An Approximate and Efficient Method for Optimal Rotation Alignment of 3D Models

Kazhdan, Michael

doi:10.1109/tpami.2007.1032

Cited by 69 publications

(43 citation statements)

References 18 publications

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“…has been widely used in computer graphics, for inverse rendering [Ramamoorthi and Hanrahan 2001], precomputed radiance transfer , and shape analysis [Kazhdan 2007]. SH are also used for importance sampling of spherical functions [Jarosz et al 2009] and for performing arbitrary BRDF shading for lowfrequency lighting .…”

Section: Spherical Harmonics In Graphics Spherical Harmonics (Sh)mentioning

confidence: 99%

Variance analysis for Monte Carlo integration

et al. 2015

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We propose a new spectral analysis of the variance in Monte Carlo integration, expressed in terms of the power spectra of the sampling pattern and the integrand involved. We build our framework in the Euclidean space using Fourier tools and on the sphere using spherical harmonics. We further provide a theoretical background that explains how our spherical framework can be extended to the hemispherical domain. We use our framework to estimate the variance convergence rate of different state-of-the-art sampling patterns in both the Euclidean and spherical domains, as the number of samples increases. Furthermore, we formulate design principles for constructing sampling methods that can be tailored according to available resources. We validate our theoretical framework by performing numerical integration over several integrands sampled using different sampling patterns.

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Section: Spherical Harmonics In Graphics Spherical Harmonics (Sh)mentioning

confidence: 99%

Variance analysis for Monte Carlo integration

et al. 2015

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“…The most natural way of the generalization of the complex moments into 3D leads through so-called spherical harmonics (e.g., [8] among others).…”

Section: Complex Moments In 3dmentioning

confidence: 99%

“…The method of geometric primitives of Xu and Li [6,7] yields the same results. Kazhdan [8] studied registration of objects differing by 3D rotation, Kakarala and Mao [9] used bispectrum for derivation of TRS invariants. The work of Lo and Don [10] has the biggest impact on this area because they derived 3D TRS invariants from complex moments and the influence of rotation symmetry on the recognition can be in this representation advantageously studied.…”

Section: Introductionmentioning

confidence: 99%

Recognition of Symmetric 3D Bodies

Suk

Flusser

2014

Symmetry

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The paper deals with the recognition of symmetric three-dimensional (3D) bodies that can be rotated and translated. We provide a complete list of all existing combinations of rotation and reflection symmetries in 3D. We define 3D complex moments by means of spherical harmonics, and the influence of individual symmetry groups on complex moment values is studied. Each particular symmetry pre-defines certain moment values. These moments can no longer differentiate between two objects of the same symmetry, which decreases the recognition power of the feature set. They should not be included when constructing the invariants. Translation and rotation invariants up to the fourth order are presented and their performance is studied on both artificial and real data.

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“…By transforming the alignment problem into a correlation problem and substituting the real valued function on a 2-sphere with their spherical harmonics expansions, efficient signal processing techniques can be used to find the optimal rotation [9]. However, the aligning result and running time is affected by the band-width of expansion.…”

Section: Related Workmentioning

confidence: 99%

Globally optimal rotation alignment of spherical surfaces with associated scalar values

Pan

Skala

Müller

2013

3D Res

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Abstract. We propose a new approach to global optimization algorithm based on controlled random search techniques for rotational alignment of spherical surfaces with associated scalar values. To reduce the distortion in correspondence and increase efficiency, the spherical surface is first re-sampled using a geodesic sphere. The rotation in space is represented using the modified Rodrigues parameters.Correspondence between two spherical surfaces is implemented in the parametric domain. We applied the methods to the alignment of beam patterns computed from the outer ear shapes of bats. The proposed method is compared with other approaches such as alignment based on principal component analysis (PCA), exhaustive search in the discrete space of rotations defined by Euler angles and direct search using uniform samples over the rotation group SO(3). Experimental results demonstrate that the proposed rotation alignment obtained using the proposed algorithm has a high degree of precision and give the best result among the other four approaches.

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An Approximate and Efficient Method for Optimal Rotation Alignment of 3D Models

Cited by 69 publications

References 18 publications

Variance analysis for Monte Carlo integration

Variance analysis for Monte Carlo integration

Recognition of Symmetric 3D Bodies

Globally optimal rotation alignment of spherical surfaces with associated scalar values

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