Spatial grids of points, lines and planes can be used for estimation of volume in 3D. Randomly oriented spatial grids of lines and planes can be used for estimation of surface area. Randomly oriented spatial grids of planes can be used for estimation of length (1, 6). We have implemented a spatial grid of lines, or fakir probe, in programs for PC (2). Spatial grid of planes can be implemented in a similar way (4). Variance of the estimators using randomly oriented grids can be calculated from the grid density and properties of the measured objects (5, 7).
- requires VRML viewer (e.g. FreeWRL).
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Volume and area in 3D can be measured effectively by
an orthogonal threefold grid |
| composed of three simple linear probes: |
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a fourfold or a sevenfold grid obtained as combination
of the threefold grid and the fourfold grid. The grid can be observed in atomic lattice of
garnet (3). |
For unbiased measurements of anisotropic objects a generally oriented probe should be used. An example of triplet with a cell chain and with intersections.
| Length in 3D can be measured by an orthogonal triplet of planar grids |
| composed of three simple planar grids. |
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A generally oriented probe should be used for unbiased measurement of anisotropic objects. An example of triplet with artificial object, a simple probe with intercepts and a triplet with intercepts.
Fakir implements generally oriented triple, quadruple or sevenfold spatial grids of lines (2) and measurement of several compartments simultaneously, Slicer implements generally oriented triple spatial grids of planes (4), for PC with MS Windows (7, 8, 8.1, 10, 11). Programs require vcredist_x64.exe from Microsoft Visual C++ 2010 SP1 Redistributable Package installed.
Sequence of images, single multiff image file or Biorad MRC 600 image file is required as input. New measurement requires setting of basic parameters (geometry of the grid), filenames and calibration parameters. The measurements can be saved. Some user hints are in "about" dialog.
| Tobacco cell 3D image | example MRC 600 file |
| Fakir grid and sampled points | example fakir grid file |
| Fakir.exe | 64 bit Windows program, version 2.0 (August 2022) |
| Neurons 3D image | example MRC 600 file |
| Slicer grid and sampled points | example slicer grid file |
| Slicer.exe | 64 bit Windows program, version 1.0 (August 2022) |
Source: Sampling_Windows.java
Installation: Drag and drop Sampling_Windows.class onto the "ImageJ" window and save it in the plugins folder.
Description: This plugin creates an overlayed grid of unbiased sampling windows on the current image or stack. You can specify the windows size, period and position, and the lines properties. Only the objects within the window or intersecting the window and not intersecting the full line are to be sampled.
(1) Cruz-Orive, L.M.: Stereology of single objects.- Journal of Microscopy 186, 93-107, 1997.
(2) Kubinova, L., Janacek, J.: Estimating surface area by the isotropic fakir method from thick slices cut in arbitrary direction. - Journal of Microscopy 191, 201-211, 1998.
(3) O'Keefe, M.: Cubic cylinder packings. - Acta Cryst. A48, 879-884, 1992.
(4) Larsen, J.O., Gundersen, H.J.G., Nielsen, J.: Global spatial sampling with isotropic virtual planes: estimators of length density and total length in thick, arbitrarily orientated sections. - Journal of Microscopy 191, 238-248, 1998.
(5) Janacek, J.: Errors of spatial grids estimators of volume and surface area, Acta Stereologica, 18 (3), 389-396), 1999. (PDF)
(6) Kubinova L., Janacek J.: Confocal microscopy and stereology: estimating volume, number, surface area and length by virtual test probes applied to three-dimensional images. - Microscopy Research and Techniques, 53, 425-435, 2001.
(7) Janáček, J., Jirák, D.: Variance of the isotropic uniform systematic sampling. Image Analysis and Stereology 38 (3), 2019, 261-267 (PDF)
Last update: August 11, 2022