Local and global structure preserving hashing for fast digital fingerprint tracing

Abstract

Digital fingerprinting is a promising approach to protect multimedia contents from unauthorized redistribution. Whereas, large scale and high dimensionality make existing fingerprint detection methods fail to trace the traitors efficiently. To handle this problem, we propose a novel local and global structure preserving hashing to conduct fast fingerprint detection. This is the first work that introduces hash-based similarity search method to perform fingerprint detection. Applying the hashing method, we obtain a neighborhood-preserving low-dimensional representation (e. g. hash code) for each fingerprint. Through hash codes, we can find the nearest neighbors of the extracted fingerprint, thereby tracing the real traitors within a small range. Preserving the local structure facilitates to find the nearest neighbors of the query fingerprint efficiently, and preserving the global structure ensures hash codes of fingerprints as discriminative as possible. These properties make the proposed approach efficient to trace the real traitors. Extensive experiments demonstrate that the proposed approach outperforms traditional linear scan detection methods in term of efficiency.

Appendix

We take converting $\sum \nolimits _{ij} W_{ij} \left \| y_{i} - y_{j} \right \|$ to t r(Y ^T L Y) as an example to show the transformations from (9) to (10).

$$ \begin{array}{llllll} & \quad \sum\nolimits_{ij} W_{ij} \left\| y_{i} - y_{j} \right\|^{2} \\ &= \sum\nolimits_{ij} W_{ij} (y_{i} - y_{j})^{T} (y_{i} - y_{j}) \\ &= \sum\nolimits_{ij} W_{ij} \left({y_{i}^{T}} y_{i} - {y_{i}^{T}} y_{j} - {y_{j}^{T}} y_{i} + {y_{j}^{T}} y_{j}\right) \\ &= 2 \left(\sum\nolimits_{ij} {W_{ij} {y_{i}^{T}} y_{i} } - \sum\nolimits_{ij} W_{ij} {y_{i}^{T}} y_{j} \right) \\ &= 2 \left(tr(Y D Y^{T} \right) - tr\left(Y W Y^{T} ) \right) \\ &= 2 tr\left(Y L Y^{T}\right) \end{array} \notag $$

where L = D − W and $D_{ii} = \sum \nolimits _{j} W_{ij}$. We can employ the same method transform $\sum \nolimits _{i} {{{\left \| {{y_{i}} - \bar {y}} \right \|}^{2}}}$ to t r(Y H Y ^T).