[Insight-users] Parzen windows vs. basis functions in alignment by max. of mutual info

[Luis Ibanez]

Hi Issac,

Approximating the images with continuous functions will not
change the discrete nature of the histograms, and will not
remove the need for Parzen windowing.

Parzen windowing (or any other histogram smoothing method) is
not needed because of the discrete nature of the image but
because of the limited number of samples that are taken for
estimating the joint histogram.

For example, in a typical Viola-Wells Mutual Information you
use from 50 to 500 samples. This samples can equally well be
taken from a continuous image and that will not change the
fact that you will only get scattered values in your joint
histogram.

That being said, it is also clear that smoothing the images,
will make the histograms more stable, and probably result in
smoother metric evaluations over the parametric space.

---

You may want to use the Mattes et al. implementation of
Mutual Information:

http://www.itk.org/Insight/Doxygen/html/classitk_1_1MattesMutualInformationImageToImageMetric.html

This implementation uses BSplines as weight functions when
performing Parzen windowing on the joint histogram. This
results in smoother estimation of the joint probability
and facilitates the computatinon of Metric derivatives.


References,
from the Doxygen link above:

[1] "Nonrigid multimodality image registration"
     D. Mattes, D. R. Haynor, H. Vesselle, T. Lewellen and W. Eubank
     Medical Imaging 2001: Image Processing, 2001,  pp. 1609-1620.

[2] "PET-CT Image Registration in the Chest Using Free-form
      Deformations"
      D. Mattes, D. R. Haynor, H. Vesselle, T. Lewellen and W. Eubank
      IEEE Transactions in Medical Imaging.
      Vol.22, No.1, January 2003. pp.120-128.

[3] "Optimization of Mutual Information for MultiResolution
      Image Registration"
      P. Thevenaz and M. Unser
      IEEE Transactions in Image Processing,
      9(12) December 2000.



   Regards,


     Luis




---------------------
Issac Trotts wrote:
> In the papers I've seen about alignment by maximization of mutual info,
> Parzen windows are used to get smooth, continuous histograms from
> discrete histograms.  I wonder if it be more accurate to first
> approximate the given images with linear combinations of smooth basis
> functions and then obtain smooth, continuous histograms by spatial
> integration.  I'd be interested to know if anyone on this has tried this
> or can tell me why Parzen windows are a better choice.  
> 
> Thanks,
> Issac Trotts
> 
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