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

Luis Ibanez luis.ibanez@kitware.com
Wed May 12 22:17:17 EDT 2004


This is a multi-part message in MIME format.
--------------050808030600010707060901
Content-Type: text/plain; charset=us-ascii; format=flowed
Content-Transfer-Encoding: 7bit




Hi Carolyn, Zhaoqiang,




The Levenberg-Marquardt optimization method does not requires
second derivatives. It only needs the Jacobian that relates
changes in the array of parameters to be optimized with respect
to the array of parameters that control the errors.


For example, if we have two sets of points and want to minimize
the sum of square distances between them by applying a rigid
transform to one of the sets, we will be able to relate the
variations in point positions to the variation of the rigid
transform parameters.  Such equation willl look like the one
in the attached image :  EquationJacobian.gif.


Where the left vector is "E" = the array of errors to be miniimized.
The matrix is the Jacobian = "J", and the array of transform paramters
is "D".  The equation in the image represents then:

                 E = J . D



Solving this problem using the Newton's method will do:

            D = ( J^T . J )^-1 . J^T . E

(that looks nicer in the attached image: EquationNewton.gif





Solving the same problem using a Gradient Descent algorithm
will use the equation:

             D = 1/lambda . J^T . E

(that looks nicer in the attached image: EquationStepest.gif





Finally, using the Levenberg-Marquardt algorithm one iteration
of the solution will compute:

             (J^T . J  + lambda . I ) . D = J^T . E

(that looks nicer in the attached image: EquationLevenbergMarquard.gif





As you can see, there is no need for second derivatives. The problem
is solved iteratively by using a linearized form of the non-linear
relationship between the parameters in D and the parameters in E.
Note that both D and E are actually differentials. That is, D is the
array of differentials from the transform parameters, while E is the
array of differentials from the errors.


As far as the software implementation goes, ITK is simply wrapping
the Levenberg-Marquardt algorithm from VXL/VNL, that in its turn
is calling the function lmderl_() from linpack.


-----



NormalizedCorrelation is not well suited to be used along with
the Levenberg-Marquardt method. In fact, no metric that returns
a single value is well suited for this optimizer.


That is, none of the Image metrics deriving from
SingleValueCostFunction:
http://www.itk.org/Insight/Doxygen/html/classitk_1_1SingleValuedCostFunction.html


You should use it only with metric deriving from
MultipleValueCostFunction:
http://www.itk.org/Insight/Doxygen/html/classitk_1_1MultipleValuedCostFunction.html



An intersting application of the Levenberg-Marquardt optimizer
can be found in the context of iterative closest point (ICP),
where the values to be minizimed are an array of distances.


You might want to look at the two ICP examples under:


      Insight/Examples/Registration/
                  IterativeClosestPoint1.cxx
                  IterativeClosestPoint2.cxx


Both of them use this optimizer.




     Regards,



       Luis



------------------------
Carolyn Johnston wrote:
> (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
> 
> 




--------------050808030600010707060901
Content-Type: image/gif;
 name="EquationJacobian.gif"
Content-Transfer-Encoding: base64
Content-Disposition: inline;
 filename="EquationJacobian.gif"
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--------------050808030600010707060901
Content-Type: image/gif;
 name="EquationDNewton.gif"
Content-Transfer-Encoding: base64
Content-Disposition: inline;
 filename="EquationDNewton.gif"
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--------------050808030600010707060901
Content-Type: image/gif;
 name="EquationStepest.gif"
Content-Transfer-Encoding: base64
Content-Disposition: inline;
 filename="EquationStepest.gif"
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--------------050808030600010707060901
Content-Type: image/gif;
 name="EquationLevenbergMarquard.gif"
Content-Transfer-Encoding: base64
Content-Disposition: inline;
 filename="EquationLevenbergMarquard.gif"
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--------------050808030600010707060901--





More information about the Insight-users mailing list