This paper proposes a novel robust digital color image watermarking algorithm which combines color image feature point extraction, shape image normalization and QPCA (quaternion principal component algorithm) basedwatermarking embedding (QWEMS) and extraction (QWEXS) schemes. The feature point extraction method called Mexican Hat wavelet scale interaction is used to select the points which can ...

The principle of dimensionality reduction with PCA is the representation of the dataset ‘X’in terms of eigenvectors ei ∈ RN  of its covariance matrix. The eigenvectors oriented in the direction with the maximum variance of X in RN carry the most      relevant information of X. These eigenvectors are called principal components [8]. Ass...

I outline a uniied approach to characterizing Fr echet, limiting Fr echet, and Clarke subgradients of an arbitrary function of the eigen-values of a real symmetric matrix. In particular, I compute various subdiierentials of the k'th largest eigenvalue. This paper summarizes the results and techniques presented in detail in 4]. 1 The author wishes to thank the University of Milan, and in particu...

The impact of the latest combined CHAMP/GRACE/terrestrial measurements Earth gravity model EIGEN-CG03C on the measurement of the Lense-Thirring effect with some linear combinations of the nodes of some of the existing Earth’s artificial satellites is presented. The 1-sigma upper bound of the systematic error in the nodenode LAGEOS-LAGEOS II combination is 3.9% (4% with EIGENGRACE02S, ∼ 6% with ...