Pamscale User Manual(0) Pamscale User Manual(0)
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
]
[
[-verbose]
[
-nomix
|
-filter=functionName [-window=functionName]
]
[-linear]
}
[pnmfile]
OPTION USAGE
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(1).
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 equivalent 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 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 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 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 trans-
parency 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 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 func-
tion 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 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 col-
ors 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 sub-
set 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 dupli-
cated 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, 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, con-
sider using pamstretch instead of pamscale to get the added pixels
interpolated instead of just copied and thereby get a smoother enlarge-
ment.
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-pix-
elized 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 officially
lost. You cannot understand this explanation. The result of this con-
volution 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 orig-
inal 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 func-
tion. The Nyquist theorem says that as long as your sample rate is at
least twice the highest frequency in your original function, the sam-
pling is perfect. So we assume that the image is a sampling of some-
thing whose highest frequency is half the sample rate (pixel resolu-
tion) 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.
<h5>Refiltering</h5>
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 sam-
pling of that.
Therefore, pamscale filters out frequencies above half the new sample
rate before picking the new samples.
<h5>Approximations</h5>
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 Black-
man function.
<h5>Filter Functions Besides Sinc</h5>
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 fact the convolution that is coincidentally
part of a resampling calculation.
For some filter functions, you can tell just by looking at the convolu-
tion 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 sam-
pling 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 when scaling down, and interpolation (ala pamstretch) when
scaling up.
<h5>Gamma</h5>
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 implementa-
tion effort.
Resampling (-filter) was new in Netpbm 10.20 (January 2004).
<h5>The filter functions</h5>
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-
tered 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
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 writ-
ten 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 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 acceptable
results (in fact, sometimes identical results) faster with pnmscale-
fixed, 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.
SEE ALSO
pnmscalefixed(1), pamstretch(1), pamditherbw(1), pbmreduce(1), pbmp-
scale(1), pamenlarge(1), pnmsmooth(1), pamcut(1), pnmgamma(1), pnm-
scale(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 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)
