In a series of ten papers published since 1994, a radically new technique for implementing a wide range of standard image processing operations has been presented, under the acronym SKIPSM (Separated-Kernel Image Processing using finite State Machines). Key steps are: (1) the operation is separated into a row operation followed by a column operation, (2) these row and column operations are put in recursive form. That is, in a form compatible with either one-step software implementation or pipelined raster-scan hardware implementation, (3) the resulting operations are realized as FSMs (finite-state machines), and (4) these FSMs are implemented in software or in inexpensive off-the-shelf integrated circuits. Note that this technique does not require separability, in the usual sense. In this paper, the SKIPSM technique is applied to computing binary openings and closings in one pass using arbitrary binary structuring elements. Whether the resulting finite state machines are implemented in software or hardware, the result is generally much faster and/or much cheaper than conventional implementations. Furthermore, this same SKIPSM architecture is highly versatile and programmable, allowing it to be software-reconfigured to perform hundreds of other software- based or pipelined image processing operations, such a binary and grey-level morphology, the Grassfire Transform, binary and grey-level template matching, binary skeletonization, etc.