Related papers: FSH3D: 3D Representation via Fibonacci Spherical H…
The mathematical representations of data in the Spherical Harmonic (SH) domain has recently regained increasing interest in the machine learning community. This technical report gives an in-depth introduction to the theoretical foundation…
Despite the impressive performance obtained by recent single-image hand modeling techniques, they lack the capability to capture sufficient details of the 3D hand mesh. This deficiency greatly limits their applications when high-fidelity…
We propose a new recursive method for simultaneous estimation of both the pose and the shape of a three-dimensional extended object. The key idea of the presented method is to represent the shape of the object using spherical harmonics,…
We discuss in some details a novel algorithm for performing partial-sky spherical harmonic transforms (SHT), building on the Fourier-sphere method of Reinecke et al (2023) handling efficiently high numbers of arbitrary locations on the…
Robot-assisted minimally invasive surgery benefits from enhancing dynamic scene reconstruction, as it improves surgical outcomes. While Neural Radiance Fields (NeRF) have been effective in scene reconstruction, their slow inference speeds…
Expressing head-related transfer functions (HRTFs) in spherical harmonic (SH) domain has been thoroughly studied as a method of obtaining continuity over space. However, HRTFs are functions not only of direction but also of frequency. This…
This paper introduces a generalised 3rd-order Spectral Representation Method for the simulation of multi-dimensional stochastic fields with asymmetric non-linearities. The simulated random fields satisfy a prescribed Power Spectrum and…
Recent progress in synthetic aperture sonar (SAS) technology and processing has led to significant advances in underwater imaging, outperforming previously common approaches in both accuracy and efficiency. There are, however, inherent…
Recent developments in machine learning and signal processing have resulted in many new techniques that are able to effectively capture the intrinsic yet complex properties of hyperspectral imagery. Tasks ranging from anomaly detection to…
Efficient frequency-domain Full Waveform Inversion (FWI) of long-offset/wide-azimuth node data can be designed with a few discrete frequencies. However, 3D frequency-domain seismic modeling remains challenging since it requires solving a…
We outline a numerical procedure to incorporate the crystal symmetries in the Helmholtz Fermi-surface harmonics basis set, which are the solutions of the Helmholtz equation defined on the Fermi surface. This improvement allows for an…
Second harmonic generation microscopy (SHG) is a powerful imaging modality which has found applications in investigating both biological and synthetic nanostructures. Like all optical microscopy techniques, the resolution of SHG is limited…
Fresnel incoherent correlation holography (FINCH) is a well-established digital holography technique for 3D imaging of objects illuminated by spatially incoherent light. FINCH has a higher lateral resolution of 1.5 times that of direct…
In this paper, we present the implicit equations for one special class of real-valued spherical harmonics with octahedral symmetry. Based on this representation, we construct the rotationally invariant measure of deviation from the…
The purpose of this work is to generalize the frozen Gaussian approximation (FGA) theory to solve the 3-D elastic wave equation and use it as the forward modeling tool for seismic tomography with high-frequency data. FGA has been previously…
Symmetry fractionalization describes the fascinating phenomena that excitations in a 2D topological system can transform under symmetry in a fractional way. For example in fractional quantum Hall systems, excitations can carry fractional…
Spherical harmonics (SH) have been extensively used as a basis for analyzing the morphology of particles in granular mechanics. The use of SH is facilitated by mapping the particle coordinates onto a unit sphere, in practice often a…
Scene understanding based on 3D Gaussian Splatting (3DGS) has recently achieved notable advances. Although 3DGS related methods have efficient rendering capabilities, they fail to address the inherent contradiction between the anisotropic…
This paper introduces a novel boundary integral approach of shape uncertainty quantification for the Helmholtz scattering problem in the framework of the so-called parametric method. The key idea is to construct an integration grid whose…
The 3D Gaussian Splatting (3D-GS) is a novel method for scene representation and view synthesis. Although Scaffold-GS achieves higher quality real-time rendering compared to the original 3D-GS, its fine-grained rendering of the scene is…