A Contourlet transform, an expansion of a wavelet transform, is a double filter bank structure composed of Laplacian Pyramid and directional filter banks. Several wavelet filters of preferable performance have been developed for wavelet transforms, e.g. CDF (Cohen, Daubechies and Feauveau) 9/7 filter. However, there is still only a limited number of wavelet filters applicable for Contourlet tra...

In his seminal work of 1981, A M Cormack has established that Radon transforms defined on two remarkable families of curves in the plane are invertible and admit explicit inversion formulas via circular harmonic decomposition. A sufficient condition for finding larger classes of curves enjoying the same property is given in this paper. We show that these generalized Cormack’s curves are given b...

Over the past 25 years, fast multi-scale algorithms such as wavelet-type pyramid transforms for hierarchical data representation, multi-grid solvers for the numerical solution of operator equations, and subdivision methods in computer-aided geometric design lead to tremendous successes in data and geometry processing, and in scientific computing in general. While linear multi-scale analysis is ...

MOS surfaces are rational surfaces in R which provide rational envelopes of the associated two-parameter family of spheres. Moreover, all the offsets admit rational parameterizations as well. Recently, it has been proved that quadratic triangular Bézier patches in R are MOS surfaces. Following this result, we describe an algorithm for computing an exact rational envelope of a two-parameter fami...

This article presents a method for removing geometric distortions in taken images of rectangular planar patterns (such as maps, pictures, or posters) in the absence of any calibration information or explicit knowledge of the imaging device. Our approach removes lens distortion form single-view images. The method is based on Least-Square-Error (LSE) approximations and Hough transforms. We approx...

Numerical transform inversion can be useful to solve stochastic models arising in the performance evaluation of telecommunications and computer systems. We contribute to this technique in this paper by extending our recently developed variant of the Laguerre method for numerically inverting Laplace transforms to multidimensional Laplace transforms. An important application of multidimensional i...

On the other hand, whether the Christoffel symbol is the only connection which can be constructed from a symmetric second–rank tensor gμν remains an open question. In this note we exhibit a constructive demonstration of the uniqueness of the Christoffel symbol. Let us start by reviewing some simple results of tensor calculus. Let M be an n–dimensional differentiable manifold. Several geometric ...

Regression predictors are usually entered into a model without transformation. However, it is not unusual for regression relationships to be distinctly nonlinear. Fractional polynomials account for nonlinearity through real-valued power transformations of primary predictors. Adaptive methods have been developed for searching through alternative fractional polynomials based on one or more primar...

Geometric attacks are among the most challenging problems in present day data hiding. Such attacks are very simple to implement yet they can defeat most of the existing data hiding algorithms without causing serious perceptual image distortion. In this research, we report a novel method to estimate the geometric manipulation. Geometric attacks can very easily confuse the decoder unless it trans...

l1li' 11' In this note we derive optimal prediction formulas to be used in solving continuous time rational expectations models. In these derivations we employ Laplace transforms in a manner analogous to the use of z transforms for solving discrete time optimal prediction problems in Hansen and Sargent (1980a, Appendix A). The formulas are intended to play the same role for continuous time mode...