In this paper, we first apply the theory of wallpaper groups to natural images and extract a novel feature to depict the symmetry property of natural images. The original proposed algorithm takes autocorrelation and correlation as a preprocessing step, which is very time-consuming. Through further analysis, we develop a set of schemes to accelerate this algorithm. Experimental results demonstrate that in performing content-based image retrieval, the proposed symmetry feature outperforms wavelet feature, which is a widely accepted descriptor of texture, and water-filling feature. The accelerated version of the algorithm improves the processing speed by a large margin while it brings little degradation to retrieval performance.