man > pamarith(1)

Pamarith User Manual(1)                General Commands Manual               Pamarith User Manual(1)

NAME
       pamarith - perform arithmetic on two Netpbm images


SYNOPSIS
       pamarith -add | -subtract | -multiply | -divide | -difference | -minimum | -maximum | -mean |
       -equal  |  -compare  |  -and  | -or | -nand | -nor | -xor | -shiftleft | -shiftright [-close‐
       ness=N] pamfile1 pamfile2 ...

       All options can be abbreviated to their shortest unique prefix.  You may use two hyphens  in‐
       stead  of  one.  You may separate an option name and its value with white space instead of an
       equals sign.


DESCRIPTION
       This program is part of Netpbm(1).

       pamarith reads two or more PBM, PGM, PPM, or PAM images as input.  It performs the  specified
       binary  arithmetic  operation on their sample values and produces an output of a format which
       is the more general of the two input formats.  The two input images must be of the same width
       and height.  The arithmetic is performed on each pair of identically located tuples to gener‐
       ate the identically located tuple of the output.

       For functions that are commutative and associative, pamarith applies
         the binary function repetitively on as many input images as you supply.  For
         example, for -add , the output is the sum of all the inputs.  For
         other functions (e.g. -subtract), the program fails if you supply
         more than two input images.  (Before Netpbm 10.93 (December 2020), the
         program always failed with more than two input images).

       For some other functions, pamarith could theoretically compute a
         meaningful result for multiple arguments, but it fails nonetheless if you
         give more than two input images.  -mean and -equal are in that
         category.


       Most of what pamarith does is not meaningful for visual images.  It
         works toward Netpbm's secondary purpose of just manipulating arbitrary
         matrices of numbers.


       For the purpose of the calculation, it assumes any PBM, PGM, or PPM input image is the equiv‐
       alent PAM image of tuple type BLACKANDWHITE, GRAYSCALE, or RGB, respectively, and if it  pro‐
       duces a PBM, PGM, or PPM output, produces the equivalent of the PAM image which is the result
       of the calculation.

       The  first pamfile argument identifies the "left" argument image; the second pamfile argument
       identifies the "right" one.

       If the output is PAM, the tuple type is the same as the tuple type of the left input image.

       pamarith performs the arithmetic on each pair of identically located tuples in the two  input
       images.

       The arithmetic operation is in all cases fundamentally a function from two integers to an in‐
       teger  (but  see  below - the functions are defined in ways that you can effectively e.g. add
       real numbers).  The operation is performed on two tuples as follows.  The  two  input  images
       must have the same depth, or one of them must have depth one.  pamarith fails if one of these
       is not the case.

       If they have the same depth, pamarith simply carries out the arithmetic one sample at a time.
       I.e.  if  at a particular position the left input image contains the tuple (s1,s2,...,sN) and
       the right input image contains the tuple (t1,t2,...tN), and the function is f, then the  out‐
       put image contains the tuple (f(s1,t1),f(s2,t2),...,f(sN,tN)).

       If  one of the images has depth 1, the arithmetic is performed between the one sample in that
       image and each of the samples in the other.  I.e. if at a particular position the left  input
       image  contains the tuple (s) and the right input image contains the tuple (t1,t2,...tN), and
       the function is f, then the output image contains the tuple (f(s,t1),f(s,t2),...,f(s,tN)).



   PBM Oddness
       If you're familiar with the PBM format, you may find pamarith's operation on PBM images to be
       nonintuitive.  Because in PBM black is represented as 1 and white as 0, you might be  expect‐
       ing black minus black to be white.

       But  the  PBM format is irrelevant, because pamarith operates on the numbers found in the PAM
       equivalent (see above).  In a PAM black and white image, black is 0 and white is 1.  So black
       minus black is black.



   Maxval
       The meanings of the samples with respect to the maxval varies according to the  function  you
       select.

       In PAM images in general, the most usual meaning of a sample (the one that applies when a PAM
       image represents a visual image), is that it represents a fraction of some maximum.  The max‐
       val  of the image corresponds to some maximum value (in the case of a visual image, it corre‐
       sponds to "full intensity."), and a sample value divided by the maxval gives the fraction.

       For pamarith, this interpretation applies to the regular arithmetic  functions:  -add,  -sub‐
       tract, -multiply, -divide, -difference, -minimum, -maximum, -mean, -equal, and -compare.  For
       those, you should think of the arguments and result as numbers in the range [0,1).  For exam‐
       ple, if the maxval of the left argument image is 100 and the maxval of the right argument im‐
       age  is  200  and the maxval of the output image is 200, and the left sample value in an -add
       calculation is 50 and the right sample is 60, the actual calculation is  50/100  +  60/200  =
       160/200, and the output sample value is 160.

       For  these  functions,  pamarith makes the output image's maxval the maximum of the two input
       maxvals, except with -equal  and -compare.  For -equal, the output maxval is always  1.   For
       -compare,  it  is always 2.  (Before Netpbm 10.14 (February 2003), there was no exception for
       -compare; in 10.14, the exception was just that the maxval was at least 2, and  sometime  be‐
       tween 10.18 and 10.26 (January 2005), it changed to being exactly 2).

       If  the  result  of  a  calculation falls outside the range [0, 1), pamarith clips it -- i.e.
       considers it to be zero or 1-.

       In many cases, where both your input maxvals are the same, you can just think of  the  opera‐
       tion  as taking place between the sample values directly, with no consideration of the maxval
       except for the clipping.  E.g. an -add of sample value 5 to  sample  value  8  yields  sample
       value 13.

       But  with  -multiply,  this  doesn't  work.  Say your two input images have maxval 255, which
       means the output image also has maxval 255.  Consider a location in the image where the input
       sample values are 5 and 10.  You might think the multiplicative product of those would  yield
       50 in the output.  But pamarith carries out the arithmetic on the fractions 5/255 and 10/255.
       It multiplies those together and then rescales to the output maxval, giving a sample value in
       the output PAM of 50/255 rounded to the nearest integer: 0.

       With  the bit string operations, the maxval has a whole different meaning.  The operations in
       question are: -and, -or, -nand, -nor, -xor, and -shiftleft, -shiftright.

       With these, each sample value in one or both input images, and in the  output  image,  repre‐
       sents  a  bit string, not a number.  The maxval tells how wide the bit string is.  The maxval
       must be a full binary count (a power of two minus one, such as 0xff) and the number  of  ones
       in  it  is  the width of the bit string.  For the dyadic bit string operations (that's every‐
       thing but the shift functions), the maxvals of the input images must be the same and pamarith
       makes the maxval of the output image the same.

       For the bit shift operations, the output maxval is the same as the left  input  maxval.   The
       right input image (which contains the shift counts) can have any maxval and the maxval is ir‐
       relevant  to  the interpretation of the samples.  The sample value is the actual shift count.
       But it's still required that no sample value exceed the maxval.



NOTE: UNARY FUNCTIONS
       pamarith applies only binary functions.  If you want to apply a unary function, e.g. "halve",
       to a single image, use pamfunc.



OPTIONS
       In addition to the options common to all programs based on libnetpbm  (most  notably  -quiet,
       see ]8;;index.html#commonoptions\ Common Options]8;;\ ), pamarith recognizes the following command line options:


   The Function
       These options select the function that pamarith applies.

       You must specify one of these, and cannot specify more than one.




       -add   Adds the two values.  If the result is larger than maxval, it is clipped.


       -subtract
              Subtracts a value in the right input image from a value in the left input image.


       -minimum
              Chooses the smaller value of the two.


       -maximum
              Chooses the larger value of the two.


       -difference
              Calculates the absolute value of the difference.


       -multiply
              Does  an  ordinary  arithmetic multiplication, but tends to produce nonobvious results
              because of the way pamarith interprets sample values.  See ]8;;#maxval\Maxval]8;;\ .


       -divide
              Divides a value in the left input image by the value in the right  input  image.   But
              like  -multiply,  it tends to produce nonobvious results.  Note that pamarith clipping
              behavior makes this of little use when the left argument (dividend)  is  greater  than
              the  right argument (divisor) -- the result in that case is always the maxval.  If the
              divisor is 0, the result is the maxval.

              -divide was new in Netpbm 10.30 (October 2005).


       -equal Produces maxval when the values in the two images are equal and  zero  when  they  are
              not.  Note that the output maxval is always 1 for -equal.

              If  the  maxvals  of the input images are not identical, pamarith may claim two values
              are not equal when in fact they are, because of the precision with which it  does  the
              arithmetic.

              You can make the equality test approximate with the -closeness option.  This gives the
              percentage of maxval by which the samples can differ and still be considered equal.

              -equal was new in Netpbm 10.93 (December 2020).


       -compare
              Produces  the value 0 when the value in the left input image is less than the value in
              the right input image, 1 when the values are equal, and 2 when  the  left  is  greater
              than the right.

              If  the  maxvals  of the input images are not identical, pamarith may claim two values
              are not equal when in fact they are, because of the precision with which it  does  the
              arithmetic.  However, it will never say A is greater than B if A is less than B.

              -compare was new in Netpbm 10.13 (December 2002).


       -and, -nand, -or, -nor, -xor
              These  consider  the input and output images to contain bit strings; they compute bit‐
              wise logic operations.  Note that if the maxval is 1, you can also look  at  these  as
              logic operations on boolean input values.  See section ]8;;#maxval\Maxval]8;;\  for the special meaning
              of maxval with respect to bit string operations such as these.


       -shiftleft, -shiftright
              These  consider  the  left  input image and output image to contain bit strings.  They
              compute a bit shift operation, with bits falling off the left or right end and  zeroes
              shifting  in, as opposed to bits off one end to the other.  The right input image sam‐
              ple value is the number of bit positions to shift.

              Note that the maxval (see ]8;;#maxval\Maxval]8;;\ ) determines the width of the frame within which  you
              are shifting.




   Other
       -closeness
              This changes the meaning of -equal.  It is not valid with any other function.  See the
              description of -equal.




SEE ALSO
       pamfunc(1), pamsummcol(1), pamsumm(1), pnminvert(1), pambrighten(1), ppmdim(1), pnmconvol(1),
       pamdepth(1), pnmpsnr(1), pnm(1), pam(1)



HISTORY
       pamarith replaced pnmarith in Netpbm 10.3 (June 2002).

       In Netpbm 10.3 through 10.8, though, pamarith was not backward compatible because it required
       the  input images to be of the same depth, so you could not multiply a PBM by a PPM as is of‐
       ten done for masking.  (It was not intended at the time that pnmarith would be  removed  from
       Netpbm -- the plan was just to rewrite it to use pamarith; it was removed by mistake).

       But  starting with Netpbm 10.9 (September 2002), pamarith allows the images to have different
       depths as long as one of them has depth 1, and that made  it  backward  compatible  with  pn‐
       marith.

       The original pnmarith did not have the -mean option.

       The -compare option was added in Netpbm 10.13 (December 2002).

       The bit string operations were added in Netpbm 10.27 (March 2005).

       The -divide option was added in Netpbm 10.30 (October 2005).

       The ability to have more than one input (operand) was added in Netpbm 10.93 (December 2020).

       The -equal option was added in Netpbm 10.93 (December 2020).

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/pamarith.html

netpbm documentation                       24 October 2020                   Pamarith User Manual(1)