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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]

       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 work 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  is  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,  pam-
       scale 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, pam-
       scale 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_fac-
       tor.

       Specifying the -reduce reduction_factor option is equivalent to specifying the  scale_fac-
       tor  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 com-
       pletely 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; other-
       wise, 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 com-
       puter-age version of blurring.

   Transparency
       pamscale understands transparency and properly mixes pixels considering the pixels' trans-
       parency.

       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 trans-
       parent 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  pix-
       els 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  continu-
       ous  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 differ-
       ent 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  sepa-
       rately.

       As  a first step in resampling, pamscale converts the source image, which is a set of dis-
       crete 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 fre-
       quency 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 fre-
       quency  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 sam-
       pling 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 func-
       tion, and then Fourier transform the result back, but there's an easier	way.   Mathemati-
       cians  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  win-
       dow 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 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  imple-
       mentation 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 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 pre-
       cisely, 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,  per-
       forms a calculation on each sample read from its input and each sample written to its out-
       put 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-propor-
       tional.	So just to save time, at the expense of some image quality, you can specify -lin-
       ear 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 con-
       vert 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.

SEE ALSO
       pnmscalefixed(1)  ,  pamstretch(1) , pamditherbw(1) , pbmreduce(1) , pbmpscale(1) , pamen-
       large(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, pnm-
       scale.	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 resam-
       pling  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 origi-
       nal Pbmplus version of pnmscale by Jef Poskanzer (1989, 1991).  But none of that  original
       code remains.

netpbm documentation			 29 December 2009		  Pamscale User Manual(0)
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