Spherical harmonics scaling

Wang, Jiaping; Xu, Kun; Zhou, Kun; Lin, Stephen; Hu, Shi‐Min; Guo, Baining

doi:10.1007/s00371-006-0057-8

Cited by 10 publications

(18 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It was noted by authors in [4] that the scaling of spherical functions may be regarded as a linear operator that acts on the vector of spherical harmonic coefficients. This method essentially provides exact scaling, with the remarks that follow.…”

Section: Comparison With An Existing Methodsmentioning

confidence: 99%

“…Since the complete spherical Fourier transform of a spherical function with the bandwidth B has B 2 samples, and given that the complexity of linear interpolation is proportional to the number of output samples, it is easy to see that the proposed method has a complexity of O(k 2 B 2 ). On the other hand, the method proposed in [4] involves multiplying the coefficient vector of size B 2 by a scaling matrix of size B 2 × B 2 . This matrix, however, is a sparse matrix, with only B(2B 2 + 1)/3 non-zero entries.…”

Section: Comparison With An Existing Methodsmentioning

confidence: 99%

“…Therefore, the complexity of their method is O(k 3 B 3 ) (again by assuming the appropriate bandwidth scaling). The method proposed in [4] requires the scaling matrices to be precomputed. If the application calls for a relatively high bandwidth, storing these matrices may become a problem.…”

Section: Comparison With An Existing Methodsmentioning

confidence: 99%

“…Various applications require scaling (dilating or contracting) of the function on a sphere and if the function is represented by its Fourier coefficients, it would be beneficial to perform the scaling directly in the Fourier domain. See for example spherical wavelets, [1], [2], spherical filter banks, [3], illumination in computer graphics [4] or spherical point density estimation, [5], [6]. Spectral computation is further facilitated by the development of fast spherical transform algorithms [7], [8] analogous to the Euclidean fast Fourier transform.…”

Section: Introductionmentioning

confidence: 99%

“…A linear operator formulation of spectral domain scaling has been proposed in [4]. We propose an approximate method that is very simple in comparison to the existing methods -it involves resampling of the spectrum, and the computational cost is equal to the cost of the resampling step.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Efficient Approximate Scaling of Spherical Functions in the Fourier Domain With Generalization to Hyperspheres

Petrinovic

2010

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

Abstract-We propose a simple model for approximate scaling of spherical functions in the Fourier domain. The proposed scaling model is analogous to the scaling property of the classical Euclidean Fourier transform. Spherical scaling is used for example in spherical wavelet transform and filter banks or illumination in computer graphics. Since the function that requires scaling is often represented in the Fourier domain, our method is of significant interest. Furthermore, we extend the result to higher-dimensional spheres. We show how this model follows naturally from consideration of a hypothetical continuous spectrum. Experiments confirm the applicability of the proposed method for several signal classes. The proposed algorithm is compared to an existing linear operator formulation.

show abstract

Section: Comparison With An Existing Methodsmentioning

confidence: 99%

Section: Comparison With An Existing Methodsmentioning

confidence: 99%

Section: Comparison With An Existing Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Efficient Approximate Scaling of Spherical Functions in the Fourier Domain With Generalization to Hyperspheres

Petrinovic

2010

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

show abstract

A Globally Optimal Approach for 3D Elastic Motion Estimation from Stereo Sequences

Wang

Tao

2010

Computer Vision – ECCV 2010

View full text Add to dashboard Cite

Dense and markerless elastic 3D motion estimation based on stereo sequences is a challenge in computer vision. Solutions based on scene flow and 3D registration are mostly restricted to simple non-rigid motions, and suffer from the error accumulation. To address this problem, this paper proposes a globally optimal approach to non-rigid motion estimation which simultaneously recovers the 3D surface as well as its non-rigid motion over time. The instantaneous surface of the object is represented as a set of points which is reconstructed from the matched stereo images, meanwhile its deformation is captured by registering the points over time under spatio-temporal constraints. A global energy is defined on the constraints of stereo, spatial smoothness and temporal continuity, which is optimized via an iterative algorithm to approximate the minimum. Our extensive experiments on real video sequences including different facial expressions, cloth flapping, flag waves, etc. proved the robustness of our method and showed the method effectively handles complex nonrigid motions.

show abstract