The ∇2G performance in the presence of noise

The Laplacian of Gaussian operator, ∇²G, is very important as an edge detector in the theory of computer vision. The bias of zero-crossing and output signal-to-noise-ratio of ∇²G under the models of four typical kinds of edges corrupted by white noise are given, and these theoretical results are confirmed by experiments. The relations among bias of zero-crossing, output and input signal-to-noise-ratio and parameter σ of ∇ ²G are presented