A novel concept for determining the root called backpropagation morphology is defined. The backpropagation morphology feeds back the immediate result to replace the input sample and continues until it scans to the end. The theorems of a two-scan algorithm using backpropagation morphology to derive the root generation without recursively applying forward morphology are developed. The algorithm's operation is independent of the object's size and saves significant computation time compared with the number of iterations in forward morphology. A systolic array for efficiently processing the two-scan operation is also presented. The array uses 3n cells to process an n × n image in 6n - 2 cycles. The cell utilization is 100%. Also studied is the implementation of the two-scan algorithm on a distributed-memory multicomputer. A programming paradigm called pipelined data parallelism is used to develop the parallel program, which is asynchronous, data driven, and very efficient. Performance of the program can be tuned by choosing appropriate partition parameters.