We formulate the problem of finding a statistical representation of shape as a best basis selection problem in which the goal is to choose the basis for optimal shape representation from a very large library of bases. In this work, our emphasis is on applying this basis selection framework using the wavelet packets library to estimate the probability density function of a class of shapes from a...

In this paper we introduce a new representation of orthogonal matrices. We show that any orthogonal matrix can be represented in the form Q = I ? Y SY T , which we call the basis-kernel representation of Q. We show that the kernel S can be chosen to be triangular and show how the familiar representation of an orthogonal matrix as a product of Householder matrices can be directly derived from a ...

We propose systems of orthogonal functions qn to represent optical transfer functions (OTF) characterized by including the diffraction-limited OTF as the first basis function q0=OTFperfect. To this end, we apply a powerful and rigorous theoretical framework based on applying the appropriate change of variables to well-known orthogonal systems. Here we depart fro...

Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods, such as the principal component analysis, to so-represented data. While initial choice of a representation may have significant impact on second phase this issue has not gained much attention past. Typically, rather ad hoc some standard basi...