Grayscale Implementation - Logic-based Nonlinear Image Processing - page 109

Figure 8.6 Erosion by a three-point flat structuring element implemented via a stack filter.

has been replaced by a simple logical operation. The circuit shown in Fig. 8.7 produces
an output in the propagation time of a simple logic gate with no sorting required.
It may also be implemented as a simple counting operation, i.e.,

i i i

1 if xxx ++≥ 2

i 0 1 2

y = (8.9)

0 otherwise

For larger median filters, the counting operation may be preferable since the imple-
mentation in terms of logic does not scale well. Rather than duplicating the digital
logic for every threshold level, other strategies for computing stack filters have
been adopted. By definition, the output values of a stack filter are y i = 1 for i k and
y i = 0 for i > k . This means that the only level of interest is k , the highest threshold
level for which the output is 1 (or the top of the signal). Various approaches have
been developed to locate this level. 18 One approach is a divide-and-conquer strat-
egy where the value of the middle threshold level y L /2 is computed. If y L /2 = 1, then k