Spherical harmonics are widely used in 3D image processing due to their compactness and rotation properties. For example, it is quite easy to obtain rotation invariance by taking the magnitudes of the representation, similar to the power spectrum known from Fourier analysis. We propose a novel approach extending the spherical harmonic representation to tensors of higher order in a very efficien...

There is a lack of unified statistical modeling framework for cerebral shape asymmetry analysis in literature. Most previous approaches start with flipping the 3D magnetic resonance images (MRI). The anatomical correspondence across the hemispheres is then established by registering the original image to the flipped image. A difference of an anatomical index between these two images is used as ...

In this paper, we study and analyze seven state-of-the-art volumetric illumination methods, in order to determine their differences with respect to the underlying theoretical mathematical models and numerical problems potentially arising during implementation. The chosen models are half angle slicing, directional occlusion shading, multidirectional occlusion shading, shadow volume propagation, ...

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Chapter 2: Riemannian Symmetric Spaces and Related Structure Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

1. Calculus on spheres 2. Spherical Laplacian from Euclidean 3. Eigenvectors for the spherical Laplacian 4. Invariant integrals on spheres 5. L spectral decompositions on spheres 6. Sup-norms of spherical harmonics on Sn−1 7. Pointwise convergence of Fourier-Laplace series 8. Irreducibility of representation spaces for O(n) 9. Hecke’s identity • Appendix: Bernstein’s proof of Weierstraß approxi...

We view a spherical topological 3-manifold M, see [11] and [13], as a prototile on its cover M̃ = S. We studied in [7] the isometric actions of O(4, R) on the 3sphere S and gave its basis as well-known homogeneous Wigner polynomials in [5] eq.(37). An algorithm due to Everitt in [3] generates the homotopies for all spherical 3-manifolds M from five Platonic polyhedra. Using intermediate Coxeter ...

This paper examines filtering on a sphere, by first examining the roles of spherical harmonic magnitude and phase. We show that phase is more important than magnitude in determining the structure of a spherical function. We examine the properties of linear phase shifts in the spherical harmonic domain, which suggest a mechanism for constructing finiteimpulse-response (FIR) filters. We show that...

We provide an efficient algorithm for calculating, at appropriately chosen points on the two-dimensional surface of the unit sphere in R, the values of functions that are specified by their spherical harmonic expansions (a procedure known as the inverse spherical harmonic transform). We also provide an efficient algorithm for calculating the coefficients in the spherical harmonic expansions of ...

An algorithm is introduced for the rapid evaluation at appropriately chosen nodes on the two-dimensional sphere S2 in R3 of functions specified by their spherical harmonic expansions (known as the inverse spherical harmonic transform), and for the evaluation of the coefficients in spherical harmonic expansions of functions specified by their values at appropriately chosen points on S2 (known as...

The volume, location of the centroid, and second order moments of a threedimensional star-shaped object are determined in terms of the spherical harmonic coefficients of its boundary function. Bounds on the surface area of the object are derived in terms of the spherical harmonic coefficients as well. Sufficient conditions under which the moments and area computed from the truncated spherical h...