Twofold Video Hashing with Automatic Synchronization

Video hashing finds a wide array of applications in content authentication, robust retrieval and anti-piracy search. While much of the existing research has focused on extracting robust and secure content descriptors, a significant open challenge still remains: Most existing video hashing methods are fallible to temporal desynchronization. That is, when the query video results by deleting or inserting some frames from the reference video, most existing methods assume the positions of the deleted (or inserted) frames are either perfectly known or reliably estimated. This assumption may be okay under typical transcoding and frame-rate changes but is highly inappropriate in adversarial scenarios such as anti-piracy video search. For example, an illegal uploader will try to bypass the 'piracy check' mechanism of YouTube/Dailymotion etc by performing a cleverly designed non-uniform resampling of the video. We present a new solution based on dynamic time warping (DTW), which can implement automatic synchronization and can be used together with existing video hashing methods. The second contribution of this paper is to propose a new robust feature extraction method called flow hashing (FH), based on frame averaging and optical flow descriptors. Finally, a fusion mechanism called distance boosting is proposed to combine the information extracted by DTW and FH. Experiments on real video collections show that such a hash extraction and comparison enables unprecedented robustness under both spatial and temporal attacks.Comment: submitted to Image Processing (ICIP), 2014 21st IEEE International Conference o

Iterative Row Sampling

There has been significant interest and progress recently in algorithms that solve regression problems involving tall and thin matrices in input sparsity time. These algorithms find shorter equivalent of a n*d matrix where n >> d, which allows one to solve a poly(d) sized problem instead. In practice, the best performances are often obtained by invoking these routines in an iterative fashion. We show these iterative methods can be adapted to give theoretical guarantees comparable and better than the current state of the art. Our approaches are based on computing the importances of the rows, known as leverage scores, in an iterative manner. We show that alternating between computing a short matrix estimate and finding more accurate approximate leverage scores leads to a series of geometrically smaller instances. This gives an algorithm that runs in $O(nnz(A) + d^{\omega + \theta} \epsilon^{-2})$ time for any $\theta > 0$, where the $d^{\omega + \theta}$ term is comparable to the cost of solving a regression problem on the small approximation. Our results are built upon the close connection between randomized matrix algorithms, iterative methods, and graph sparsification.Comment: 26 pages, 2 figure

On quasi modules at infinity for vertex algebras

A theory of quasi modules at infinity for (weak) quantum vertex algebras including vertex algebras was previously developed in \cite{li-infinity}. In this current paper, quasi modules at infinity for vertex algebras are revisited. Among the main results, we extend some technical results, to fill in a gap in the proof of a theorem therein, and we obtain a commutator formula for general quasi modules at infinity and establish a version of the converse of the aforementioned theorem.Comment: 18 page