[Insight-developers] Problems with affine MI registration

[Paul Hughett]

Lydia Ng has written:

> How many iterations are you running?

I increased the number of iterations from 300 to 30000 at each of three
learning rates; I still don't converge to the right answer but I am
beginning to suspect that at least part of the problem is a poorly
chosen test image.  The test image is taken directly from the repository
file

itkImageToImageAffineMutualInformationGradientDescentRegistrationTest.cxx

and consists of a gaussian centered in a 100 x 100 image.  I've
modified the program to dilate one axis by 1.414; the solution that
the program returns is a dilation of 0.898035 on one axis and 1.26751
on the other.  Notice that the ratio of these is almost exactly 1.41.
Now recall that mutual information is supposed to be insensitive to
intensity differences, as long as there is a systematic mapping of
intensities between the two images.  Now visualize the contours
generated by a gaussian function and observe that the effect of
isotropically enlarging the image is almost the same as shifting the
levels at which the contours are drawn.  That is, for a gaussian
image, MI cannot distinguish between an isotropic magnification and an
intensity mapping.  Hence--as far as MI can tell--my anisotropic
magnification is indistinguishable from a smaller anisotropic magnification,
a compensating isotropic magnification, and an intensity mapping.

I am going to modify my test program to read some real brain images--
probably midsagittal images already segmented into gray, white, CSF, 
and other--and see what kind of results I get on them.


Paul Hughett