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Pseudocode for ANTs/itkV4 Registration
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Definitions
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f
  fixed image

m 
  moving image 

M 
  similarity metric 

A 
  Affine transform --- set to identity, pulls moving to fixed by m(A(x)) 

D 
  Demons deformation field transform --- set to identity, pulls m to fixed by m(D(A(x))).

x
  physical position in domain


Metric Derivative Computation
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The partial derivative with respect to metric, in general: 

.. math::

  \frac{ \partial M( f(x),m(t(x)))}{\partial x}=\frac{\partial M}{\partial m}\frac{\partial m}{ \partial t}\frac{  \partial t }{ \partial x}

The following portion is metric independent:

.. math::

  \frac{\partial m}{ \partial t}\frac{  \partial t }{ \partial x}

It may be implemented in either the metric base class or in each
transformation class. 

Demons Registration Pseudocode
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for all resolutions ; do
  smooth f, m by sigma related to resolution

  pass smoothed images to metrics

  resample deformation to current resolution

  for N iterations or until convergence

     1.  call M (e.g. MeanSquaresImageToImageMetric) with f, m, (D compose A ) as input
     2.  smooth gradient from 1. ( e.g. through a call to a RegularizationMetric or Regularization Filter ? )
     3.  update (A+D) ( through call to the transformation classes? ) 
     4.  smooth output of 3 as in step 2.
     
  done
  
done

Does the DemonsTransformation class take care of resampling the images
properly for the metric and algorithm?   SyN would do something
different .... metric would not know about how this is done.