Re: Lanczos interpolation

[EMAIL PROTECTED] wrote:
> 
> "Turkowski [16] used windowed sinc functions for image resampling. He
> found the Lanczos window superior in terms of reduction of aliasing,
> sharpness, and minimal ringing as conclusion of an empirical
> experiment.
> 
> "[16] Turkowski. Filters for common resampling tasks. In Andrew
> S. Glassner, editor, Graphics Gems I, pages 147{165. Academic Press,
> 1990."
> 
> So, I guess that's the answer.

Yes, that's the answer I also found when asking me the question.
However, I assume that the Hann, Hamming, or Blackman windows
(based on cosine terms) would deliver similar results.

If you have JPEG (DCT) data, you can directly use the IDCT for
efficient interpolation:

  The inverse discrete cosine transform IDCT, which is of course
  exact, is

    f = 1/2 C SUM( F cos((2v + 1)*u*pi)/(2N)) ); v=0,1,...,(N-1). (2)

  Observe that we can use the formula 2 to define an interpolated
  signal for all time in the interval 0 < t < 1 by setting t =
  ((2v + 1)/(2N)). We adopt the notation f(t) for the result, to
  emphasize that f(t) is a continuous function of time:

    f(t) = 1/2 C SUM( F cos(t*u*pi) ); 0 < t < 1

  Clearly f(t) = f at the sampling points t = ((2v + 1)/(2N)), so
  that f(t) is an exact interpolation formula.  Note that the first
  sampling point occurs at t = 1/(2N) but neighbouring sampling
  points are separated by an interval of 1/N.  This is the Shannon
  sampling theorem for discrete cosine transforms.  In essence it
  says that we can recreate the complete function f(t) over the
  whole interval (0,1) by specifying the values at the N time
  points t = ((2v + 1)/(2N)), for v = 0,...,(N-1).  The particular
  feature of interest here is the explicit procedure for obtaining
  the sampling points that enable us to reconstruct the given
  function exactly knowing only the values of the function at the
  sampled points.  Such properties are also held by wavelet
  approximations (Daubechies 1992) who notes the connection
  between Shannon's sampling theorem and Reproducing Kernel
  Hilbert Spaces.  However, wavelet approximations do not
  generally allow of a simple representation in terms of
  a set of uniformly sampled data points.

This is a quote from paragraph 2.1 "Inverse DCT as interpolation
formula" from Bob Henery "Overlapping DCT for image compression":

  http://jpegclub.org/stuff/

My new Direct DCT scaling developments can be interpreted in
this context:

  http://jpegclub.org/djpeg/

I have found that only windowed sinc interpolation (e.g. Lanczos)
comes close to the quality of results of this method, but at
considerably higher computation cost.

Regards
Guido