Grayscale Implementation - Logic-based Nonlinear Image Processing - page 118

tion” (NO OP). There should never be more than one nonzero bit in the intersection,
and a formal proof is given in the paper. The bit vectors must be pre-computed. A fur-
ther look-up take is used to convert the interval label to the output value.
For functions of more variables, the same principle applies and an architecture
for nonincreasing filters is shown in Fig. 8.13. The value of each variable within the
filter window maps to a pre-computed bit vector. All of these bit vectors are
ANDed together and the result contains at most one nonzero bit. The position of
this bit identifies the label of interval required and this label is then converted to the
output value via a look-up table. If there are no nonzero bits, then the result is no op-
eration. A slightly simpler version of the architecture exists for increasing filters.
In practice, computational morphology is too general for many applications
and aperture filters are used instead. Aperture filters operate over a smaller set of in-
put values by clipping the input range into the filter window. They partition the in-
put values into intervals and return an output for each interval. This is therefore
ideally suited to implementation in a bit-vector architecture.
Figure 8.13 Bit-vector architecture. A bit vector has been pre-computed for each of the n in-
put variables. All of the bit vectors are ANDed together and a result is produced. If all of the
resultant bits are 0 then the output is a NO OP. Otherwise, the position of the remaining bit in-
dicates the label of the interval identified. This label is then passed to the look-up table which
returns the output value.