Locally linear embedding (LLE) has been widely used in data processing, such as data clustering, video identification and face recognition, but its application in image hashing is still limited. In this work, we investigate the use of LLE in image hashing and find that embedding vector variances of LLE are approximately linearly changed by content-preserving operations. Based on this observation, we propose a novel LLE-based image hashing. Specifically, an input image is firstly mapped to a normalized matrix by bilinear interpolation, color space conversion, block mean extraction, and Gaussian low-pass filtering. The normalized matrix is then exploited to construct a secondary image. Finally, LLE is applied to the secondary image and the embedding vector variances of LLE are used to form image hash. Hash similarity is determined by correlation coefficient. Many experiments are conducted to validate our efficiency and the results illustrate that our hashing is robust to content-preserving operations and reaches a good discrimination. Comparisons of receiver operating characteristics (ROC) curve indicate that our hashing outperforms some notable hashing algorithms in classification between robustness and discrimination. 
Robust image hashing with embedding vector variance of LLE