Abstract: Two edge detection operators of second de ivative model, the discrete Laplacian of Gaussian (DLOG) and Laplacian of binomial distribution (LOB) operators are introduced in this paper. A digital edge contaminated by an independent Gaussian noise is used as an edge image model. After convolving the image model with the edge detection operators of second derivative model, a plane fitting in the least squares sense is used to detect the zero crossing points as edge points. The Probabilities Pa of edge location and the Probabilities Pf of false edge detection are derived to compare the performances of various edge detection operators of second derivative model.