The Kustaanheimo-Stiefel transform turns a gravitational two-body problem into a harmonic oscillator, by going to four dimensions. In addition to the mathematicalphysics interest, the KS transform has proved very useful in N -body simulations, where it helps handle close encounters. Yet the formalism remains somewhat arcane, with the role of the extra dimension being especially mysterious. This...

In this chapter, we illustrate the properties of the continuous shearlet transform with respect to its ability to describe the set of singularities of multidimensional functions and distributions. This is of particular interest since singularities and other irregular structures typically carry the most essential information in multidimensional phenomena. Consider, for example, the edges of natu...

We propose a stable and fast reconstruction technique for parallel-beam (PB) tomographic X-ray imaging, relying on the discrete pseudo-polar (PP) Radon transform. Our main contribution is a resampling method, based on modern sampling theory, that transforms the acquired PB measurements to a PP grid. The resampling process is both fast and accurate, and in addition, simultaneously denoises the m...

In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this der...

It is now widely acknowledged that analyzing the intrinsic geometrical features of an underlying image is essentially needed in image processing. In order to achieve this, several directional image representation schemes have been proposed. In this report, we develop the discrete shearlet transform (DST) which provides efficient multiscale directional representation. We also show that the imple...

Currently popular feature extraction tools (e.g., Gabor, wavelet analysis) do not economically represent edges in images. As a step towards solving this problem, the wedgelet transform was recently proposed [1]; this transform provides nearly optimal representation of objects in the Horizon model, as measured by the minimax mean-squared error. However, there is no reason to assume that the comp...

Transform image processing methods are methods that work in domains of image transforms, such as Discrete Fourier, Discrete Cosine, Wavelet and alike. They are the basic tool in image compression, in image restoration, in image resampling and geometrical transformations and can be traced back to early 1970-ths. The paper presents a review of these methods with emphasis on their comparison and r...

The skeleton is a continuous planar shape for representation as a kind of primitive of the original. The skeleton efficiently concentrates the topological information of the original shape. It is particularly useful for representing amorphous, irregular shapes that cannot be treated by more conventional geometrical methods. The possible applications include the creation of shape primitives, cur...

This work employs high-resolution 3D thermomechanical numerical models of the incipient oceanic spreading to investigate nucleation and long-term evolution of ridge-transform spreading patterns. The Eulerian–Lagrangian visco-plastic model allows for large strains and accounts for plate cooling by both heat conduction and hydrothermal circulation as well as for partial melting of the asthenosphe...