CGAL users discussion list

[Andreas Fabri <>]

Hello,

What about discussing with your master's thesis supervisor.
That's what they are for.

andreas

On 02/05/2012 10:00, mq_wei wrote:
> ------------------------------------------------------------------------
> 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