Journal: Methods in enzymology

Article Title: Fundamentals of three-dimensional reconstruction from projections

doi: 10.1016/S0076-6879(10)82001-4

Figure Lengend Snippet: Principle of the Gridding-based Direct Fourier 3D Reconstruction algorithm (GDFR). (a) 2D FFT of input projection image. (b) The reverse gridding is used to resample 2D Fourier input image into 2D polar Fourier coordinates. (c) “Gridding weights” are computed as cell areas of a 2D Voronoi diagram on a unit sphere (grey polygons) to compensate for the non-uniform distribution of the grid points. (d) Gridding using a convolution kernel with subsequent 3D inverse FFT yields samples on a 3D Cartesian grid. (e) Removal of weights in real space yields the reconstructed 3D object.

Article Snippet: Such weights can be obtained as volumes of 3D Voronoi cells obtained from the distribution of sampling points ( Okabe et al. , 2000 ).

Techniques:

Journal: STAR Protocols

Article Title: Protocol for multicolor three-dimensional dSTORM data analysis using MATLAB-based script package Grafeo

doi: 10.1016/j.xpro.2021.100808

Figure Lengend Snippet: The Grafeo GUI window Different sections discussed in the protocol are highlighted with red boxes. The main menu bar permits, among others, importing the raw single-molecule data in the different formats (here, only Nikon NSTORM 'txt' format is discussed). The raw dSTORM data is converted to Matlab ".mat" file format that can be loaded as a single color file and combined to a multicolor file (see "Load data" red box). The single-molecule data can be filtered by applying the threshold to photon number (PN), localization precision (LP), and the Voronoi diagram density (VD) (see "Filtering parameters" red box). Multicolor data can be aligned automatically (see the main menu bar, "2–3 color Voronoi") or manually (see "Channel alignment" red box). The data can be visualized using still, or animated scatter plots (see "Data visualization" box), Voronoi diagrams, and Delaunay triangulation (see "Data clustering" red box). Data visualization and analysis require prior creation of a region of interest (ROI) in the main axes. The different types of ROI can be drawn: polygonal or polygonal freehand ROI (No. 1, 2, 5), square ROI (No. 3), and twin ROI (Twin poly roi, No. 4, not used for the data visualization). The data can be analyzed using Ripley's K and L functions, point correlation function (PCF), and using Delaunay triangulation (graph-based segmentation) (see "Data clustering" red box).

Article Snippet: When using “3d Voronoi” function, the average VD in a ROI will be displayed in the Matlab command window both before and after suppressing the large/small VPs.

Techniques:

Journal: STAR Protocols

Article Title: Protocol for multicolor three-dimensional dSTORM data analysis using MATLAB-based script package Grafeo

doi: 10.1016/j.xpro.2021.100808

Figure Lengend Snippet: Data importation and filtering (A) Importing a single file (A(i)) or multiple files in a batch processing mode (A(ii)). (B) The data importation input parameters. From the top to bottom: (1) the total number of columns in a molecular list file, (2–3) the column numbers for the X (2) and Y (3) coordinate, (4) photon count, (5) localization precision, (6) frame index at which the molecule was detected, (7) column index with the channel tag (in the Nikon NIS elements software, the name for each channel can be set, e.g., 488, then the same name will be used in the molecular list file), (8) trace length (the number of subsequent image frames the single molecule appeared), (9) Z coordinate column, (10) a flag for the molecules for which Z position fit failed (in the Nikon file it is ‘Z Rejected’, and this tag replaces the channel tag), (11) a binary tag specifying whether to import all the data (set to 0) or only the molecules with a successful Z position fit (set to 1), (12) the two element vector specifying the minimum number of photons and the maximum localization precision (the molecules with fewer number of photons or greater localization precision will be discarded from the subsequent analyses), (13) the number of header lines preceding the column data, and finally (14) the file space delimiter (for Tab use ‘∖t’). (C) Once the data is imported to the Matlab format, it can be loaded to the Grafeo memory. C(i) Chanel selection dropdown menu, C(ii) “Re-threshold” push button applies a new filtering parameters, “Save ML” saves the updated molecular list file. (D) Data filtering panel using a minimum photon number (PN), a maximum localization precision (LP), and a minimum Voronoi diagram density (VD). The last four rows correspond to a minimum, maximum, mean, and median of the Voronoi diagram density for each channel and are populated automatically whenever the filtering parameters are changed or a new file is loaded.

Article Snippet: When using “3d Voronoi” function, the average VD in a ROI will be displayed in the Matlab command window both before and after suppressing the large/small VPs.

Techniques: Software, Plasmid Preparation, Selection

Journal: STAR Protocols

Article Title: Protocol for multicolor three-dimensional dSTORM data analysis using MATLAB-based script package Grafeo

doi: 10.1016/j.xpro.2021.100808

Figure Lengend Snippet: Voronoi diagrams and Delaunay triangulation (A–C) (A and C) Voronoi diagram (violet) and (A and B) Delaunay triangulation (green) calculated for a set of points (orange). In (C) a red arrowhead indicates a point associated with a large Voronoi polygon (dispersed data, noise) and black arrow shows a point associated with a small Voronoi polygon (dense, clustered data). This propriety is implemented to efficiently filter the data based on the Voronoi polygon size and permits separating dense clustered data from the noise or dispersed points. (D and E) The results of graph segmentation in lateral xy view – (D), and in 3D view – (E).

Article Snippet: When using “3d Voronoi” function, the average VD in a ROI will be displayed in the Matlab command window both before and after suppressing the large/small VPs.

Techniques:

Journal: STAR Protocols

Article Title: Protocol for multicolor three-dimensional dSTORM data analysis using MATLAB-based script package Grafeo

doi: 10.1016/j.xpro.2021.100808

Figure Lengend Snippet: Visualizing the segmented clusters (A) (left) A 3D scatter plot of the data subject to data clustering. Channel 1 – violet (CBM3), channel 2 – green (Callose), channel 3 – orange (Hetero-mannans). (right) The close up on the data enclosed by the white rectangle. (B and C) The result of the graph-based cluster segmentation for B) channels 2 and 3, and C) channels 1 and 3. The data is displayed as the 3D graphs (3D disconnected Delaunay triangulation). (right) The close up on the data enclosed by the white rectangle. (D) The data displayed as the 3D Voronoi polygons. The Voronoi diagram was disconnected by applying the upper and lower bounds for the VD Voronoi diagram density (see also Figure 13 ).

Article Snippet: When using “3d Voronoi” function, the average VD in a ROI will be displayed in the Matlab command window both before and after suppressing the large/small VPs.

Techniques:

Journal: STAR Protocols

Article Title: Protocol for multicolor three-dimensional dSTORM data analysis using MATLAB-based script package Grafeo

doi: 10.1016/j.xpro.2021.100808

Figure Lengend Snippet: The input parameters for the Voronoi polygon (VP) visualization From top to bottom: the minimum and the maximum Voronoi diagram density. The last option permits displaying the individual 3D Voronoi polygons as a convex hull.

Article Snippet: When using “3d Voronoi” function, the average VD in a ROI will be displayed in the Matlab command window both before and after suppressing the large/small VPs.

Techniques:

Journal: STAR Protocols

Article Title: Protocol for multicolor three-dimensional dSTORM data analysis using MATLAB-based script package Grafeo

doi: 10.1016/j.xpro.2021.100808

Figure Lengend Snippet: Segmented graphs data description

Article Snippet: When using “3d Voronoi” function, the average VD in a ROI will be displayed in the Matlab command window both before and after suppressing the large/small VPs.

Techniques: Plasmid Preparation, Single Molecule Counting

Journal: Materials

Article Title: Review Study on Mechanical Properties of Cellular Materials

doi: 10.3390/ma17112682

Figure Lengend Snippet: Research articles on the prescription of cellular materials.

Article Snippet: In addition, it examines computer-based models including 3D Additive Manufacturing (AM) structures, Laguerre tessellation, 2D and 3D Voronoi diagrams, ABAQUS-based models, tetradecahedral (Kelvin) structures, in situ X-ray tomography Scanning, finite element modeling, and Bravais lattice systems to explain mechanical properties through homogenized equations.

Techniques: Modification, Control, Shear, Homogenization, Derivative Assay

Journal: Materials

Article Title: Review Study on Mechanical Properties of Cellular Materials

doi: 10.3390/ma17112682

Figure Lengend Snippet: Difference between open and closed cell foam.

Article Snippet: In addition, it examines computer-based models including 3D Additive Manufacturing (AM) structures, Laguerre tessellation, 2D and 3D Voronoi diagrams, ABAQUS-based models, tetradecahedral (Kelvin) structures, in situ X-ray tomography Scanning, finite element modeling, and Bravais lattice systems to explain mechanical properties through homogenized equations.

Techniques: Insulation

Journal: Materials

Article Title: Review Study on Mechanical Properties of Cellular Materials

doi: 10.3390/ma17112682

Figure Lengend Snippet: Processing techniques for the Microstructure formation of Cellular Material.

Article Snippet: In addition, it examines computer-based models including 3D Additive Manufacturing (AM) structures, Laguerre tessellation, 2D and 3D Voronoi diagrams, ABAQUS-based models, tetradecahedral (Kelvin) structures, in situ X-ray tomography Scanning, finite element modeling, and Bravais lattice systems to explain mechanical properties through homogenized equations.

Techniques: In Situ, Micro-CT

Journal: Materials

Article Title: Review Study on Mechanical Properties of Cellular Materials

doi: 10.3390/ma17112682

Figure Lengend Snippet: Computational techniques for the Microstructure formation of Cellular Material.

Article Snippet: In addition, it examines computer-based models including 3D Additive Manufacturing (AM) structures, Laguerre tessellation, 2D and 3D Voronoi diagrams, ABAQUS-based models, tetradecahedral (Kelvin) structures, in situ X-ray tomography Scanning, finite element modeling, and Bravais lattice systems to explain mechanical properties through homogenized equations.

Techniques: Homogenization, Computed Tomography

Journal: Materials

Article Title: Review Study on Mechanical Properties of Cellular Materials

doi: 10.3390/ma17112682

Figure Lengend Snippet: Voronoï diagram of the hexagonal honeycomb: ( a ) regular control points; ( b ) generated regular hexagons; and ( c ) coordinate perturbation at each control point i .

Article Snippet: In addition, it examines computer-based models including 3D Additive Manufacturing (AM) structures, Laguerre tessellation, 2D and 3D Voronoi diagrams, ABAQUS-based models, tetradecahedral (Kelvin) structures, in situ X-ray tomography Scanning, finite element modeling, and Bravais lattice systems to explain mechanical properties through homogenized equations.

Techniques: Control, Generated

Journal: Materials

Article Title: Review Study on Mechanical Properties of Cellular Materials

doi: 10.3390/ma17112682

Figure Lengend Snippet: ( a ) 3D Voronoi structure; ( b ) Corresponding cell base on the FE model; and ( c ) middle section perpendicular to the 2nd direction .

Article Snippet: In addition, it examines computer-based models including 3D Additive Manufacturing (AM) structures, Laguerre tessellation, 2D and 3D Voronoi diagrams, ABAQUS-based models, tetradecahedral (Kelvin) structures, in situ X-ray tomography Scanning, finite element modeling, and Bravais lattice systems to explain mechanical properties through homogenized equations.

Techniques: