Related papers: Squares that Look Round: Transforming Spherical Im…
We study the spherical mean transform on $\rN^n$. The transform is characterized by the Euler-Poisson-Darboux equation. By looking at the spherical harmonic expansions, we obtain a system of 1+1-dimension hyperbolic equations, which provide…
Recent advances in implicit neural representations have made them a popular choice for modeling 3D geometry, achieving impressive results in tasks such as shape representation, reconstruction, and learning priors. However, directly editing…
Spin (spherical) random fields are very important in many physical applications, in particular they play a key role in Cosmology, especially in connection with the analysis of the Cosmic Microwave Background radiation. These objects can be…
Stable and reliable numerical integration of second-order radial equations in the fields of classical black holes can be performed by using the Pr\"ufer transformation and by passing to the use of phase functions, which allows uniquely…
Spherical manifolds yield cosmic spaces with positive curvature. They result by closing pieces from the sphere used by Einstein for his initial cosmology. Harmonic analysis on the manifolds aims at explaining the observed low amplitudes at…
A novel effect of rotation in the optical image of structures in an opaque screen is presented. Theoretical calculations and experimental validation are presented. The features and the conditions of this effect are discussed.
We review the methods used to study the orbital structure and chaotic properties of various galactic models and to construct self-consistent equilibrium solutions by Schwarzschild's orbit superposition technique. These methods are…
We give a simplified proof of J. A. Wolf's classification of finite groups that can act freely and isometrically on a round sphere of some dimension. We slightly improve the classification by removing some non-obvious redundancy. The groups…
The regular fractional transformations of the extended quaternionic space have been recently introduced as variants of the classical linear fractional transformations. These variants have the advantage of being included in the class of…
Connected operators are filtering tools that act by merging elementary regions of an image. A popular strategy is based on tree-based image representations: for example, one can compute an attribute on each node of the tree and keep only…
We present a flexible interactive 3D morpho-kinematical modeling application for astrophysics. Compared to other systems, our application reduces the restrictions on the physical assumptions, data type and amount that is required for a…
We propose to use transformation optics to generate a general illusion such that an arbitrary object appears to be like some other object of our choice. This is achieved by using a remote device that transforms the scattered light outside a…
Covariance representations are developed for the uniform distributions on the Euclidean spheres in terms of spherical gradients and Hessians. They are applied to derive a number of Sobolev type inequalities and to recover and refine the…
In this paper, we study an unconventional but practically meaningful reversibility problem of commonly used image filters. We broadly define filters as operations to smooth images or to produce layers via global or local algorithms. And we…
We consider rational surface automorphisms with positive entropy. A Fatou component is said to be a rotation domain if the automorphism induces a torus action on it. Here we construct a rational surface automorphism with positive entropy…
The spinor representation of spin-1/2 states can equally well be mapped to a single unit quaternion, yielding a new perspective despite the equivalent mathematics. This paper first demonstrates a useable map that allows Bloch-sphere…
Metamorphism is a recently introduced integral transform, which is useful in solving partial differential equations. Basic properties of metamorphism can be verified by direct calculations. In this paper we present metamorphism as a sort of…
We present in this paper new multiscale transforms on the sphere, namely the isotropic undecimated wavelet transform, the pyramidal wavelet transform, the ridgelet transform and the curvelet transform. All of these transforms can be…
This work presents a novel framework for spherical mesh parameterization. An efficient angle-preserving spherical parameterization algorithm is introduced, which is based on dynamic Yamabe flow and the conformal welding method with solid…
The photorealistic rendering of the transparent effect of translucent objects is a hot research topic in recent years. A real-time photorealistic rendering and material dynamic editing method for the diffuse scattering effect of translucent…