Crystallographic symmetry classifications of noisy 2D periodic images in the presence of pseudo-symmetries of the Fedorov type

Moeck, Peter; Dempsey, Andrew

doi:10.1017/s1431927619010419

Cited by 3 publications

(28 citation statements)

References 6 publications

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“…In addition, fully objective, i.e. completely researcher independent approaches the crystallographic symmetry classifications become available when geometric Akaike Information Criteria are utilized (as in the author's more recent work on this subject [16][17][18][19][20][21][22][23]).…”

Section: Analytical Plane Symmetry Group Classifications In 2dmentioning

confidence: 99%

“…Better "symmetrizations" of noisy 2D periodic images have always been the desired outcome of the standard crystallographic image processing method that is used by the 2D crystallography, transmission electron microscopy, and scanning probe microscopy communities [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and works in Fourier space. These symmetrizations combine the noiseremoval feature of traditional Fourier filtering with the crystallographic averaging over all asymmetric units in the whole image, have been utilized for over 50 years, and contributed to the Nobel Prize in Chemistry to Sir Aaron Klug 8 in the year 1982.…”

Section: Analytical Plane Symmetry Group Classifications In 2dmentioning

confidence: 99%

“…The derived mathematical framework is nowadays utilized for the classification of (i) highly magnified but necessarily noisy experimental images from crystals that are sufficiently thin (so that quasi-kinematic imaging conditions prevail) and crystal surfaces as recorded with modern transmission electron and scanning probe microscopes [7][8][9][10][11][12][13][14][15][16][17][18], of (ii) both perfectly 2D periodic and noisy synthetic images [18][19][20][21][22][23][24][25][26], as well as of (iii) more or less 2D periodic images from rugs, windows, a honeycomb, both a tiled floor and wall, metal gates, a metallic anti-skid surface [26], industrially manufactured wallpapers [27][28][29], textiles, and decorative ceramic tiles [29][30][31][32][33], medieval Islamic building ornaments [34], and images of (iv) many other objects and scenes [35].…”

Section: Introductionmentioning

confidence: 99%

“…Similarly obvious is the fact that members of the communities that traditionally perform direct space classifications may benefit from becoming informed about the opportunities that the Fourier/reciprocal space offers with respect to crystallographic symmetry classifications of more or less 2D periodic images [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Members of the 2D crystallography, transmission electron microscopy, and scanning probe microscopy communities are conversely bound to benefit from an analysis of what has been achieved so far in direct space classification of the crystallographic symmetries of more or less 2D periodic images [26][27][28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

“…The author's other crystallographic symmetry classification approaches, i.e. into Bravais lattice types [18][19][20] and crystallographic [16,23] as well as non-crystallographic Laue classes, are discussed in some detail elsewhere as they serve other purposes than identifying the plane symmetry group that can with the highest likelihood be assigned to a noisy 2D periodic image. Note that it is this particular identification that enables the most meaningful crystallographic averaging in the spatial frequency domain that is of paramount interest to 2D crystallographers, transmission electron and scanning probe microscopists.…”

Section: Introductionmentioning

confidence: 99%

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On Classification Approaches for Crystallographic Symmetries of Noisy 2D Periodic Patterns

Moeck

2019

IEEE Trans. Nanotechnology

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The existing types of classification approaches for the crystallographic symmetries of patterns that are more or less periodic in two dimensions (2D) are reviewed. Their relative performance is evaluated in a qualitative manner. Pseudosymmetries of different kinds are discussed as they present severe challenges to most classification approaches when noise levels are moderate to high. The author's information theory based approaches utilize digital images and geometric Akaike Information Criteria. They perform well in the presence of pseudo-symmetries and turn out to be the only ones that allow for fully objective (completely researcher independent) and generalized noise level dependent classifications of the full range of crystallographic symmetries, i.e. Bravais lattice type, Laue class, and plane symmetry group, of noisy real-world images. His method's identification of the plane symmetry group that can with the highest likelihood be assigned to a noisy 2D periodic image enables the most meaningful crystallographic averaging in the spatial frequency domain. This kind of averaging suppresses generalized noise much more effectively than traditional Fourier filtering. Taking account of the fact that it is fundamentally unsound to assign an abstract mathematical concept such as a single symmetry type, class, or group with 100 % certainty to a more or less 2D periodic record of a noisy real-world imaging experiment that involved a real-world sample, the author's information theory based approaches to crystallographic symmetry classifications deliver probabilistic (rather than definitive) classifications. Recent applications of deep convolutional neural networks (DCNNs) to classifications of crystallographic translation symmetry types in 2D and crystals in three dimensions (3D) are discussed as these "correlation detection and optimization" machines deliver probabilistic classifications by other -non-analytical -means. The discussed DCNN classifications ignore the fact that many crystallographic symmetries are hierarchic, i.e. that the classification classes are often non-disjoint. They are currently also incapable of dealing with pseudo-symmetries. DCNNs for classifications of crystals in 3D are discussed separately in an appendix.

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Section: Analytical Plane Symmetry Group Classifications In 2dmentioning

confidence: 99%

Section: Analytical Plane Symmetry Group Classifications In 2dmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Classification Approaches for Crystallographic Symmetries of Noisy 2D Periodic Patterns

Moeck

2019

IEEE Trans. Nanotechnology

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Information theory-based plane symmetry classifications: revealing pseudo-symmetries in the presence of noise

Moeck¹

2021

Acta Cryst Sect A

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Information theory-based methods [1][2][3][4] for the classification of more or less 2D periodic images from real-world crystals with atomic or molecular resolution into plane symmetry groups and projected Laue classes are described and applied to both synthetic patterns and experimental transmission electron microscope images of intrinsic membrane proteins. The synthetic patterns are per design either free of noise or contain approximately Gaussian distributed noise and are also highly pseudo-symmetric so that it is, for human beings on the basis of a visual inspection alone, very difficult to identify the underlying plane symmetry of the noisy patterns. This is because all genuine symmetries and pseudo-symmetries are broken by the added noise so that their differences are diminished. The new information theory-based classification methods, on the other hand, overcomes such challenges.

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Objective crystallographic symmetry classifications of a noisy crystal pattern with strong Fedorov-type pseudosymmetries and its optimal image-quality enhancement

Moeck¹

2022

Acta Crystallogr A Found Adv

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Statistically sound crystallographic symmetry classifications are obtained with information-theory-based methods in the presence of approximately Gaussian distributed noise. A set of three synthetic patterns with strong Fedorov-type pseudosymmetries and varying amounts of noise serve as examples. Contrary to traditional crystallographic symmetry classifications with an image processing program such as CRISP, the classification process does not need to be supervised by a human being and is free of any subjectively set thresholds in the geometric model selection process. This enables crystallographic symmetry classification of digital images that are more or less periodic in two dimensions (2D), also known as crystal patterns, as recorded with sufficient structural resolution from a wide range of crystalline samples with different types of scanning probe and transmission electron microscopes. Correct symmetry classifications enable the optimal crystallographic processing of such images. That processing consists of the averaging over all asymmetric units in all unit cells in the selected image area and significantly enhances both the signal-to-noise ratio and the structural resolution of a microscopic study of a crystal. For sufficiently complex crystal patterns, the information-theoretic symmetry classification methods are more accurate than both visual classifications by human experts and the recommendations of one of the popular crystallographic image processing programs of electron crystallography.

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Crystallographic symmetry classifications of noisy 2D periodic images in the presence of pseudo-symmetries of the Fedorov type

Cited by 3 publications

References 6 publications

On Classification Approaches for Crystallographic Symmetries of Noisy 2D Periodic Patterns

On Classification Approaches for Crystallographic Symmetries of Noisy 2D Periodic Patterns

Information theory-based plane symmetry classifications: revealing pseudo-symmetries in the presence of noise

Objective crystallographic symmetry classifications of a noisy crystal pattern with strong Fedorov-type pseudosymmetries and its optimal image-quality enhancement

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