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A basic question about computing this derivative

  1. Aug 8, 2013 #1

    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) = [itex]\int CC_{p}(I,J)dp[/itex]

    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 [itex]\frac{\partial E}{\partial v}[/itex]

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

    [itex]\frac{\partial E}{\partial v} = \frac{\partial CC_{p}}{\partial v}[/itex]

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

  2. jcsd
  3. Aug 8, 2013 #2


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    Science Advisor

    You can interchange the order of the integration and differentiation and write:
    [tex]\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[/tex]

    But what you wrote is not correct. Does this help?
  4. Aug 8, 2013 #3
    Yes, thank you!
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