A basic question about computing this derivative

[anja.ende]

Hello,

This is my first post and I must emphasise that I do not have a science/maths training background and this might be a very basic question. I apologise if it is too basic to belong here.

I have a function defined as follows:

E(I,J) = \int CC_{p}(I,J)dp

Just a little context, I am trying to do some image processing and E is some energy function (based on two images I and J) that needs to be maximised. CC is the cross correlation in an image neighbourhood p and the total energy is given by the summing up these local contributions.

Anyway, to maximise this function with respect to some variable 'v', I need to compute the derivative \frac{\partial E}{\partial v}

My question is can I use the fundamental theorem of calculus and say that

\frac{\partial E}{\partial v} = \frac{\partial CC_{p}}{\partial v}

I get a bit confused about this. I would really appreciate your help.

Thanks,
Anja

 

[phyzguy]

You can interchange the order of the integration and differentiation and write:
\frac{\partial E(I,J)}{\partial v} = \frac{\partial}{\partial v}\int CC_p(I,J) dp = \int \frac{\partial CC_p(I,J)}{\partial v} dp

But what you wrote is not correct. Does this help?

 

[anja.ende]

Yes, thank you!