The theory of optimal stack filtering has been used in difference of estimates(DoE) approach to the detection of intensity edges in noisy image. In this approach, stack filters are applied to a noisy image to obtain local estimates of the dilated and eroded versions of the noise-free image. Thresholding the difference between these two estimates produces the estimated edge map. In this paper, the DoE approach is modified by imposing a symmetry condition of the data used to train the two stack filers. Under this condition, the stack filters obtained are duals of each other. Only one filter must therefore be trained;the other is simply its dual. They also produce statistially unbiased estimates. This new technique is called the symmetric Difference of Estimates (SDoE) approach.