scheme uses weigthed regression where the weights are computed from previous residuals. It is close to the scheme described by John D'Errico in Optimization Tips and Tricks, section 33 (File ID: #8553).

The periodic condition forces endpoint derivatives to be equal. Example: A cubic spline with endpoints x=1 and x=4 (period length 3) satisfies the conditions y(1) = y(4), y'(1) = y'(4) and y"(1) = y"(4). This is perhaps not evident in the code where the B-splines at the endpoints are matched (pairwise) to have the same shape (and the same derivatives).

[Jonathan]

Splinefit works great for 1D data, and I see ND support, but it looks like this simply facilitates batch processing several sets of 1D data. Is it possible to use this to generate 2D (an higher dimensional) splines? If so, some examples would be great!

[Jonas Lundgren]

Jonathan, SPLINEFIT is a curve fitting tool and deals with mappings from R to R^N. SPLINEFIT mimics SPLINE and the ND support can of course be replaced by a for-loop, but that will be less efficient.

If you are looking for a surface fitting tool i can recommend GRIDFIT by John D'Errico or SMOOTHN by Damien Garcia.

[Gulcan]

Really appreciate the work, thank you. I have a question though. Cubic spline does not go through all knots that I've selected. Is it related to some constraints that I forget to indicate?

[Jonas Lundgren]

Gulcan, the smoothing spline is not intended to go through the knots/breaks. The curve fits to noisy data in the least square sense, also for knots. Use the constraint argument if you have exact data.

Example: If the curve must go through the points (0,5) and (2,3) use the constraint
con = struct('xc',[0 2],'yc',[5 3])

[Stefan]

Vey nice tool! Is there also a possibility to enter non-equalities in the constraints?
eg= slope at certain points should be greater then 2

[Jonas Lundgren]

Stefan, only equality constraints so far.

[Dani]

Will it be possible in future versions to add monotonicity constrains to the spline?

[Jonas Lundgren]

Dani, I have no plans for more extensions of splinefit. If you have the Optimization Toolbox you should try SLM.

[Naveen]

 

[K B]

 

[Fer]

 

[Sander Aerts]

Outstanding work with the splinefit function, this is exactely what i have been looking for. Very clean code and good documentation including the published examples.
I also like the ppdiff and the ppint function, how they work seamlessly with the standard piecewise functions.

This one certainly deserves a five star rating, congrats on the job

[Moncef]

good guess

[Elena]

Works very well and includes excellent documentation and examples