SYNOPSIS
pamscale
[
]
[
}
[pnmfile]


Minimum unique abbreviation of option is acceptable. You may use dou-
ble hyphens instead of single hyphen to denote options. You may use
white space in place of the equals sign to separate an option name
from its value.


DESCRIPTION
This program is part of Netpbm.

pamscale scales a Netpbm image by a specified factor, or scales indi-
vidually horizontally and vertically by specified factors.

You can either enlarge (scale factor > 1) or reduce (scale factor <
1).


The Scale Factors
When you specify an absolute size or scale factor for both dimensions,
pamscale scales each dimension independently without consideration of
the aspect ratio.

If you specify one dimension as a pixel size and don't specify the
other dimension, pamscale scales the unspecified dimension to preserve
the aspect ratio.

If you specify one dimension as a scale factor and don't specify the
other dimension, pamscale leaves the unspecified dimension unchanged
from the input.

If you specify the scale_factor parameter instead of dimension
options, that is the scale factor for both dimensions. It is equiva-
lent to -xscale=scale_factor -yscale=scale_factor.

Specifying the -reduce reduction_factor option is equivalent to speci-
fying the scale_factor parameter, where scale_factor is the recipro-
cal of reduction_factor.

-xyfit specifies a bounding box. pamscale scales the input image to
the largest size that fits within the box, while preserving its aspect
ratio. -xysize is a synonym for this. Before Netpbm 10.20 (January
2004), -xyfit did not exist, but -xysize did.

-xyfill is similar, but pamscale scales the input image to the small-
est size that completely fills the box, while preserving its aspect
ratio. This option has existed since Netpbm 10.20 (January 2004).

-pixels specifies a maximum total number of output pixels. pamscale
scales the image down to that number of pixels. If the input image is
already no more than that many pixels, pamscale just copies it as out-
put; pamscale does not scale up with -pixels.

If you enlarge by a factor of 3 or more, you should probably add a
pnmsmooth step; otherwise, you can see the original pixels in the
resulting image.



Usage Notes
A useful application of pamscale is to blur an image. Scale it down
(without -nomix) to discard some information, then scale it back up
using pamstretch.

Or scale it back up with pamscale and create a 'pixelized' image,
which is sort of a computer-age version of blurring.



Transparency
pamscale understands transparency and properly mixes pixels consider-
ing the pixels' transparency.

Proper mixing does not mean just mixing the transparency value and the
color component values separately. In a PAM image, a pixel which is
not opaque represents a color that contains light of the foreground
color indicated explicitly in the PAM and light of a background color
to be named later. But the numerical scale of a color component sam-
ple in a PAM is as if the pixel is opaque. So a pixel that is sup-
posed to contain half-strength red light for the foreground plus some
light from the background has a red color sample that says full red
and a transparency sample that says 50% opaque. In order to mix pix-
els, you have to first convert the color sample values to numbers that
represent amount of light directly (i.e. multiply by the opaqueness)
and after mixing, convert back (divide by the opaqueness).


Input And Output Image Types
pamscale produces output of the same type (and tuple type if the type
is PAM) as the input, except if the input is PBM. In that case, the
output is PGM with maxval 255. The purpose of this is to allow mean-
ingful pixel mixing. Note that there is no equivalent exception when
the input is PAM. If the PAM input tuple type is BLACKANDWHITE, the
PAM output tuple type is also BLACKANDWHITE, and you get no meaningful
pixel mixing.

If you want PBM output with PBM input, use pamditherbw to convert pam-
scale's output to PBM. Also consider pbmreduce.

pamscale's function is essentially undefined for PAM input images that
are not of tuple type RGB, GRAYSCALE, BLACKANDWHITE, or the _ALPHA
variations of those. (By standard Netpbm backward compatibility, this
includes PBM, PGM, and PPM images).

You might think it would have an obvious effect on other tuple types,
but remember that the aforementioned tuple types have gamma-adjusted
sample values, and pamscale uses that fact in its calculations. And
it treats a transparency plane different from any other plane.

pamscale does not simply reject unrecognized tuple types because
there's a possibility that just by coincidence you can get useful
function out of it with some other tuple type and the right combina-
tion of options (consider -linear in particular).



Methods Of Scaling
There are numerous ways to scale an image. pamscale implements a
bunch of them; you select among them with invocation options.

Pixel Mixing

Pamscale's default method is pixel mixing. To understand this, imag-
ine the source image as composed of square tiles. Each tile is a
pixel and has uniform color. The tiles are all the same size. Now
lay over that a transparent sheet of the same size, marked off in a
square grid. Each cell in the grid stands for a pixel of the target
image. For example, if you are scaling a 100x200 image up by 1.5, the
source image is 100 x 200 tiles, and the transparent sheet is marked
off in 150 x 300 cells.

Each cell covers parts of multiple tiles. To make the target image,
just color in each cell with the color which is the average of the
colors the cell covers -- weighted by the amount of that color it cov-
ers. A cell in our example might cover 4/9 of a blue tile, 2/9 of a
red tile, 2/9 of a green tile, and 1/9 of a white tile. So the target
pixel would be somewhat unsaturated blue.

When you are scaling up or down by an integer, the results are simple.
When scaling up, pixels get duplicated. When scaling down, pixels get
thrown away. In either case, the colors in the target image are a
subset of those in the source image.

When the scale factor is weirder than that, the target image can have
colors that didn't exist in the original. For example, a red pixel
next to a white pixel in the source might become a red pixel, a pink
pixel, and a white pixel in the target.

This method tends to replicate what the human eye does as it moves
closer to or further away from an image. It also tends to replicate
what the human eye sees, when far enough away to make the pixelization
disappear, if an image is not made of pixels and simply stretches or
shrinks.

Discrete Sampling

Discrete sampling is basically the same thing as pixel mixing except
that, in the model described above, instead of averaging the colors of
the tiles the cell covers, you pick the one color that covers the most
area.

The result you see is that when you enlarge an image, pixels get
duplicated and when you reduce an image, some pixels get discarded.

The advantage of this is that you end up with an image made from the
same color palette as the original. Sometimes that's important.

The disadvantage is that it distorts the picture. If you scale up by
1.5 horizontally, for example, the even numbered input pixels are dou-
bled in the output and the odd numbered ones are copied singly. If
you have a bunch of one pixel wide lines in the source, you may find
that some of them stretch to 2 pixels, others remain 1 pixel when you
enlarge. When you reduce, you may find that some of the lines disap-
pear completely.

You select discrete sampling with pamscale's -nomix option.

Actually, -nomix doesn't do exactly what I described above. It does
the scaling in two passes - first horizontal, then vertical. This can
produce slightly different results.

There is one common case in which one often finds it burdensome to
have pamscale make up colors that weren't there originally: Where one
is working with an image format such as GIF that has a limited number
of possible colors per image. If you take a GIF with 256 colors, con-
vert it to PPM, scale by .625, and convert back to GIF, you will prob-
ably find that the reduced image has way more than 256 colors, and
therefore cannot be converted to GIF. One way to solve this problem
is to do the reduction with discrete sampling instead of pixel mixing.
Probably a better way is to do the pixel mixing, but then color quan-
tize the result with pnmquant before converting to GIF.

When the scale factor is an integer (which means you're scaling up),
discrete sampling and pixel mixing are identical -- output pixels are
always just N copies of the input pixels. In this case, though, con-
sider using pamstretch instead of pamscale to get the added pixels
interpolated instead of just copied and thereby get a smoother
enlargement.

pamscale's discrete sampling is faster than pixel mixing, but pamen-
large is faster still. pamenlarge works only on integer enlargements.

discrete sampling (-nomix) was new in Netpbm 9.24 (January 2002).


Resampling

Resampling assumes that the source image is a discrete sampling of
some original continuous image. That is, it assumes there is some
non-pixelized original image and each pixel of the source image is
simply the color of that image at a particular point. Those points,
naturally, are the intersections of a square grid.

The idea of resampling is just to compute that original image, then
sample it at a different frequency (a grid of a different scale).

The problem, of course, is that sampling necessarily throws away the
information you need to rebuild the original image. So we have to
make a bunch of assumptions about the makeup of the original image.

You tell pamscale to use the resampling method by specifying the -fil-
ter option. The value of this option is the name of a function, from
the set listed below.

To explain resampling, we are going to talk about a simple one dimen-
sional scaling -- scaling a single row of grayscale pixels horizon-
tally. If you can understand that, you can easily understand how to
do a whole image: Scale each of the rows of the image, then scale each
of the resulting columns. And scale each of the color component
planes separately.

As a first step in resampling, pamscale converts the source image,
which is a set of discrete pixel values, into a continuous step
function. A step function is a function whose graph is a staircase-y
thing.

Now, we convolve the step function with a proper scaling of the filter
function that you identified with -filter. If you don't know what the
mathematical concept of convolution (convolving) is, you are offi-
cially lost. You cannot understand this explanation. The result of
this convolution is the imaginary original continuous image we've been
talking about.

Finally, we make target pixels by picking values from that function.

To understand what is going on, we use Fourier analysis:

The idea is that the only difference between our step function and the
original continuous function (remember that we constructed the step
function from the source image, which is itself a sampling of the
original continuous function) is that the step function has a bunch of
high frequency Fourier components added. If we could chop out all the
higher frequency components of the step function, and know that
they're all higher than any frequency in the original function, we'd
have the original function back.

The resampling method assumes that the original function was sampled
at a high enough frequency to form a perfect sampling. A perfect sam-
pling is one from which you can recover exactly the original continu-
ous function. The Nyquist theorem says that as long as your sample
rate is at least twice the highest frequency in your original func-
tion, the sampling is perfect. So we assume that the image is a sam-
pling of something whose highest frequency is half the sample rate
(pixel resolution) or less. Given that, our filtering does in fact
recover the original continuous image from the samples (pixels).

To chop out all the components above a certain frequency, we just mul-
tiply the Fourier transform of the step function by a rectangle func-
tion.

We could find the Fourier transform of the step function, multiply it
by a rectangle function, and then Fourier transform the result back,
but there's an easier way. Mathematicians tell us that multiplying in
the frequency domain is equivalent to convolving in the time domain.
That means multiplying the Fourier transform of F by a rectangle func-
tion R is the same as convolving F with the Fourier transform of R.
It's a lot better to take the Fourier transform of R, and build it
into pamscale than to have pamscale take the Fourier transform of the
input image dynamically.

That leaves only one question: What is the Fourier transform of a
rectangle function? Answer: sinc. Recall from math that sinc is
defined as sinc(x) = sin(PI*x)/PI*x.

Hence, when you specify -filter=sinc, you are effectively passing the
step function of the source image through a low pass frequency filter
and recovering a good approximation of the original continuous image.

Refiltering

There's another twist: If you simply sample the reconstructed original
continuous image at the new sample rate, and that new sample rate
isn't at least twice the highest frequency in the original continuous
image, you won't get a perfect sampling. In fact, you'll get some-
thing with ugly aliasing in it. Note that this can't be a problem
when you're scaling up (increasing the sample rate), because the fact
that the old sample rate was above the Nyquist level means so is the
new one. But when scaling down, it's a problem. Obviously, you have
to give up image quality when scaling down, but aliasing is not the
best way to do it. It's better just to remove high frequency compo-
nents from the original continuous image before sampling, and then get
a perfect sampling of that.

Therefore, pamscale filters out frequencies above half the new sample
rate before picking the new samples.

Approximations

Unfortunately, pamscale doesn't do the convolution precisely. Instead
of evaluating the filter function at every point, it samples it --
assumes that it doesn't change any more often than the step function
does. pamscale could actually do the true integration fairly easily.
Since the filter functions are built into the program, the integrals
of them could be too. Maybe someday it will.

There is one more complication with the Fourier analysis. sinc has
nonzero values on out to infinity and minus infinity. That makes it
hard to compute a convolution with it. So instead, there are filter
functions that approximate sinc but are nonzero only within a manage-
able range. To get those, you multiply the sinc function by a window
function, which you select with the -window option. The same holds
for other filter functions that go on forever like sinc. By default,
for a filter that needs a window function, the window function is the
Blackman function.

Filter Functions Besides Sinc

The math described above works only with sinc as the filter function.
pamscale offers many other filter functions, though. Some of these
approximate sinc and are faster to compute. For most of them, I have
no idea of the mathematical explanation for them, but people do find
they give pleasing results. They may not be based on resampling at
all, but just exploit the convolution that is coincidentally part of a
resampling calculation.

For some filter functions, you can tell just by looking at the convo-
lution how they vary the resampling process from the perfect one based
on sinc:

The impulse filter assumes that the original continuous image is in
fact a step function -- the very one we computed as the first step in
the resampling. This is mathematically equivalent to the discrete
sampling method.

The box (rectangle) filter assumes the original image is a piecewise
linear function. Its graph just looks like straight lines connecting
the pixel values. This is mathematically equivalent to the pixel mix-
ing method (but mixing brightness, not light intensity, so like pam-
scale -linear) when scaling down, and interpolation (ala pamstretch)
when scaling up.

Gamma

pamscale assumes the underlying continuous function is a function of
brightness (as opposed to light intensity), and therefore does all
this math using the gamma-adjusted numbers found in a PNM or PAM
image. The -linear option is not available with resampling (it causes
pamscale to fail), because it wouldn't be useful enough to justify the
implementation effort.

Resampling (-filter) was new in Netpbm 10.20 (January 2004).

The filter functions

Here is a list of the function names you can specify for the -filter
option. For most of them, you're on your own to figure out just what
the function is and what kind of scaling it does. These are common
functions from mathematics.



point The graph of this is a single point at X=0, Y=1.


box The graph of this is a rectangle sitting on the X axis and cen-


triangle


quadratic

cubic

catrom

mitchell

gauss

sinc

bessel

hanning

hamming

blackman

kaiser

normal

hermite

lanczos




Linear vs Gamma-adjusted
The pixel mixing scaling method described above involves intensities
of pixels (more precisely, it involves individual intensities of pri-
mary color components of pixels). But the PNM and PNM-equivalent PAM
image formats represent intensities with gamma-adjusted numbers that
are not linearly proportional to intensity. So pamscale, by default,
performs a calculation on each sample read from its input and each
sample written to its output to convert between these gamma-adjusted
numbers and internal intensity-proportional numbers.

Sometimes you are not working with true PNM or PAM images, but rather
a variation in which the sample values are in fact directly propor-
tional to intensity. If so, use the -linear option to tell pamscale
this. pamscale then will skip the conversions.

The conversion takes time. In one experiment, it increased the time
required to reduce an image by a factor of 10. And the difference
between intensity-proportional values and gamma-adjusted values may be
small enough that you would barely see a difference in the result if
you just pretended that the gamma-adjusted values were in fact inten-
sity-proportional. So just to save time, at the expense of some image
quality, you can specify -linear even when you have true PPM input and
expect true PPM output.

For the first 13 years of Netpbm's life, until Netpbm 10.20 (January
2004), pamscale's predecessor pnmscale always treated the PPM samples
as intensity-proportional even though they were not, and drew few com-
plaints. So using -linear as a lie is a reasonable thing to do if
speed is important to you. But if speed is important, you also should
consider the -nomix option and pnmscalefixed.

Another technique to consider is to convert your PNM image to the lin-
ear variation with pnmgamma, run pamscale on it and other transforma-
tions that like linear PNM, and then convert it back to true PNM with
pnmgamma -ungamma. pnmgamma is often faster than pamscale in doing
the conversion.

With -nomix, -linear has no effect. That's because pamscale does not
concern itself with the meaning of the sample values in this method;
pamscale just copies numbers from its input to its output.



Precision
pamscale uses floating point arithmetic internally. There is a speed
cost associated with this. For some images, you can get the accept-
able results (in fact, sometimes identical results) faster with pnm-
scalefixed, which uses fixed point arithmetic. pnmscalefixed may,
however, distort your image a little. See the pnmscalefixed user man-
ual for a complete discussion of the difference.


SEE ALSO
pnmscalefixed, pamstretch, pamditherbw, pbmreduce, pbmp-
scale, pamenlarge, pnmsmooth, pamcut, pnmgamma, pnm-
scale, pnm, pam


HISTORY
pamscale was new in Netpbm 10.20 (January 2004). It was adapted from,
and obsoleted, pnmscale. pamscale's primary difference from pnmscale
is that it handles the PAM format and uses the "pam" facilities of the
Netpbm programming library. But it also added the resampling class of
scaling method. Furthermore, it properly does its pixel mixing arith-
metic (by default) using intensity-proportional values instead of the
gamma-adjusted values the pnmscale uses. To get the old pnmscale
arithmetic, you can specify the -linear option.

The intensity proportional stuff came out of suggestions by Adam M
Costello in January 2004.

The resampling algorithms are mostly taken from code contributed by
Michael Reinelt in December 2003.

The version of pnmscale from which pamscale was derived, itself
evolved out of the original Pbmplus version of pnmscale by Jef
Poskanzer (1989, 1991). But none of that original code remains.



netpbm documentation 18 February 2005 Pamscale User Manual(0)