A real-time, compact architecture is presented for translation-invariant windowed nonlinear discrete operators represented in computational mathematical morphology. The architecture enables output values to be computed in a fixed number of operations and thus can be pipelined. Memory requirements for an operator are proportional to its basis size. An operator is implemented by three steps: (1) each component of a vector observation is used as an index into a table of bit vectors; (2) all retrieved bit vectors are "ANDed" together; and (3) the position of the first nonzero bit is used as an index to a table of output values. Computational mathematical morphology is described, the new architecture is illustrated through examples, and formal proofs are given. A modification of the basic architecture provides for increasing operators.