Preston said:
: "Scanning at an increased sampling density may
not offer any more resolution in the image, but it certainly cannot make
it any less sharp or softer!" and, later, "But as you can see, from your
first quoted line above which you have conveniently retained throughout
this thread, your statement concerned high resolution scanning, not
resampling."
Obviously not!
If an image
is printed at a particular size from two otherwise similar files of
different resolutions, the image from the higher-res original will be
softer and appear less sharp.
That is complete rubbish - the higher resolution image will always,
unless you have had to degrade it in some way to meet the constraints of
your printer, be much sharper than the lower resolution image (assuming
that the image contains adequate fine detail with which to observe the
difference in the first place).
Where on earth did you ever get the idea that higher resolution meant
less sharp results?
Whether from scanning or resizing, the
higher-res image will be softer, will it not?
Definitely not. A higher resolution scan will contain finer detail and
sharper edges than a lower resolution scan, if the information is
present in the image in the first place. Even when it is not, it cannot
be less sharp than the lower resolution scan, only as sharp. A resized
image can never contain any more detail or sharper edges than it already
has. How much the resized image softens depends on the algorithm used.
For example, nearest neighbour interpolation will retain apparent edge
sharpness completely, whilst bicubic will soften it slightly and
bilinear more so. None of these algorithms will provide an image as
sharp as a higher resolution scan - again assuming that the image has
higher resolution content to bring out in the first place.
[See page 12 of the PDF at
http://www.ledet.com/margulis/PP7_Ch15_Resolution.pdf (or page 306 of
the book).]
Not the same thing at all. Both images have been resampled to exactly
the same resolution for presentation on the page. This is fairly
obvious if you zoom into the images in the pdf file you referenced -
although the upper image has been scanned at 3x the resolution it has
exactly the same pixel dimensions as the lower image.
What you are looking at here is 3rd (and higher, odd) harmonic
distortion caused by reproducing each sample as a square pixel on the
page. (Recall harmonic distortion in audio - well you get it in images
too!) Each sample, however, only represents the image at an infinitely
small point in space, called a delta function, which has a volume equal
to the average light incident on the CCD sensor centred at that point.
The sample, in reality does not exist anywhere else, however an array of
delta functions is not a particularly useful thing to look at - for one
thing they require an infinite video bandwidth to reproduce on your
monitor, and an infinite dpi printer to represent them. So each delta
function is represented instead by a pixel, which has a finite dimension
but is, in fact, a completely false representation. What should occur
between the samples depends on how the user chooses to reproduce the
delta function in pixel terms - how he *interpolates* between the
samples. Block pixels are simply a uniform square interpolation -
introducing every odd harmonic spatial frequency above what is possible
for the samples to contain, which is simply false information. However
they do make the image look artificially sharp. It is important to draw
a distinction right away between the use of the term interpolation here
and what is normally referred to by the same term in upscaling - this
is simply how each sample is represented by a pixel, in terms of it
size, shape and intensity profile, in the final image.
That conventional square uniform pixel reconstruction process is no more
valid than a linear interpolated pixel, where each pixel is represented
by an intensity at its centre prportional to the volume of the delta
function it represents and which linearly merges to reach the intensity
of the neighbouring pixels at their centres. In the simplest, bilinear,
case each pixel is effectively a square based pyramid (height
representing intensity), with the corners incident on the centre of the
neighbouring pixels. Although bilinear is the simplest version of this
and implements the linear merging only in the horizontal and vertical
axes, you can imagine octagonal interpolation where the intensity of
each pixel merges to the 8 nearest neighbours, or even circularly
symmetric interpolation. Clearly such interpolation schemes cannot be
linear, since the sum of the uniform samples must also be a uniform
illumination field but, nevertheless, such interpolation is possible.
Similarly there are higher order profile pixels which have intensities
which are polynomial curves, even pixels which extend their intensity
profile well beyond their nearest neighbours, although being constrained
to zero at them. Indeed, the ideal pixel reproduction, which introduces
no spatial harmonic distortion on the image at all, would have just such
a profile, extending to infinity in all directions.
What you are doing when you upscale an image using bilinear, bicubic or
any other interpolation method is *simulating* that pixel representation
by using higher resolution pixels to create the intermediate samples.
What you therefore perceive as a reduction in sharpness through bilinear
upscaling is merely the effect of a different pixel reproduction, not a
loss in sharpness over the original lower sampling density original.
The proof of this? Simply upscale using nearest neighbour
interpolation. That gives you a simulation of the square uniform pixel
reproduction using several new pixels to represent each old one but now,
of course, the effect of sharpness is retained.
In short, the effective sharpness of a scaled image is nothing to do
with the resolution, simply how each pixel is represented in the first
place. Quite different from increased scanning resolution, where
information conveying true image sharpness is pulled off of the original
medium, rather than synthetic odd harmonic distortions.
Mike was not referring to how the image was printed or reproduced in his
comments, merely what happened when an image was scanned - hence my
original question.
Nevertheless, since you clearly believe that higher resolution scans are
softer and thus, by default, that lower resolution scans are sharper,
can we expect to see your Minolta film scanner appearing on e-bay whilst
you "trade up" to a sharper 300, perhaps only 100ppi, piece of
antiquity? Why don't you just go the whole hog and flash a single
photodiode at your slides to get an ultrasharp 1x1 pixel rendition of
the entire image on each slide. the next step is just to remove the
sensor completely and type a random character into a file called
"image.raw" and observe the infinite sharpness of it all. ;-)
