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LOG filter for image edge detection consists of Gaussian filter and Laplace operator. Based on the central limit theorem and the separating characteristic of two dimensional Gaussian filter, Gaussian approximation filter is constructed. The digital filtering algorithm for Gaussian approximation filter is concluded through the bilinear transformation method and zero phase shift filtering technology. The algorithm combined with the Laplace operator has been successfully applied in the implementation of LOG filtering for edge detection. Applying Gaussian approximation filter in LOG filtering is helpful for multi-scale LOG filtering because only one parameter in the algorithm needs to be changed. This method is more convenient than the template method in which the coefficients of the whole mask of LOG filter with different scale need to be refreshed. This is a new implementation for LOG filter.