[Insight-users] Are these metrics based on "correlation ratio"?

[Luis Ibanez]

Hi Pinpress,

One of  the many pleasures of using Open Source software
is that you can see what the software does, just by reading
the source code.


If you open in an editor the file:


Insight/Code/Algorithms/
  itkCorrelationCoefficientHistogramImageToImageMetric.txx


and looks at lines 28-34


::EvaluateMeasure(HistogramType& histogram) const
{
  const MeasureType varianceX  = this->VarianceX(  histogram );
  const MeasureType varianceY  = this->VarianceY(  histogram );
  const MeasureType covariance = this->Covariance( histogram );
  return vcl_fabs(covariance /( vcl_sqrt(varianceX )* vcl_sqrt(varianceY
)));
}


Which is equivalent to the "correlation coefficient"  p(x,y) as defined
in page 5 of the article that you kindly sent, but it is not equivalent
to the "correlation ratio" as defined in equation (3) in page 4.


In order to make them equivalent you need to compute

                                         E(Y/X)

for every value of X.

You can get this from the Joint histogram of Y and X values
by computing the average of Y values for a given value of X.

once you have those values stored in an Array, you can
easily compute

                        Var(  Y - E(Y/X) )  /  Var( Y )

You could do this by modifying the code of the existing

itkCorrelationCoefficientHistogramImageToImageMetric.txx


and of course, we strongly encourage you to contribute that
new class to the Insight Journal

            http://www.insight-journal.org


---

The class itkCorrelationCoefficientHistogramImageToImageMetric.
was added to ITK on August  2003:

http://public.kitware.com/cgi-bin/viewcvs.cgi/Code/Algorithms/itkCorrelationCoefficientHistogramImageToImageMetric.txx?root=Insight&view=log


Therefore,
it has been in ITK even before the ITK 2.2 release:

http://www.itk.org/Wiki/ITK_Previous_Releases

---

Note that the class

itkNormalizedCorrelationImageToImageMetric

is described in the ITK Software Guide

    http://www.itk.org/ItkSoftwareGuide.pdf


and you can see its computation in the file:

Insight/Code/Algorithms/
  itkNormalizedCorrelationImageToImageMetric.txx

in lines 94 -128

which are equivalent to

              Var(  X * Y ) / Var( X ) * Var( Y )

and therefore, not really the "correlation ratio" that
is defined in the paper.


     Regards,


            Luis


-----------------------------------------------------------------------------------------
On Tue, Apr 20, 2010 at 2:07 PM, pinpress <sb_ji at yahoo.com> wrote:

>
> Hi,
>
> I am in need to perform registration in ITK using correlation ratio as
> image
> similarity measure (Its reference can be found here:
>
> http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.20.1164&rep=rep1&type=pdf
> ). I found from ITK classes the following two:
>
> CorrelationCoefficientHistogramImageToImageMetric
>
> NormalizedCorrelationImageToImageMetric
>
> My question is, do they implement the "correlation ratio" as similarity
> measure? What are their differences? Thanks very much.
> --
> View this message in context:
> http://old.nabble.com/Are-these-metrics-based-on-%22correlation-ratio%22--tp28287905p28287905.html
> Sent from the ITK - Users mailing list archive at Nabble.com.
>
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