Abstract: (1) Several basic ideas for △2G as an edge detector are studied. Although these ideas are different, the results are similar. (2) The biological implications of △2G are discussed and the experiments testify the similarity between△2G and receptive fields DOG of retinal ganglion cells. (3) The noise resisting ability of △2G is analysed. The bias of zero-crossing and the output signal-noise ratio 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 between bias of zero-crossing and output signal-noise ration and between parameter σ of △2G and input signal-noise ratio are presented.