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[mq_wei <>]

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Hello,

Hopefully some of you can help me out! I have to use the Full Multigrid Algorithm from chapter 20.6 in Numerical reciepts in c++.

For my master's thesis I have to reimplement a paper about gradient domain high dynamic range compression. In this paper the gradient field of a luminance image is manipulated by attenuating the magnitudes of large gradients. Then a low dynamic range image is obtained by solving a Poisson equation on the modified gradient field. The paper uses the Full Multigrid Algorithm from NR3 for this.

The Poisson equation:
V²I = div G
with
V = triangle upside down
I = image
G = gradient field

The Laplacian of the equation is approximated as follows:
V²I(x, y) = I(x + 1, y) + I(x - 1, y) + I(x, y + 1) + I(x, y - 1) - 4 * I(x, y)

The gradient is approximated using forward difference:
VH(x, y) = (H(x + 1, y) - H(x, y), H(x, y + 1) - H(x, y))

div G is approximated using backward difference:
div G = Gx(x, y) - Gx(x - 1, y) + Gy(x, y) - Gy(x, y - 1)

from the paper:
"the difference scheme yields a large system of linear equations - one for each pixel in the image, but the corresponding matrix has only five nonzero elements in each row, since each pixel is coupled only with its four neighbours."

Questions:

I have not the slightest idea how to put these equations into the input matrix for the mglin function Which format is necessary for the algorithm to perform correctly?

The comment in the code listing mglin.h says "On input u[0..n-1][0..n-1] contains the right-hand side p,..."

Is p = div G ?

What does the output look like? Does each row of u contains the new luminance value for the corresponding pixel?

Thanks in advance for any help you can give me.

The paper:
http://www.cs.huji.ac.il/%7Edanix/hdr/hdrc.pdf

 

Best regards,

Dong WEI