FFTs for the 2-Sphere-Improvements and Variations

By D. Healy, D. Rockmore, Peter J. Kostelec, S. Moore. 1996

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Spherical CNNs (2018, background): “Other important works include (Driscoll and Healy, 1994; Healy et al., 2003; Potts et al., 1998; Kunis and Potts, 2003; Drake et al., 2008; Maslen, 1998; Rockmore, 2004; Kostelec and Rockmore, 2007; 2008; Potts et al., 2009; Makadia et al., 2007; Gutman et al., 2008).”
FFTs on the Rotation Group (2008, methodology): “The behavior reflected in the results in Table 6 is similar to that reported in [18].”
A fast algorithm for nonequispaced Fourier transforms on the rotation group (2009, methodology): “Other stabilization methods for the fast spherical harmonic transform were presented in [30, 11].”
Wavelets on the sphere: implementation and approximations (2002, background): “An example of a different choice, both for the weights and for the discretization technique, is that of a band-limited spherical function, as considered in [13].”
Tools for 3D-object retrieval: Karhunen-Loeve transform and spherical harmonics (2001, background): “We cannot give more details here and refer to the survey and software in [1].”
3D object classification and retrieval with Spherical CNNs (2017, background): “Note that there are faster algorithms available [9, 14], which we did not attempt to implement.”
Group theoretical methods in machine learning (2008, background): “One of the best sources of inspiration for applications of these ideas is the sequence of papers [Maslen and Rockmore, 1997][Rockmore, 1997] and [Healy et al., 1996], while without question the key book on applying ideas from finite group theory to statistics is [Diaconis, 1988] .”
Genus zero surface conformal mapping and its application to brain surface mapping (2004, methodology): “to using the fast spherical harmonic transformation as described in [25].”
Shape Registration with Spherical Cross Correlation (2008, methodology): “Spherical harmonics were computed with the spherical FFT of [13] and cross correlation was computed with the help of the fftw library [14].”
SHREC 2007 3 D Shape Retrieval Contest (2006, methodology): “[19] Princeton Shape Benchmark, http://shape.”
The design of an optimal filter for monthly GRACE gravity models (2008, unknown): “(17) efficiently (e.g. Healy et al. 2003).”
A novel set of rotationally and translationally invariant features for images based on the non-commutative bispectrum (2007, methodology): “We represent an image as an intensity function h : R2 → [0, 1] with support confined to a compact region of the plane, for example, the square [−0.5, 0.5] 2 .”
Correspondence-free Structure from Motion (2007, methodology): “Jin et al. (2003) have applied a direct method for simultaneous matching of regions and 3D-motion estimation over time by exploiting photometric constraints.”