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Re: Bicubic interpolation suddenly is no better than bilinear.

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Dangling Pointer schrieb:
> Still, something is wrong. Iterative BILINEAR rescaling is*supposed*
> to achieve comparable quality to SCALE_AREA_AVERAGING, and bicubic is

Most probably your claim is wrong, even with the best
rounding in the world. We have ideally:

    x1 + .... + x2n     x1 + x2        x2n-1 + x2n
    --------------- =   -------        -----------
          2^n              2                2
                                 ....
                          -------------------
                                   2

Now a rounding function r(x/n) can be viewed as
an nummerator correction c(x/n) function:

     r(x/n) = (x + c(x/n)) / n

For /2 the nummerator correction is either -1 or 0
when you round down. So there might be a maximal
correction of -1 * 2^(n-1) in the first iteration of
bilinear. Then -1 * 2 * 2^(n-2) in the next iteration,
and so on: Total maximal correction:

      -n*2^(n-1)

For /2^n the numeration correction is somewhere
between -2^n+1 and 0 when you round down. So maximal
correction is:

     -2^n+1

When is the iteration correction by 2^n bigger
than the area correction? Lets make a little table:

n	-n*2^(n-1)	-2^n+1	diff	2^n
1	-1	-1	0	2
2	-4	-3	1	4
3	-12	-7	5	8
4	-32	-15	17	16
5	-80	-31	49	32
6	-192	-63	129	64
7	-448	-127	321	128

So I guess for 4 iteration we could eventually
construct an example where the error would be
at least one color value step, since the
maximal numerator correction difference is
then greater than the denumerator 2^n.

Let's give it a try:

Iterative:
3 0 1 0 0 1 0 3
1 0 0 1
0 0
0

Area:
3 0 1 0 0 1 0 3
1

Yes we have found an example where iterative is
different from area by one color pixel value step.

Bye

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Thread

Bicubic interpolation suddenly is no better than bilinear. Dangling Pointer <dpointer2@gmail.com> - 2012-05-18 22:58 -0700
  Re: Bicubic interpolation suddenly is no better than bilinear. Roedy Green <see_website@mindprod.com.invalid> - 2012-05-18 23:12 -0700
    Re: Bicubic interpolation suddenly is no better than bilinear. Roedy Green <see_website@mindprod.com.invalid> - 2012-05-20 22:23 -0700
  Re: Bicubic interpolation suddenly is no better than bilinear. "John B. Matthews" <nospam@nospam.invalid> - 2012-05-19 07:26 -0400
    Re: Bicubic interpolation suddenly is no better than bilinear. Dangling Pointer <dpointer2@gmail.com> - 2012-05-19 08:07 -0700
      Re: Bicubic interpolation suddenly is no better than bilinear. Dangling Pointer <dpointer2@gmail.com> - 2012-05-19 09:13 -0700
        Re: Bicubic interpolation suddenly is no better than bilinear. Jan Burse <janburse@fastmail.fm> - 2012-05-19 20:48 +0200
        Re: Bicubic interpolation suddenly is no better than bilinear. "John B. Matthews" <nospam@nospam.invalid> - 2012-05-20 09:02 -0400
        Re: Bicubic interpolation suddenly is no better than bilinear. BGB <cr88192@hotmail.com> - 2012-05-20 11:59 -0500

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