Related papers: Sifting Convolution on the Sphere
We revisit the spherical Radon transform, also called the Funk-Radon transform, viewing it as an axisymmetric convolution on the sphere. Viewing the spherical Radon transform in this manner leads to a straightforward derivation of its…
We present a description of the function space and the smoothness class associated with a convolutional network using the machinery of reproducing kernel Hilbert spaces. We show that the mapping associated with a convolutional network…
Topological transforms are parametrized families of topological invariants, which, by analogy with transforms in signal processing, are much more discriminative than single measurements. The first two topological transforms to be defined…
We consider the optical and transport properties in a model two-dimensional Hamiltonian which describes the merging of two Dirac points. At low energy, in the presence of an energy gap parameter $\Delta$, there are two distinct Dirac points…
We use spherical coordinates to devise a new exact solution to the governing equations of geophysical fluid dynamics for an inviscid and incompressible fluid with a general density distribution and subjected to forcing terms. The latter are…
Dorff, proved in [2] that the convolution of two harmonic right-half plane mappings is convex in the direction of real axis provided that the convolution is locally univalent and sense preserving. Later, it was shown in [3] that the…
We present a family of kernels for analysis of data generated by dynamical systems. These so-called cone kernels feature an explicit dependence on the dynamical vector field operating in the phase-space manifold, estimated empirically…
Our understanding of quantum field theory rests largely on explicit and controlled calculations in perturbation theory. Because of this, much recent effort has been devoted to improve our grasp of perturbative techniques on cosmological…
We consider the motion of a particle on a surface which is a small perturbation of the standard sphere. One may qualitatively describe the motion by means of a precessing great circle of the sphere. The observation is employed to derive a…
Deep Convolutional Neural Networks (CNNs) are empirically known to be invariant to moderate translation but not to rotation in image classification. This paper proposes a deep CNN model, called CyCNN, which exploits polar mapping of input…
We propose a spherical kernel for efficient graph convolution of 3D point clouds. Our metric-based kernels systematically quantize the local 3D space to identify distinctive geometric relationships in the data. Similar to the regular grid…
Convolution is a broadly useful operation with applications including signal processing, machine learning, probability, optics, polynomial multiplication, and efficient parsing. Usually, however, this operation is understood and implemented…
Euclidean deep learning is often inadequate for addressing real-world signals where the representation space is irregular and curved with complex topologies. Interpreting the geometric properties of such feature spaces has become paramount…
The large variety of Fourier transforms in geometric algebras inspired the straight forward definition of ``A General Geometric Fourier Transform`` in Bujack et al., Proc. of ICCA9, covering most versions in the literature. We showed which…
In this paper, we derive new shape descriptors based on a directional characterization. The main idea is to study the behavior of the shape neighborhood under family of transformations. We obtain a description invariant with respect to…
In this paper, we investigate the relationship between positive definite functions on the unit sphere $\sph$ and on the Euclidean space $\RR^d$. For the dimension $d$ to be odd, a new technique is developed to establish the inheritance of…
On a manifold or a closed subset of a Euclidean vector space, a retraction enables to move in the direction of a tangent vector while staying on the set. Retractions are a versatile tool to perform computational tasks such as optimization,…
Convolutional neural networks (CNNs) have been widely used in various vision tasks, e.g. image classification, semantic segmentation, etc. Unfortunately, standard 2D CNNs are not well suited for spherical signals such as panorama images or…
We consider a semi-classical Dirac operator in arbitrary spatial dimensions with a smooth potential whose partial derivatives of any order are bounded by suitable constants. We prove that the distribution kernel of the inverse operator…
Dirac operators on curved space-times are introduced with the help of a new point-view that observers have to be included in the formulation of natural laws. The class of Dirac operators are Lorentz invariant in the sense that the…