http://imagej.273.s1.nabble.com/fitting-y-f-x-data-to-arbitrary-functions-in-ImageJ-tp5020273p5020312.html
invalid range. Then the CurveFitter will avoid this range.
boundary', however.
> On fits to some data the parameters returned are obnoxiously bad.
situation.
Parameter numbers that are not set should be -1. Note that 0 refers to
parameter 'a', 1 to 'b', etc. Since you can specify only two out of the
to be -1.
setOffsetMultiplySlopeParams call should look like.
I'll have a look at it.
order of magnitude of the initial parameters. Better, specify also the
initialParamVariations (e.g. for each parameter 1/10 of the range that
it may have).
> Greetings,
>
> First, thanks for expounding on CurveFitter.
>
> I have a few questions and a bug.
>
> a) Is there any way to keep the fitting within a given range for each
> parameter? On fits to some data the parameters returned are obnoxiously bad.
> The input data resembles data that fits reasonably, i.e., I do not suspect
> that the initial parameters are outside the local minimum. This is not using
> setOffsetMultiplySlopeParams.
>
> b) When using the method setOffsetMultiplySlopeParams and passing a value to
> doCustionFit's initialParamVariations parameter, set to what is documented as
> the default value that would be used if null is passed, the fitting is
> effectively a linear fit; see example below. A reasonable fit is had if the
> call to setOffsetMultiplySlopeParams is commented out. If this worked what
> kind of improvement would I expect to see in efficiency or goodnees-of-fit?
>
> b) When using the method setOffsetMultiplySlopeParams and passing a null value
> to doCustionFit's initialParamVariations parameter, a null pointer exception
> is thrown:
> ImageJ 1.50h; Java 1.8.0_91 [64-bit]; Linux 4.5.5-300.fc24.x86_64; 287MB of
> 1820MB (15%)
>
> java.lang.NullPointerException
> at ij.measure.CurveFitter.modifyInitialParamsAndVariations(CurveFitter.java:835)
> at ij.measure.CurveFitter.doFit(CurveFitter.java:178)
> at ij.measure.CurveFitter.doCustomFit(CurveFitter.java:283)
> at My_Plugin2.nonlinearFit(My_Plugin2.java:38)
> at My_Plugin2.run(My_Plugin2.java:14)
> at ij.plugin.PlugInExecuter.runCompiledPlugin(Compiler.java:318)
> at ij.plugin.PlugInExecuter.run(Compiler.java:307)
> at java.lang.Thread.run(Thread.java:745)
>
> Thanks in advance,
>
> Fred
>
> ----------------------------
> import ij.*;
> import ij.process.*;
> import ij.gui.*;
> import java.awt.*;
> import ij.plugin.*;
> import ij.plugin.frame.*;
> import ij.measure.*;
>
> public class My_Plugin2 implements PlugIn {
>
> public void run(String arg) {
> double[] x = {0.10,0.25,0.50,0.75,1.00,1.25,1.50,1.75,2.00,5.00};
> double[] y =
> {1123.175,838.206,469.320,453.003,725.135,1094.360,1450.741,1787.361,2128.119,4670.120};
> double[] p = nonlinearFit(x,y);
> Plot plot = new Plot("","x","y");
> plot.setLineWidth(2);
> plot.setColor(Color.black);
> plot.addPoints(x,y,PlotWindow.X);
> double[] y2 = new double[y.length];
> for(int i=0; i<y.length; i++)
> y2[i] = Math.abs( p[1] + p[2]*Math.exp(-x[i]/p[0]) );
> plot.setColor(Color.blue);
> plot.addPoints(x,y2,PlotWindow.LINE);
> plot.show();
>
> }
>
> private double[] nonlinearFit(double[] x, double[] y) {
>
> CurveFitter cf = new CurveFitter(x, y);
> double[] params = {1, 2*y[0], -(y[0]+y[y.length-1])};
> double[] ipv = new double[params.length];
> for(int i=0; i<ipv.length; i++)
> ipv[i] = Math.abs(params[i]*0.1);
>
> cf.setMaxIterations(200);
> cf.setOffsetMultiplySlopeParams(1, 2, -1);
> cf.doCustomFit(new UserFunction() {
> @Override
> public double userFunction(double[] p, double x) {
> return Math.abs( p[1] + p[2]*Math.exp(-x/p[0]) );
> }
> }, params.length, "", params, ipv, false);
> //IJ.log(cf.getResultString());
>
> return cf.getParams();
> }
> }
>
>
>
> On Tue, March 13, 2018 2:30 pm, Michael Schmid wrote:
>> Hi Kenneth,
>>
>> Concerning fitting an 8-parameter function:
>>
>> If the fit is not linear (as in the case of a difference of Gaussians),
>> having 8 fit parameters is a rather ambitious task, and there is a high
>> probability that the fit will run into a local minimum or some point
>> that looks like a local minimum to the fitting program.
>>
>> It would be best to reduce the number of parameters, e.g. using a fixed
>> ratio between the two sigma values in the Difference of Gaussians.
>>
>> You also need some reasonable guess for the initial values of the
>> parameters.
>>
>> For the ImageJ CurveFitter, if there are many parameters it is very
>> important to specify roughly how much the parameters can vary, these are
>> the 'initialParamVariations'
>> If cf is the CurveFitter, you will have
>> cf.doCustomFit(UserFunction userFunction, int numParams,
>> String formula, double[] initialParams,
>> double[] initialParamVariations, boolean showSettings
>>
>> For the initialParamVariations, use e.g. 1/10th of how much the
>> respective parameter might deviate from the initial guess (only the
>> order of magnitude is important).
>>
>> If you have many parameters and your function can be written as, e.g.
>> a + b*function(x; c,d,e...)
>> or
>> a + b*x + function(x; c,d,e)
>>
>> you should also specify these parameters via
>> cf.setOffsetMultiplySlopeParams(int offsetParam, int multiplyParam,
>> int slopeParam)
>> where 'offsetParam' is the number of the parameter that is only an
>> offset (in the examples above, 0 for 'a', 'multiplyParam' would be 1 for
>> 'b' in the first example above, or 'slopeParam' would be 1 for 'b' in
>> the second type of function above. You cannot have a 'multiplyParam' and
>> a 'slopeParam' at the same time, set the unused one to -1.
>>
>> Specifying an offsetParam and multiplyParam (or slopeParam) makes the
>> CurveFitter calculate these parameters via linear regression, so the
>> actual minimization does not include these parameters. In other words,
>> you get fewer parameters, which makes the fitting much more likely to
>> succeed.
>>
>> In my experience, if you end up with 3-4 parameters (not counting the
>> parameters eliminated by setOffsetMultiplySlopeParams), there is a good
>> chance that the fit will work very well, with 5-6 parameters it gets
>> difficult, and above 6 parameters the chance to get the correct result
>> is rather low.
>>
>> If you need to control the minimization process in detail, before
>> starting the fit, you can use
>> Minimizer minimizer = cf.getMinimizer()
>> to get access to the Minimizer that will be used and you can use the
>> Minimizer's methods to control its behavior (e.g. allow it to do more
>> steps than by default by minimizer.setMaxIterations, setting it to try
>> more restarts, use different error values for more/less accurate
>> convergence, etc.
>>
>> Best see the documentation in the source code, e.g.
>>
https://github.com/imagej/imagej1/blob/master/ij/measure/CurveFitter.java>>
https://github.com/imagej/imagej1/blob/master/ij/measure/Minimizer.java>>
>> -------------
>>
>> > Bonus question for Java Gurus:
>> > How to declare the user function as a variable, call it,
>> > and pass it to another function?
>>
>> public class MyFunction implements UserFunction {...
>> public double userFunction(double[] params, double x) {
>> return params[0]+params[1]*x;
>> }
>> }
>>
>> public class PassingClass { ...
>> UserFunction exampleFunction = new MyFunction(...);
>> otherClass.doFitting(xData, yData, exampleFunction)
>> }
>>
>> Public class OtherClass { ...
>> public void doFitting(double[] xData, double[] yData,
>> UserFunction userFunction) {
>> CurveFitter cf = new CurveFitter(xData, yData);
>> cf.doCustomFit(userFunction, /*numParams=*/2, null,
>> null, null, false);
>> }
>> }
>>
>> -------------
>>
>> Best,
>>
>> Michael
>> ________________________________________________________________
>>
>>
>> On 13/03/2018 18:56, Fred Damen wrote:
>>> Below is a routine to fit MRI Inversion Recover data for T1.
>>>
>>> Note:
>>> a) CurveFitter comes with ImageJ.
>>> b) Calls are made to UserFunction once for each x.
>>> c) If your initial guess is not close it does not seem to converge.
>>>
>>> Bonus question for Java Gurus:
>>> How to declare the user function as a variable, call it, and pass it to
>>> another function?
>>>
>>> Enjoy,
>>>
>>> Fred
>>>
>>> private double[] nonlinearFit(double[] x, double[] y) {
>>>
>>> CurveFitter cf = new CurveFitter(x, y);
>>> double[] params = {1, 2*y[0], -(y[0]+y[y.length-1])};
>>>
>>> cf.setMaxIterations(200);
>>> cf.doCustomFit(new UserFunction() {
>>> @Override
>>> public double userFunction(double[] p, double x) {
>>> return Math.abs( p[1] + p[2]*Math.exp(-x/p[0]) );
>>> }
>>> }, params.length, "", params, null, false);
>>> //IJ.log(cf.getResultString());
>>>
>>> return cf.getParams();
>>> }
>>>
>>>
>>> On Tue, March 13, 2018 11:06 am, Kenneth Sloan wrote:
>>>> I have some simple data: samples of y=f(x) at regularly spaced discrete
>>>> values
>>>> for x. The data
>>>> is born as a simple array of y values, but I can turn that into (for
>>>> example)
>>>> a polyline, if that
>>>> will help. I'm currently doing that to draw the data as an Overlay. The
>>>> size
>>>> of the y array is between 500 and 1000. (think 1 y value for every integer
>>>> x-coordinate in an image - some y values may be recorded as "missing").
>>>>
>>>> Is there an ImageJ tool that will fit (more or less) arbitrary functions to
>>>> this data? Approximately 8 parameters.
>>>>
>>>> The particular function I have in mind at the moment is a difference of
>>>> Gaussians. The Gaussians
>>>> most likely have the same location (in x) - but this is not guaranteed, and
>>>> I'd prefer
>>>> to use this as a sanity check rather than impose it as a constraint.
>>>>
>>>> Note that the context is a Java plugin - not a macro.
>>>>
>>>> If not in ImageJ, perhaps someone could point me at a Java package that
>>>> will
>>>> do this. I am far
>>>> from an expert in curve fitting, so please be gentle.
>>>>
>>>> If not, I can do it in R - but I prefer to do it "on the fly" while
>>>> displaying
>>>> the image, and the Overlay.
>>>>
>>>> --
>>>> Kenneth Sloan
>>>>
[hidden email]
>>>> Vision is the art of seeing what is invisible to others.
>>>>
>>>> --
>>>> ImageJ mailing list:
http://imagej.nih.gov/ij/list.html>>>>
>>>
>>> --
>>> ImageJ mailing list:
http://imagej.nih.gov/ij/list.html>>>
>>
>> --
>> ImageJ mailing list:
http://imagej.nih.gov/ij/list.html>>
>
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