On improving the collision property of robust hashing based on projections

In this paper, we study the collision property of one of the robust hash functions proposed. This method was originally proposed for robust hash generation from blocks of image data and is based on projection of image block data on pseudo-random matrices. We show that collision performance of this robust hash function is not optimal when used to extract hash bits from a moment invariants feature matrix for video fingerprinting. We identify that the collision performance of this hash extraction method could be improved if the pseudo-random matrices are selected carefully. We propose two methods that use an offline training set to improve the collision property. Both of the methods attempt to select the matrices that minimize cross-correlation among the projected features. The first method uses an iterative procedure to select the matrices that satisfy a cross-correlation threshold. The second method used Singular Value Decomposition (SVD) of the feature covariance matrix and hence the crosscorrelation of the projected values is zero. We show the improved collision performance of both these methods on the same dataset. Also, we interpret the projection matrices obtained through the SVD procedure and show that they capture appearance and motion information from the moment invariants feature matrix.