Provided by: netpbm_11.08.02-1_amd64 
NAME
pamscale - scale a Netpbm image
SYNOPSIS
pamscale
[
scale_factor
|
{-xyfit | -xyfill | -xysize}
cols rows
|
-reduce reduction_factor
|
[-xsize=cols | -width=cols | -xscale=factor]
[-ysize=rows | -height=rows | -yscale=factor]
|
-pixels n
]
[
-nomix
|
-filter=functionName [-window=functionName]
]
[-linear]
[-reportonly]
[-verbose]
[pnmfile]
Minimum unique abbreviation of option is acceptable. You may use double 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(1).
pamscale scales a Netpbm image by a specified factor, or scales individually horizontally
and vertically by specified factors.
You can either enlarge (scale factor > 1) or reduce (scale factor < 1).
pamscale works on multi-image streams, scaling each one independently. But before Netpbm
10.49 (December 2009), it scales only the first image and ignores the rest of the stream.
The Scale Factors
The options -width, -height, -xsize, -ysize, -xscale, -yscale, -xyfit, -xyfill, -reduce,
and -pixels control the amount of scaling. For backward compatibility, there are also
-xysize and the scale_factor argument, but you shouldn't use those.
-width and -height specify the width and height in pixels you want the resulting image to
be. See below for rules when you specify one and not the other.
-xsize and -ysize are synonyms for -width and -height, respectively.
-xscale and -yscale tell the factor by which you want the width and height of the image to
change from source to result (e.g. -xscale 2 means you want to double the width; -xscale
.5 means you want to halve it). See below for rules when you specify one and not the
other.
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 equivalent to -xscale=scale_factor
-yscale=scale_factor.
Specifying the -reduce reduction_factor option is equivalent to specifying the
scale_factor parameter, where scale_factor is the reciprocal 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 smallest 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 output; 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.
-reportonly
The option -reportonly causes pamscale not to scale the image, but instead to report to
Standard Output what scaling the options and the input image dimensions indicate. For
example, if you specify
-xyfill 100 100 -reportonly
and the input image is 500 x 400, pamscale tells you that this means scaling by .25 to end
up with a 125 x 100 image.
You can use this information with other programs, such as pamscalefixed, that don't have
as rich facilities as pamscale for choosing scale factors.
The output is intended to be convenient for machine processing. In the example above, it
would be
500 400 0.250000 0.250000 125 100
The output is a single line of text per input image, with blank-separated tokens as
follows.
• input width in pixels, decimal unsigned integer
• input height in pixels, decimal unsigned integer
• horizontal scale factor, floating point decimal, unsigned
• vertical scale factor, floating point decimal, unsigned
• output width in pixels, decimal unsigned integer
• output height in pixels, decimal unsigned integer
-reportonly was new in Netpbm 10.86 (March 2019).
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 considering 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 sample
in a PAM is as if the pixel is opaque. So a pixel that is supposed 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
pixels, 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 meaningful 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 pamscale'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 combination 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, imagine 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 take a transparent sheet the size of the target image, marked with
a square grid of tiles the same size. Stretch or compress the source image to the size of
the sheet and lay the sheet over the source.
Each cell in the overlay 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 covers. 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 doubled 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 disappear 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, convert it to PPM, scale by .625, and convert back to GIF, you will probably 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 quantize
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, consider 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 pamenlarge 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 -filter 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 dimensional scaling --
scaling a single row of grayscale pixels horizontally. 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 officially 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 sampling is one from which you can
recover exactly the original continuous function. The Nyquist theorem says that as long
as your sample rate is at least twice the highest frequency in your original function, the
sampling is perfect. So we assume that the image is a sampling 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 multiply the Fourier
transform of the step function by a rectangle function.
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 function 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
something 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 components 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
manageable 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. Hanning, Hamming, and Kaiser are alternatives.
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 convolution 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 mixing method (but mixing brightness, not light intensity, so like
pamscale -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 and window functions
Here is a list of the function names you can specify for the -filter or -windowoption.
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. Note that some of these
make sense only as filter functions and some make sense only as window functions.
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 centered on the Y axis
with height 1 and base 1.
triangle
The graph of this is an isosceles triangle sitting on the X axis and centered on
the Y axis with height 1 and base 2.
quadratic
cubic
catrom
mitchell
gauss
sinc
bessel
hanning
hamming
blackman
kaiser
normal
hermite
lanczos
Not documented
Linear vs Gamma-adjusted
The pixel mixing scaling method described above involves intensities of pixels (more
precisely, it involves individual intensities of primary 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 proportional 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 by a factor of 10 the time
required to reduce an image. 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 intensity-
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 complaints. 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 linear variation with
pnmgamma, run pamscale on it and other transformations 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 acceptable results (in fact, sometimes identical
results) faster with pnmscalefixed, which uses fixed point arithmetic. pnmscalefixed may,
however, distort your image a little. See the pnmscalefixed user manual for a complete
discussion of the difference.
OPTIONS
In addition to the options common to all programs based on libnetpbm (most notably -quiet,
see
Common Options ⟨index.html#commonoptions⟩ ), pamscale recognizes the following command
line options:
-width
-height
-xsize
-ysize
-xscale
-yscale
-xyfit
-xyfill
-reduce
-pixels
-xysize
These options determine the horizontal and vertical scale factors.
See The Scale Factors ⟨#scalefactor⟩ .
-reportonly
This causes pamscale not to scale the image, but instead to
report to Standard Output what scaling the options and the input image
dimensions indicate.
See -reportonly ⟨#reportonly⟩ .
-nomix
This option selects discrete sampling ⟨#sampling⟩ as the
method of scaling ⟨#methods⟩ .
-filter=functionName
This option selects resampling ⟨#resampling⟩ as the
method of scaling ⟨#methods⟩ .
-window=functionName
This option selects a window function to modify the filter function
specified with -filter.
See Resampling ⟨#resampling⟩ .
-verbose
This option causes pamscale to issue messages to Standard Error about
the scaling.
SEE ALSO
pnmscalefixed(1), pamstretch(1), pamstretch-gen(1), pamditherbw(1), pbmreduce(1),
pbmpscale(1), pamenlarge(1), pnmsmooth(1), pamcut(1), pnmgamma(1), pnmscale(1), pnm(1),
pam(1)
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
arithmetic (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.
DOCUMENT SOURCE
This manual page was generated by the Netpbm tool 'makeman' from HTML source. The master
documentation is at
http://netpbm.sourceforge.net/doc/pamscale.html