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For an image accompanied by Gaussian noise, image smoothing is usually achieved through adopting the classical Gaussian smoothing mask. This may sometimes blur the edges and other fine details. Noise removing and edges blurring are two conflicting requirements. And δ , as a key factor in the Gaussian function, can greatly affect noise removing, edges blurring and even brightness of an image after processing. In fact, the classical Gaussian mask is not a sole member in the family of Gaussian masks. There are countless Gaussian masks based on the different values of δ in theory. In this paper, we try to find out the relation between the value of δ and the result of image smoothing. Primary simulation confirms the proposed theory. The relation gives us an implies that we should select appropriate values of δ according to the values of SNR in different regions of an image, then establish the Gaussian smoothing masks to obtain the best result of image smoothing. After the new Gaussian self-adaptive algorithm being used, we can obtain fine details remaining in partial regions at the cost of a little reducing of the SNR character in the whole image.