Digital BW, The Print

John Moody wrote:


> We sound like a broken record here but...  Qimage..excellent.  CS2 is pretty
> good as well assuming you are not trying to scale too excessively.

Since I have a few minutes free, John's comment seems like a good 
opportunity to talk a little more about splines....

What spline(s) does Qimage implement? According to the website, they 
support "Lanczos, Vector, and Pyramid" interpolation. Are these the only 
three? I understand 'vector' and 'pyramid' to be spline classes, which 
makes it hard to understand exactly what Qimage is claiming. There are 
good and bad pyramid splines (when it comes to applying them to images, 
at least), and I expect the same is true of vector splines. Lanczos, 
however, is a specific way to compute the spline, and it is quite good 
with a typical photographic image and doesn't do at all poorly on 
graphics designs with lots of smooth lines, either. I'm also a little 
unclear on whether Qimage will allow you to open a TIFF, compute its 
spline, and save it back as a TIFF for more work in Photoshop, or 
whether it is a print output tool only.

Photoshop is strictly 18th and 19th century in terms of its spline 
support. And I mean that quite literally - the math behind all three of 
their methods is at minimum well over a century out of date. The three 
methods are bicubic, bilinear, and nearest neighbor. Bicubic is an 
excellent way to undersample, but is a rather problematical algorithm 
for oversampling - more on this in a moment. Bilinear is something of a 
special-case spline, not usually appropriate for upsampling photographs. 
And nearest neighbor is a blunt instrument that I think I independently 
invented when I was 16 for interpolating values from Cepheid light 
curves on an Atari 400 in CPM/BASIC. It is possible this spline was 
invented prior to the year 1500. You don't want to go there. Photoshop 
is in pretty serious need of spline improvement.

I think it is still true that Genuine Fractals is proprietary (hence my 
previous reference to "mystery math"). If so, nobody really knows what 
it does. I do agree with another poster that GF is almost always better 
than bicubic for oversampling, especially at certain ratios where 
bicubic tends to resonate.

Photozoom Pro supports the S-spline, Lanczos, Hermite, Bell, Mitchell, 
Catmull-Rom, B, Nearest-Neighbor, Bicubic, and Bilinear splines. I can't 
say my experience is extensive with most of these.

Part of the "problem" with some splines is that they are either patented 
(for example, S and B) and rarely or never licensed, or they are trade 
secrets (for example, Genuine Fractals). Also, spline computation is a 
very fast-moving area of math these days. All this accounts for the 
fragmentation of the spline market and the reason there are a dozen 
tools out there. However, the patents also mean you can go read all 
about the method, sometimes including the math.

S spline is particularly interesting in this respect. It avoids aliasing 
entirely, as far as I can tell (actually, I think it would alias at 
ridiculously high frequency proportions, well beyond what would ever be 
encountered in real life). The technique does not make any changes to 
the proportional tonality of the image (some other interpolations, but 
by no means all, do). It almost fully preserves, but does not enhance, 
acutance (this avoids the excessive shadowing along tonal boundaries, 
similar to overusing USM, that some splines introduce). Mathematically, 
the image coming out of s spline has bulk properties (acutance, edge 
sharpness, histogram) nearly identical to the original.

 From my experience with it, I think the S spline is currently the gold 
standard against which all other methods of computing a spline should be 
compared. It can be used pretty effectively at any point in the 
workflow, including (I believe, somewhat heretically) being applied 
after sharpening if you are using something other than USM. In the 
spirit of making a meaningful comparison to S, I'll say:

Lanczos: comes fairly close to S, tending to introduce certain artifacts 
on medium-contrast boundaries but doing very well with sharp graphic 
design edges and not bad at all on most photographs. Does not preserve 
image acutance as well as S, but it is a small difference. If you have a 
tool that does Lanczos, you probably don't need to move to a tool that 
has S.

Genuine Fractals: notably inferior to S based on my experiences a few 
years back. It fails to preserve acutance as well as S or Lanczos, and 
bulk tonality changes can result in images with multiple high contrast 
boundaries. However, it is far better than Bicubic.

Bicubic: really, really stinks compared to S, Lanczos, and GF. It 
aliases, resonates, and introduces several different kinds of artifacts 
including one which appears similar to noise, and another which is 
similar to a ghost image of brightly toned image elements. It also fails 
to preserve image acutance, doing far worse than GF in this respect.

I'd be curious to hear what people have thought about Lanczos or GF in 
comparison to algorithms such as Qimage's Pyramid and Vector, and the 
T-spline (if anyone is using it). Also, I'm perfectly open to being told 
my impressions of the four splines above are wrong - there are some 
unavoidable mathematical *facts* about all of them, and I really like 
dealing in facts; but their application is aesthetic in this context, 
and that makes all the difference. I'm not married to my spline by any 
means.

-- 
Jeff Medkeff
Eagle River, Alaska