Principal Components Analysis (PCA) is an appearance based technique used widely for the dimensionality reduction and it records a great performance in face recognition. PCA based approaches typically include two phases: training and classification (Draper et al 2003). In the training phase, an Eigen space is established from the training samples using PCA and the training face images are mappe...

Conditions for the construction of polynomial eigen–operators for the Hamiltonian of collective string field theories are explored. Such eigen–operators arise for only one monomial potential v(x) = μx2 in the collective field theory. They form a w∞– algebra isomorphic to the algebra of vertex operators in 2d gravity. Polynomial potentials of orders only strictly larger or smaller than 2 have no...

Following Futurism, we show how periodic motions can be represented by a small number of eigen-shapes that capture the whole dynamic mechanism of periodic motions. Spectral decomposition of a silhouette of an object in motion serves as a basis for behavior classiÿcation by principle component analysis. The boundary contour of the walking dog, for example, is ÿrst computed eÆciently and accurate...

Both the theoretical and practical investigations of various dynamical systems need to extend the definitions of various functions defined on the real axis to the set of matrices. To this end one uses mainly three methods which are based on 1) the Jordan canonical forms, 2) the polynomial interpolation, and 3) the Cauchy integral formula. All these methods give the same result, say g(A), when t...

We propose an approach for the simultaneous bounding box estimation of multiple organs in volumetric CT images. Local eigen-organ spaces are constructed for different types of training organs, and a global eigen-space, which describes the spatial relationships between the organs, is also constructed. Each volume of interest in the abdominal CT image is projected into the local eigen-organ space...