Related papers: Second-Generation Curvelets on the Sphere
A new construction of a directional continuous wavelet analysis on the sphere is derived herein. We adopt the harmonic scaling idea for the spherical dilation operator recently proposed by Sanz et al. but extend the analysis to a more…
This paper constructs the first quantum algorithm for wavelet packet transforms with a "parabolic scaling" tree structure, sometimes called wave atom transforms. Classically, wave atoms are used to construct sparse representations of…
The two-dimensional discrete wavelet transform has a huge number of applications in image-processing techniques. Until now, several papers compared the performance of such transform on graphics processing units (GPUs). However, all of them…
In a recent paper, we analyzed the properties of a new kind of spherical wavelets (called needlets) for statistical inference procedures on spherical random fields; the investigation was mainly motivated by applications to cosmological…
A fundamental challenge in text-to-3D face generation is achieving high-quality geometry. The core difficulty lies in the arbitrary and intricate distribution of vertices in 3D space, making it challenging for existing models to establish…
In analogy to classical spherical t-design points, we introduce the concept of t-design curves on the sphere. This means that the line integral along a t-design curve integrates polynomials of degree t exactly. For low degrees we construct…
A fast and exact algorithm is developed for the spin +-2 spherical harmonics transforms on equi-angular pixelizations on the sphere. It is based on the Driscoll and Healy fast scalar spherical harmonics transform. The theoretical exactness…
In this work, we propose "tangent images," a spherical image representation that facilitates transferable and scalable $360^\circ$ computer vision. Inspired by techniques in cartography and computer graphics, we render a spherical image to…
We describe a hybrid Fourier/direct space convolution algorithm for compact radial (azimuthally symmetric) kernels on the sphere. For high resolution maps covering a large fraction of the sky, our implementation takes advantage of the…
New implicit and implicit-explicit time-stepping methods for the wave equation in second-order form are described with application to two and three-dimensional problems discretized on overset grids. The implicit schemes are single step,…
Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation…
A fast algorithm for Antoine and Vandergheynst's (1998) directional continuous spherical wavelet transform (CSWT) is presented. Computational requirements are reduced by a factor of O(\sqrt{N}), when N is the number of pixels on the sphere.…
Omnidirectional images and spherical representations of $3D$ shapes cannot be processed with conventional 2D convolutional neural networks (CNNs) as the unwrapping leads to large distortion. Using fast implementations of spherical and…
Estimating accurate high-dimensional transformations remains very challenging, especially in a clinical setting. In this paper, we introduce a multiscale parameterization of deformations to enhance registration and atlas estimation in the…
We present an efficient, trivially parallelizable algorithm to compute offset surfaces of shapes discretized using a dexel data structure. Our algorithm is based on a two-stage sweeping procedure that is simple to implement and efficient,…
Real-world graphs naturally exhibit hierarchical or cyclical structures that are unfit for the typical Euclidean space. While there exist graph neural networks that leverage hyperbolic or spherical spaces to learn representations that embed…
In an exploration paper, {\it L. Chen, Algorithms for Deforming and Contracting Simply Connected Discrete Closed Manifolds (I)}, we designed algorithms for deforming and contracting a simply connected discrete closed manifold to a discrete…
Wavelet-based segmentation approaches are widely used for texture segmentation purposes because of their ability to characterize different textures. In this paper, we assess the influence of the chosen wavelet and propose to use the…
We propose a differentiable sphere tracing algorithm to bridge the gap between inverse graphics methods and the recently proposed deep learning based implicit signed distance function. Due to the nature of the implicit function, the…
Transposed convolution is crucial for generating high-resolution outputs, yet has received little attention compared to convolution layers. In this work we revisit transposed convolution and introduce a novel layer that allows us to place…