Algorithm 888: Spherical Harmonic Transform Algorithms
ACM Transactions on Mathematical Software (TOMS)
Representations of SO(3) and angular polyspectra
Journal of Multivariate Analysis
Eigendecomposition of images correlated on S1, S2, and SO(3) using spectral theory
IEEE Transactions on Image Processing
An illustration of eigenspace decomposition for illumination invariant pose estimation
SMC'09 Proceedings of the 2009 IEEE international conference on Systems, Man and Cybernetics
On azimuthally symmetric 2-sphere convolution
Digital Signal Processing
Short note: Efficient and accurate rotation of finite spherical harmonics expansions
Journal of Computational Physics
On the effective dimension of light transport
EGSR'10 Proceedings of the 21st Eurographics conference on Rendering
Journal of Approximation Theory
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We pose and solve the analogue of Slepian's time-frequency concentration problem on the surface of the unit sphere to determine an orthogonal family of strictly bandlimited functions that are optimally concentrated within a closed region of the sphere or, alternatively, of strictly spacelimited functions that are optimally concentrated in the spherical harmonic domain. Such a basis of simultaneously spatially and spectrally concentrated functions should be a useful data analysis and representation tool in a variety of geophysical and planetary applications, as well as in medical imaging, computer science, cosmology, and numerical analysis. The spherical Slepian functions can be found by solving either an algebraic eigenvalue problem in the spectral domain or a Fredholm integral equation in the spatial domain. The associated eigenvalues are a measure of the spatiospectral concentration. When the concentration region is an axisymmetric polar cap, the spatiospectral projection operator commutes with a Sturm--Liouville operator; this enables the eigenfunctions to be computed extremely accurately and efficiently, even when their area-bandwidth product, or Shannon number, is large. In the asymptotic limit of a small spatial region and a large spherical harmonic bandwidth, the spherical concentration problem reduces to its planar equivalent, which exhibits self-similarity when the Shannon number is kept invariant.