Spherical harmonic-based random fields based on real particle 3D data: Improved numerical algorithm and quantitative comparison to real particles

We present a general method for estimating the isotropy violation of random fields on a sphere using a Bayesian formalism. We use Bipolar Spherical Harmonic (BipoSH) representation of general covariance structure on the sphere. Our approach promises to provide a robust quantitative evaluation of the evidence for SI violation-related anomalies in the CMB sky by estimating the BipoSH spectra along with their complete posterior.

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Invariant Features for 3D-Data based on Group Integration using Directional Information and Spherical Harmonic Expansion

18th International Conference on Pattern Recognition (ICPR'06) ◽

10.1109/icpr.2006.721 ◽

2006 ◽

Cited By ~ 14

Author(s):

M. Reisert ◽

H. Burkhardt

Keyword(s):

Spherical Harmonic ◽

Spherical Harmonic Expansion ◽

Directional Information ◽

Invariant Features ◽

3D Data ◽

Group Integration

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Spherical harmonic-based random fields for aggregates used in concrete

Powder Technology ◽

10.1016/j.powtec.2006.03.026 ◽

2006 ◽

Vol 166 (3) ◽

pp. 123-138 ◽

Cited By ~ 49

Author(s):

M. Grigoriu ◽

E. Garboczi ◽

C. Kafali

Keyword(s):

Random Fields ◽

Spherical Harmonic

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Isotropic sparse regularization for spherical harmonic representations of random fields on the sphere

Applied and Computational Harmonic Analysis ◽

10.1016/j.acha.2019.01.005 ◽

2020 ◽

Vol 49 (1) ◽

pp. 257-278 ◽

Cited By ~ 4

Author(s):

Quoc Thong Le Gia ◽

Ian H. Sloan ◽

Robert S. Womersley ◽

Yu Guang Wang

Keyword(s):

Random Fields ◽

Spherical Harmonic ◽

Sparse Regularization

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3D Data Segmentation by Local Classification and Markov Random Fields

2011 International Conference on 3D Imaging, Modeling, Processing, Visualization and Transmission ◽

10.1109/3dimpvt.2011.34 ◽

2011 ◽

Cited By ~ 8

Author(s):

Federico Tombari ◽

Luigi Di Stefano

Keyword(s):

Random Fields ◽

Markov Random Fields ◽

Local Classification ◽

Markov Random ◽

Data Segmentation ◽

3D Data

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Toward an alignment of the actin molecule within the actin filament

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100075981 ◽

1983 ◽

Vol 41 ◽

pp. 450-451

Author(s):

P.R. Smith ◽

W.E. Fowler ◽

U. Aebi

Keyword(s):

Actin Filament ◽

Diffraction Data ◽

Quantitative Estimate ◽

Molecular Model ◽

Quantitative Comparison ◽

Regulatory Proteins ◽

Essential Information ◽

X Ray ◽

Maximum Resolution ◽

Lack Of Information

An understanding of the specific interactions of actin with regulatory proteins has been limited by the lack of information about the structure of the actin filament. Molecular actin has been studied in actin-DNase I complexes by single crystal X-ray analysis, to a resolution of about 0.6nm, and in the electron microscope where two dimensional actin sheets have been reconstructed to a maximum resolution of 1.5nm. While these studies have shown something of the structure of individual actin molecules, essential information about the orientation of actin in the filament is still unavailable.The work of Egelman & DeRosier has, however, suggested a method which could be used to provide an initial quantitative estimate of the orientation of actin within the filament. This method involves the quantitative comparison of computed diffraction data from single actin filaments with diffraction data derived from synthetic filaments constructed using the molecular model of actin as a building block. Their preliminary work was conducted using a model consisting of two juxtaposed spheres of equal size.

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Direct phase determination in electron crystallography: small organic molecules

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100130468 ◽

1992 ◽

Vol 50 (2) ◽

pp. 1166-1167

Author(s):

Douglas L. Dorset

Keyword(s):

Organic Molecules ◽

Data Sets ◽

Temperature Structure ◽

3D Analysis ◽

Intensity Data ◽

Electron Crystallography ◽

Phase Determination ◽

Measured Intensity ◽

3D Data

The quantitative use of electron diffraction intensity data for the determination of crystal structures represents the pioneering achievement in the electron crystallography of organic molecules, an effort largely begun by B. K. Vainshtein and his co-workers. However, despite numerous representative structure analyses yielding results consistent with X-ray determination, this entire effort was viewed with considerable mistrust by many crystallographers. This was no doubt due to the rather high crystallographic R-factors reported for some structures and, more importantly, the failure to convince many skeptics that the measured intensity data were adequate for ab initio structure determinations.We have recently demonstrated the utility of these data sets for structure analyses by direct phase determination based on the probabilistic estimate of three- and four-phase structure invariant sums. Examples include the structure of diketopiperazine using Vainshtein's 3D data, a similar 3D analysis of the room temperature structure of thiourea, and a zonal determination of the urea structure, the latter also based on data collected by the Moscow group.

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The quantitative comparison of experimental and simulated diffraction contrast images

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010013688x ◽

1995 ◽

Vol 53 ◽

pp. 102-103

Author(s):

Stuart McKernan

Keyword(s):

Image Processing ◽

Personal Computer ◽

Close Agreement ◽

Quantitative Comparison ◽

Image Simulation ◽

Computing Power ◽

Diffraction Contrast ◽

Simulated Images ◽

Made In

For many years the concept of quantitative diffraction contrast experiments might have consisted of the determination of dislocation Burgers vectors using a g.b = 0 criterion from several different 2-beam images. Since the advent of the personal computer revolution, the available computing power for performing image-processing and image-simulation calculations is enormous and ubiquitous. Several programs now exist to perform simulations of diffraction contrast images using various approximations. The most common approximations are the use of only 2-beams or a single systematic row to calculate the image contrast, or calculating the image using a column approximation. The increasing amount of literature showing comparisons of experimental and simulated images shows that it is possible to obtain very close agreement between the two images; although the choice of parameters used, and the assumptions made, in performing the calculation must be properly dealt with. The simulation of the images of defects in materials has, in many cases, therefore become a tractable problem.

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Discrete sample estimation for gaussian random fields generated by stochastic partial differential equations

Communication in Statistics- Theory and Methods ◽

10.1080/03610929808828954 ◽

1998 ◽

Vol 14 (4) ◽

pp. 883-903

Author(s):

Jaroslav Mohapl

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Random Fields ◽

Stochastic Partial Differential Equations ◽

Gaussian Random Fields ◽

Partial Differential ◽

Discrete Sample

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Time consumption and quality of an automated fusion tool for SPECT and MRI images of the brain

Nuklearmedizin ◽

10.1055/s-0038-1625192 ◽

2003 ◽

Vol 42 (05) ◽

pp. 215-219

Author(s):

G. Platsch ◽

A. Schwarz ◽

K. Schmiedehausen ◽

B. Tomandl ◽

W. Huk ◽

...

Keyword(s):

Data Sets ◽

3D Mri ◽

Clinical Routine ◽

Fusion Procedure ◽

3D Data ◽

Mri Scans ◽

2D Data ◽

Time Required ◽

The Brain ◽

Manual Correction

Summary: Aim: Although the fusion of images from different modalities may improve diagnostic accuracy, it is rarely used in clinical routine work due to logistic problems. Therefore we evaluated performance and time needed for fusing MRI and SPECT images using a semiautomated dedicated software. Patients, material and Method: In 32 patients regional cerebral blood flow was measured using 99mTc ethylcystein dimer (ECD) and the three-headed SPECT camera MultiSPECT 3. MRI scans of the brain were performed using either a 0,2 T Open or a 1,5 T Sonata. Twelve of the MRI data sets were acquired using a 3D-T1w MPRAGE sequence, 20 with a 2D acquisition technique and different echo sequences. Image fusion was performed on a Syngo workstation using an entropy minimizing algorithm by an experienced user of the software. The fusion results were classified. We measured the time needed for the automated fusion procedure and in case of need that for manual realignment after automated, but insufficient fusion. Results: The mean time of the automated fusion procedure was 123 s. It was for the 2D significantly shorter than for the 3D MRI datasets. For four of the 2D data sets and two of the 3D data sets an optimal fit was reached using the automated approach. The remaining 26 data sets required manual correction. The sum of the time required for automated fusion and that needed for manual correction averaged 320 s (50-886 s). Conclusion: The fusion of 3D MRI data sets lasted significantly longer than that of the 2D MRI data. The automated fusion tool delivered in 20% an optimal fit, in 80% manual correction was necessary. Nevertheless, each of the 32 SPECT data sets could be merged in less than 15 min with the corresponding MRI data, which seems acceptable for clinical routine use.

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