Stochastic computation that performs in probabilistic domain has been recently exploited for area-efficient hardware implementation, while it requires large number of bits to represent probabilities, increasing the switching activity and hence power dissipation. In this paper, an early-stage operation-skipping scheme, where stochastic computation is terminated at the early stage by monitoring the intermediate computation result, is introduced for low-power stochastic image processors. In case that the proposed scheme is applied in edge-detection processing as a typical example of image processing, a non-candidate pixel is predicted using a simple threshold detector before the completion of the stochastic edge-detection process. Once the pixel is found, the edge-detection process is stopped, eliminating the stochastic computation at the rest of bits. As a design example, a Robert's operator based stochastic edge detector is implemented using MATLAB. Based on the simulation results, a correlation between an output-image quality using a peak signal-to-noise ratio (PSNR) criteria and the reduction ratio of bits is discussed.