[Insight-users] Question about levenberg-marguardt optimization for the normalized correlation metric

[Carolyn Johnston]

(Forwarded question from a colleague -- C)

When optimizing the mean square error metric with levenberg-marquart
approach, the second derivative matrix (Hessian matrix) of chisq metric
function can be approximated to the product of the first derivative of
chisq metric w.r.t. to parameters, after ignoring the second derivatives.
Is this approach still valid for normalized correlation metric? 

>From our derivation, the second derivative matrix of this metric is quite
different from the above approximation, i.e. the product of two first
derivatives. We looked through itk source codes and only see the first
derivative is calculated in the itkNormalizedCorrelationImageToImageMetric.txx file, but no second
derivative calculation is calculated. We didn't find itk source codes
that generate the Hessen matrix for levenberg-marquardt optimizer. Are
we missing something here?

Thanks, Zhaoqiang Bi


-- 
Dr. Carolyn Johnston
Sr. Research Engineer, Vexcel Corporation
1690 38th Street, Boulder, CO 80301
ph: 303-583-0273
fax: 303-583-0246
http://www.vexcel.com