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, 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 -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. 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.

The Operations¶

Most of the operations are obvious from the option name. The following 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 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. 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, 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, 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 operations 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 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.

Notes¶

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