Related papers: Differentiable and accelerated wavelet transforms …

Very recently, Window-based Transformers, which computed self-attention within non-overlapping local windows, demonstrated promising results on image classification, semantic segmentation, and object detection. However, less study has been…

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 general construction of two types of differential forms, based on any $(n{-}3)$-dimensional subspace in the kinematic space of $n$ massless particles. The first type is the so-called projective, scattering forms in kinematic…

The recent success of neural networks enables a better interpretation of 3D point clouds, but processing a large-scale 3D scene remains a challenging problem. Most current approaches divide a large-scale scene into small regions and combine…

Efficient representations of multivariate functions are critical for the design of state-of-the-art methods of data restoration and image reconstruction. In this work, we consider the representation of spatio-temporal data such as temporal…

Real time visualization and tracking of colloidal particles with 3D resolution is essential for probing the local structure and dynamics in complex fluids. Although tracking translational motion of spherical colloids is well-known,…

The suboptimal performance of wavelets with regard to the approximation of multivariate data gave rise to new representation systems, specifically designed for data with anisotropic features. Some prominent examples of these are given by…

We propose a new convolution called Dynamic Region-Aware Convolution (DRConv), which can automatically assign multiple filters to corresponding spatial regions where features have similar representation. In this way, DRConv outperforms…

Existing networks directly learn feature representations on 3D point clouds for shape analysis. We argue that 3D point clouds are highly redundant and hold irregular (permutation-invariant) structure, which makes it difficult to achieve…

A wavelet scattering network computes a translation invariant image representation, which is stable to deformations and preserves high frequency information for classification. It cascades wavelet transform convolutions with non-linear…

We explore the use of multiresolution analysis techniques as texture attributes for seismic image characterization, especially in representing subsurface structures in large migrated seismic data. Namely, we explore the Gaussian pyramid,…

In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…

In this paper, we investigate in detail the structures of the variational characterization $A_{N,t}$ of the spherical $t$-design, its gradient $\nabla A_{N,t}$, and its Hessian $\mathcal{H}(A_{N,t})$ in terms of fast spherical harmonic…

Transformers are widely used deep learning architectures. Existing transformers are mostly designed for sequences (texts or time series), images or videos, and graphs. This paper proposes a novel transformer model for massive (up to a…

Video prediction is a pixel-wise dense prediction task to infer future frames based on past frames. Missing appearance details and motion blur are still two major problems for current predictive models, which lead to image distortion and…

We describe a new method involving wavelet transforms for deriving the wind velocity associated with atmospheric turbulence layers from Generalized SCIDAR measurements. The algorithm analyses the cross-correlation of a series of…

Upper-ocean flows are a multi-scale jigsaw puzzle of turbulence and waves. Characterizing these flows is essential for understanding their role in redistributing heat, carbon, and nutrients, yet power spectral analysis cannot always…

An algorithm is presented to update the multi-fractal spectrum of a time series in constant time when new data arrives. The discrete wavelet transform (DWT) of the time series is first updated for the new data value. This is done optimally…

Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…

Dense pixelwise prediction such as semantic segmentation is an up-to-date challenge for deep convolutional neural networks (CNNs). Many state-of-the-art approaches either tackle the loss of high-resolution information due to pooling in the…