SYNOPSIS
pamarith -add | -subtract | -multiply | -divide | -difference | -mini-
mum | -maximum | -mean | -compare | -and | -or | -nand | -nor | -xor |
-shiftleft | -shiftright pamfile1 pamfile2

All options can be abbreviated to their shortest unique prefix. You
may use two hyphens instead 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.

pamarith reads two 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 generate the identically located tuple of the out-
put.

For the purpose of the calculation, it assumes any PBM, PGM, or PPM
input image is the equivalent PAM image of tuple type BLACKANDWHITE,
GRAYSCALE, or RGB, respectively, and if it produces 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 integer. 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 arith-
metic 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 output 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)).


Maxval
The meanings of the samples with respect to the maxval varies accord-
ing 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 maxval of the image corre-
sponds 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, -subtract, -multiply, -divide, -difference, -minimum,
-maximum, -mean, and -compare. For those, you should think of the
arguments and result as numbers in the range [0,1). For example, if
the maxval of the left argument image is 100 and the maxval of the
right argument image 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 max-
imum of the two input maxvals, except with -compare, where pamarith
uses an output maxval of 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 between 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 operation 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. Con-
sider 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 mean-
ing. 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, represents 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 everything 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 irrelevant to the inter-
pretation of the samples. The sample value is the actual shift count.
But it's still required that no sample value exceed the maxval.


The Operations
Most of the operations are obvious from the option name. The follow-
ing paragraphs cover those that aren't.

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

-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 sam-
ple values. See Maxval .

-divide divides a value in the left input image by the value in the
left 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 argu-
ment (divisor) -- the result in that case is always the maxval. If
the divisor is 0, the result is the maxval. This option was new in
Netpbm 10.30 (October 2005).

-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, due to the pre-
cision 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, and -xor consider the input and output images
to contain bit strings; they compute bitwise logic operations. Note
that if the maxval is 1, you can also look at these as logic opera-
tions on boolean input values. See section Maxval for the special
meaning of maxval with respect to bit string operations such as these.

-shiftleft and -shiftright 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 Maxval ) determines the width of the frame
within which you are shifting.


Notes
If you want to apply a unary function, e.g. "halve", to a single
image, use pamfunc.


SEE ALSO
pamfunc, pamsummcol, pamsumm, pnminvert, ppmbrighten,
ppmdim, pnmconvol, pamdepth, pnmpsnr, pnm, pam



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

In Netpbm 10.3 through 10.8, though, pamarith was not backward compat-
ible because it required the input images to be of the same depth, so
you could not multiply a PBM by a PPM as is often 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 pnmarith.

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).



netpbm documentation 08 April 2007 Pamarith User Manual(0)