Could someone point me in the direction of how to solve this?
I = [I1, . . . , In] is a 1D grayscale image and D = [D1, . . . , Dn] represents the second derivative of I. I am given the four pixel intensities I1, I2, In−1, In] and the second derivative values D3, . . . , Dn−2. How would I compute the rest of I’s intensities?
What I have tried so far: Each Ix intensity can be approximated via Taylor series: Ix = I(0) + x(dI(o)/dx) + (1/2)x^2(d^2I(x)/dx^2).
I am sure the trick is in using the sliding window algorithm for fitting a 2nd degree polynomial, and that a matrix is involved in solving. However, I am unsure how big the sliding window should be (3, 5 pixels?), etc.