Spherical Harmonics

By Feng Dai, Yuan Xu. 2013

507 citations recorded by the source corpus.

This is Chapter 1 of the book {\it Approximation Theory and Harmonic Analysis on Spheres and Balls} by the authors. It provides a self-contained introduction to spherical harmonics. The book will be published as a title in {\it Springer Monographs in Mathematics} by Springer in 2013. The table of contents of the book is attached at the end of this file.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/b6db9ba1c6fdb13c897d5b18668312dab2b4a49c

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In Computational Theory and Mathematics

Citations in the corpus

Robust Optimality of Gaussian Noise Stability (2012, background): “A slightly less brief introduction is contained in [30]; for a full treatment, see [37].”
Reconstruction of Personalized 3D Face Rigs from Monocular Video (2016, methodology): “Since the scene is assumed to be purely Lambertian, the global illumination in the scene is represented using a spherical environment based on Spherical Harmonics (SH) basis functions [Müller 1966].”
State of the Art on Neural Rendering (2020, background): “ed to represent dense, distant scene lighting. These environment maps can be stored as non-parametric textures on a sphere or cube, or can be approximated by coefﬁcients of a spherical harmonic basis [Mül66]. Any of the parameters of a scene might be modeled as varying over time, allowing both anima”
InverseFaceNet: Deep Single-Shot Inverse Face Rendering From A Single Image (2017, methodology): “We thus represent the incident illumination on the face using second-order spherical harmonics (SH) [31, 34].”
Plane wave approximation of homogeneous Helmholtz solutions (2011, unknown): “,l are a basis of spherical harmonics of order l (see [6, 15, 19] or the Appendix of [12]).”
MoFA: Model-Based Deep Convolutional Face Autoencoder for Unsupervised Monocular Reconstruction (2017, methodology): “Illumination Model We represent scene illumination using Spherical Harmonics (SH) [34].”
Real-time expression transfer for facial reenactment (2015, methodology): “This suggests the use of a Sherical Harmonics (SH) basis [Müller 1966] for a low dimensional representation of the incident illumination.”
Learning an animatable detailed 3D face model from in-the-wild images (2020, methodology): “Illumination model: For face reconstruction, the most frequently-employed illumination model is based on Spherical Harmonics (SH) [44].”