One well-studied image processing task is the removal of impulse noise from images. Impulse noise can be introduced during image capture, during transmission, or during storage. The signal-dependent rank order mean (SD-ROM) filter has been shown to be effective t removing impulses from 2-D scalar-valued signals. Excellent results were presented for both two-state and multi-state version of the filter. The two-state SD-ROM filter relies on the selection of set of threshold values. In this paper, we examine the performance of the algorithm with respect to the thresholds. We take three different approaches. First, we discuss the performance of the algorithm with respect to its root signals. Second, we present probabilistic model for the SD-ROM filter. This model characterizes the performance of the algorithm in terms of the probability of detecting corrupted pixel while voiding uncorrupted pixels. Finally, we apply the insight gained from the root signal analysis and the statistical model to optimized thresholds found using computerized search algorithm for large number of images and noise conditions.