In my on-going research to reduce the filter artifacts noted in
http://bugzilla.gnome.org/show_bug.cgi?id=166130 , I found many references
to a promising improvement on the cubic convolution kernel approach I have
been using.

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As noted in the bug report using a convolution kernel entirely removes the
somewhat obvious staircasing produced by the current interpolation at the
expence of a slight softening of the image.
In all the research I have done I have come up constantly to references to
work done by R.G. Keys where he uses 6 point spline fitting instead of the
usual four, but despite extensive efforts I have not been able to find any
reference to the actual piecewise polynomials he derives.
Since the way this technique fits into the code is virtually identical to
the lanczos implementation a six-point approach would envolve exactly the
same calculation effort as lanczos and the larger window and the increased
order of convergence would almost certainly improve the quality and
precision of the filter.
It would seem reasonable to assume this would bring us close to a best of
both worlds situation, a clean interpolaton without the softening.
http://64.233.183.104/search?q=cache:pcUIULp7cboJ:ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19870013008_1987013008.pdf+fourth-order+convergence+catmull-rom&hl=en&ct=clnk&cd=3&client=opera
>>
Keysâ€™ cubic is a local, six-point inter-
polant whose interpolation function is again given by
piecewise cubic polynomials. However, in contrast to
PCC, there are no free parameters. The algorithm is
fourth order convergent (ref.
8) which is the highest
order which can be achieved with cubic polynomials;
>>
All references to Keys' work seem to lead to papers published by IEEE and
available on a per article subscription. I assume the charge for one or
two articles would be fairly nominal. Would this be a good use of some of
the gimp projects donations fund?
If the idea is acceptable I'll look into the details.
/gg.
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