[Insight-users] xxxxxSPAMxxxxx Cost Function Definition

[Iván Macía]

Hi Rocío,

MulipleValuedCostFunction is just a generic virtual base class for cost
functions whose value is not a single scalar but a vector (or something you
can put in the form of a vector). In fact it defines a return value that is
a variable size Array, the size is defined by the actual cost function
implemented (in the virtual GetNumberOfValues() ). I ignore which function
you mention (CumulativeGaussianCostFunction maybe) but that is just a
derived class.

Are you sure you need a MultipleValuedCostFunction? Is that a vector or
matrix formula? I guess it is.

In order to define your cost function you need to reimplement:

GetValue() return cost function value given parameters
GetNumberOfParameters() (3 in your case A, a and b)
GetNumberOfValues() (this is the size of the return array of computed
values)
GetDerivative() compute derivative given parameters. You may leave the
implementation empty if your optimizer does not use derivatives

Best regards

Iván


-----Mensaje original-----
De: insight-users-bounces at itk.org [mailto:insight-users-bounces at itk.org] En
nombre de RCL
Enviado el: jueves, 22 de julio de 2010 15:13
Para: insight-users at itk.org
Asunto: [Insight-users] xxxxxSPAMxxxxx Cost Function Definition


Hello,

I'm new using ITK and I'm trying to model the temporal intensity variations
in contrast enhanced MR images. The function of the model has been already
defined and I need to minimize a cost function to obtain the model
parameters that best fit my data. I want to use the
itk::LevenbergMarquardtOptimizer to minimize my cost function. I know that
the SetCostFunction requires a variable of the type of
MultipleValuedCostFunction, but from what I've read, these functions are
only a sum of Gaussians (please correct me if this is not the case). Is
there any way I can define a cost function with this form:

sin(pi/2 - atan(A/(2*a - 2*b)*(a*exp(-a*(t + 1/A/(a*exp(-a*t) -
b*exp(-b*t))*(I + A/(a - b)*(exp(-a*t) - exp(-b*t)))*(a - b))) - b*exp(-b*(t
+ 1/A/(a*exp(-a*t) - b*exp(-b*t))*(I + A/(a - b)*(exp(-a*t) - exp(-b*t)))*(a
- b)))) + A*(a*exp(-a*t) - b*exp(-b*t))/(2*a - 2*b)))*(I + (A*(1/exp(a*t) -
1/exp(b*t)))/(a - b))

in order to obtain the model parameters "A", "a" and "b" ? 

Thanks,

RCL
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