This work presents a novel parallel technique to implement stack morphological filters for image processing. The method relies on applying the image bitwise decomposition to manipulate the grayscale image at a bit-plane level, while simple logical operations and Positive Boolean Functions (PBF's) are executed in parallel to derive the transformed bit-planes. The relationship between the bitwise and threshold decomposition is closely investigated and analysed, which lead us to derive an algorithm whose control flow is full binary encoded. Furthermore, the algorithm exhibits an interesting performance, which depends on the image histogram thanks to its hierarchical processing and the study of the relationship among binary decompositions.