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computer-visioncalculus

why are we differentiating then integrating in active contour energy calculation

so I was reading on active contour and the equation doesn't really make much sense to me, I looked for other resources but none of the resources really explained this enter image description here

enter image description here

what does the integral of the derivative of a squared function mean?

Solution

  • The derivative is the change of the function so if we want a smooth function we would want small changes along the function meaning a small derivative. A derivative of zero is a constant function which is the most smooth function that we can get.

    We use the squared distance of the derivative (L2) and zero so we get the square.

    In order to get a smooth function along the curve we would like that the sum of the change along the curve will be small. The sum is the integral of the derivative along the curve.