Related papers: Spherical framelets from spherical designs
This paper focuses on real-time all-frequency image-based rendering using an innovative solution for run-time computation of light transport. The approach is based on new results derived for non-linear phase shifting in the Haar wavelet…
In the study of nanobubbles, nanodroplets or nanolenses immobilised on a substrate, a cross-section of a spherical-cap is widely applied to extract geometrical information from atomic force microscopy (AFM) topographic images. In this…
We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet…
The detection and characterization of gravitational wave signals from compact binary coalescence events relies on accurate waveform templates in the frequency domain. The stationary phase approximation (SPA) can be used to compute…
Shearlet theory has become a central tool in analyzing and representing 2D data with anisotropic features. Shearlet systems are systems of functions generated by one single generator with parabolic scaling, shearing, and translation…
Convolutional Neural Networks (CNNs) are a cornerstone of the Deep Learning toolbox and have led to many breakthroughs in Artificial Intelligence. These networks have mostly been developed for regular Euclidean domains such as those…
It is a challenging task to accurately perform semantic segmentation due to the complexity of real picture scenes. Many semantic segmentation methods based on traditional deep learning insufficiently captured the semantic and appearance…
The recent researches in Deep Convolutional Neural Network have focused their attention on improving accuracy that provide significant advances. However, if they were limited to classification tasks, nowadays with contributions from…
This paper proposes a sketching strategy based on spherical designs, which is applied to the classical spherical basis function approach for massive spherical data fitting. We conduct theoretical analysis and numerical verifications to…
Inspired by recent interest in geometric deep learning, this work generalises the recently developed Slepian scale-discretised wavelets on the sphere to Riemannian manifolds. Through the sifting convolution, one may define translations and,…
Recent progress in large-scale metasurfaces requires phase profiles beyond traditional hyperbolic designs. We show hyperbolic phase distributions cause spherical aberration from mismatched light propagation geometry and unrealistic phase…
Inspired by the boolean discrepancy problem, we study the following optimization problem which we term \textsc{Spherical Discrepancy}: given $m$ unit vectors $v_1, \dots, v_m$, find another unit vector $x$ that minimizes $\max_i \langle x,…
Spherical CNNs generalize CNNs to functions on the sphere, by using spherical convolutions as the main linear operation. The most accurate and efficient way to compute spherical convolutions is in the spectral domain (via the convolution…
The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…
Automatic vessel segmentation is paramount for developing next-generation interventional navigation systems. However, current approaches suffer from suboptimal segmentation performances due to significant challenges in intraoperative images…
In the fields of nanoscience and nanotechnology, it is important to be able to functionalize surfaces chemically for a wide variety of applications. Scanning tunneling microscopes (STMs) are important instruments in this area used to…
In this talk we present the exact solution of the most general one-dimensional $O(N)$-invariant spin model taking values in the sphere $S^{N-1}$, with nearest-neighbour interactions, and we discuss the possible continuum limits. All these…
Objective: The present study introduces a fractional wavelet scattering network (FrScatNet), which is a generalized translation invariant version of the classical wavelet scattering network (ScatNet). Methods: In our approach, the FrScatNet…
Finding efficient representations is one of the most challenging and heavily sought problems in mathematics. Representation using shearlets recently receives a lot of attention due to their desirable properties in both theory and…
Ensuring data privacy and protection has become paramount in the era of deep learning. Unlearnable examples are proposed to mislead the deep learning models and prevent data from unauthorized exploration by adding small perturbations to…