Non-scaling Stochastic Computing adder and subtracter architectures are introduced. They are modeled using Markov Chains to obtain important statistical properties enabling their design optimization. To demonstrate their efficacy, they are used to realize a stochastic computing-based image sharpening filter which is simulated in MATLAB and Synopsys. The filter’s computational efficiency is showcased with standard image processing metrics while its hardware resources are compared to those of the standard binary filter, highlighting the advantages of the proposed approach.