Multimedia Tools and Applications

, Volume 52, Issue 2–3, pp 325–345 | Cite as

Lexicographical framework for image hashing with implementation based on DCT and NMF

  • Zhenjun Tang
  • Shuozhong Wang
  • Xinpeng Zhang
  • Weimin Wei
  • Yan Zhao


Image hash is a content-based compact representation of an image for applications such as image copy detection, digital watermarking, and image authentication. This paper proposes a lexicographical-structured framework to generate image hashes. The system consists of two parts: dictionary construction and maintenance, and hash generation. The dictionary is a large collection of feature vectors called words, representing characteristics of various image blocks. It is composed of a number of sub-dictionaries, and each sub-dictionary contains many features, the number of which grows as the number of training images increase. The dictionary is used to provide basic building blocks, namely, the words, to form the hash. In the hash generation, blocks of the input image are represented by features associated to the sub-dictionaries. This is achieved by using a similarity metric to find the most similar feature among the selective features of each sub-dictionary. The corresponding features are combined to produce an intermediate hash. The final hash is obtained by encoding the intermediate hash. Under the proposed framework, we have implemented a hashing scheme using discrete cosine transform (DCT) and non-negative matrix factorization (NMF). Experimental results show that the proposed scheme is resistant to normal content-preserving manipulations, and has a very low collision probability.


Image hashing Lexicographic framework Image retrieval Digital rights management (DRM) Non-negative matrix factorization (NMF) 



This work was supported by the Natural Science Foundation of China (60773079, 60872116, and 60832010), the High-Tech Research and Development Program of China (2007AA01Z477), and the Innovative Research Foundation of Shanghai University for Ph.D. Programs (shucx080148). The authors would like to thank the anonymous referees for their valuable comments and suggestions.


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Zhenjun Tang
    • 1
  • Shuozhong Wang
    • 1
  • Xinpeng Zhang
    • 1
  • Weimin Wei
    • 1
  • Yan Zhao
    • 1
  1. 1.School of Communication and Information EngineeringShanghai UniversityShanghaiPeople’s Republic of China

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