The effect of median filtering on edge location estimation

We study the effect of noise reduction preprocessing, specifically median filtering and averaging, on the accuracy of edge location estimation using least squares. The original edge is either a step or a linear ramp, corrupted by white Gaussian noise or binary symmetrical channel noise. The surprising conclusion is that in the case of white Gaussian noise, neither median filtering nor averaging improves the estimation accuracy. In the case of binary symmetrical channel noise, median filtering does improve the estimation accuracy for ramp edges, which are reasonable models for real-life edges.