Spatial Statistics

This measurement allows one to analyse a pattern of objects that can be assimilated to points by comparison to a random model.
The implmentation relies on the work of Dr. Philippe Andrey, so when using this plugin please refer to this paper:

Andrey, P., Kiêu, K., Kress, C., Lehmann, G., Tirichine, L., Liu, Z., … Debey, P. (2010). Statistical Analysis of 3D Images Detects Regular Spatial Distributions of Centromeres and Chromocenters in Animal and Plant Nuclei. PLoS Computational Biology, 6(7), e1000853. doi:10.1371/journal.pcbi.1000853

Principle

• A feature of a pattern of points is computed by a descriptor (such as F, G function).
• A sampler allows one to draw points within the same nucleus according to a random model.
• The desciptor is computed on the observed pattern and on simulated patterns
• The observed descriptors is compared to simulated descriptors by an evaluator
• The normalised index of the observed desciptor within all the simulated descriptors is called SDI (Spatial Distribution Index)

This methodology allows one to:

1. Compare observed distribution to a model at the population level
2. Normalise against nucleus size and shape variations at the single cell level (using the chosen model as a reference in each cell) in order to compare several observed populations, because each nucleus is used as its own reference.

For furter information, see Andrey et al. 2010.

Sampler

A sampler allows one to draw points within a the nuclear space, according to a random model. The available models are:

• Uniform distribution: totaly random within the nuclear space. The number of points can be a constant or the same as the observed structure
• Constrained distance:

Samplers are modules, a developper can add one as any other tango plugin, by implementing the interface: tango.plugin.sampler.Samper

Descriptor

Evaluator

Output