A new approach to extracting periodicity of a regular texture based on autocorrelation functions is proposed in this paper. From the peaks in the autocorrelation function of an image, the displacement vectors and texture primitives in the image can be effectively determined. Moreover, the area of the extracted texture primitive is relatively small. This fact benefits in further processing of the image, such as data compression, feature extraction, and pattern analysis. The proposed approach needs no preprocessing, such as image thresholding or quantization, on the input image. However, it keeps tolerant to distortions in the texture, such as noises, intensity changes, and geometric variants. A synthesized texture with high regularity can be constructed by arranging the obtained texture primitives according to the displacement vectors. Experimental results support the effectiveness and efficiency of the proposed approach.