Pamarith User Manual

# pamarith

Updated: 24 October 2020
Table Of Contents

## 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 [-closeness=N] 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 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 generate 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 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 (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 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)).

### 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 expecting 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 maxval of the image corresponds to some maximum value (in the case of a visual image, it corresponds 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, -equal, 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 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 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. 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, 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 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 Common Options), 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 Maxval.
-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 bitwise logic operations. Note that if the maxval is 1, you can also look at these as logic operations on boolean input values. See section Maxval 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 sample 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.

### Other

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

## SEE ALSO

pamfunc, pamsummcol, pamsumm, pnminvert, pambrighten, 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 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 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).

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).

## Table Of Contents

- SYNOPSIS
- DESCRIPTION
  - PBM Oddness
  - Maxval
- NOTE: UNARY FUNCTIONS
- OPTIONS
  - The Function
- SEE ALSO
- HISTORY