Spherical Harmonics: Difference between revisions
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Spherical Harmonics are a set of orthonormal basis functions | Spherical Harmonics are a set of orthonormal basis functions | ||
==Background== | |||
===Harmonic Function=== | |||
[https://en.wikipedia.org/wiki/Harmonic_function Wikipedia Reference]<br> | |||
A function <math>f: \mathbb{R}^n \rightarrow \mathbb{R}</math> is a harmonic function if it satisfies Laplace's equation: | |||
* The Laplacian (or trace of the hessian) is zero. | |||
* <math>\Delta f = \frac{\partial^2f}{\partial x_1^2} + \frac{\partial^2f}{\partial x_2^2} + \cdots + \frac{\partial^2f}{\partial x_n^2} = 0</math> | |||
==Definition== | ==Definition== | ||
Revision as of 13:20, 6 November 2019
Spherical Harmonics are a set of orthonormal basis functions
Background
Harmonic Function
Wikipedia Reference
A function \(\displaystyle f: \mathbb{R}^n \rightarrow \mathbb{R}\) is a harmonic function if it satisfies Laplace's equation:
- The Laplacian (or trace of the hessian) is zero.
- \(\displaystyle \Delta f = \frac{\partial^2f}{\partial x_1^2} + \frac{\partial^2f}{\partial x_2^2} + \cdots + \frac{\partial^2f}{\partial x_n^2} = 0\)
Definition
Applications
Saliency
Ruofei did a project on Saliency using Spherical Harmonics as part of his PhD dissertation.