A technique that approximates the output of the soft morphological operators is described. The soft operators can be viewed as a voting process across neighborhoods defined by the structuring element. Instead of processing all votes across a neighborhood, this approximation technique randomly samples elements in the neighborhood and uses these values as inputs to a two-state finite state machine, where the state of the machine corresponds to the output at a given pixel. When properly designed, the machines sample a small fraction of the neighborhood, obtain output that is 91 to 100% accurate at each pixel, and is one to two orders of magnitude faster than conventional algorithms. Experiments on binary textures and digits confirm the theoretical results.