[Cross-posted on the Wolfram Community.]
Is anyone aware of any Wofram image-processing tutorial or documentation/example that specifically address:
1) Intensity Correlation Coefficient-Based: (e.g. Pearson’s correlation coefficient [Soper et al., 1917] and Manders’ coefficient [Maanders et al., 1993]) or an extension of them, the Costes’ approach [Costes et al., 2004].
2)Object-based Approach based on distance: [Lachmanovich et al., 2003] and [Boutte, 2006].
Addenum: Here is more context to this question;
The Intensity Correlation Coefficient-Based co-localization is a global statistic approach whereby a correlation coefficient between two channels (e.g. Red and Green) is computed based on the comparison between their respective intensities for each pixel coordinate.
The most popular and widely used metrics utilized in this context are the Pearson’s coefficient and the Manders’ coefficient thanks to Fabrice P. Cordelières, Institut Curie, Orsay (France) imageJ pluging JACOP (https://imagej.nih.gov/ij/plugins/track/jacop2.html).
However, these methods can be tricky as they are critically noise-sensitive.
Gives a value between -1 and 1 as a quantification of the degree of spatial overlapping (co-localization) between two channels whereby -1,0 and 1 mean negative, no or positive correlation respectively. In an RGB image it is computed as follows:
where R is signal intensity of pixels in the Red channel, G is signal intensity of pixels in the Green channel, further /R and /G are average intensity for both respectively.
Also correlates intensities but excludes the average intensity values of the Channels. It varies from 0 (no overlap) to 1(100% overlap) and is computed as follows
Object-based Approach (e.g. Euclidean distance)
From the object-based perspective, the co-localization is a reflection of the distance between centers of mass of objects to be tested for co-localization . If that distance is below a certain threshold, the latter is typically considered to be the optical resolution, then we conclude that these two objects co-localize.
- [Soper et al., 1917] Soper, H., Young, A., Cave, B., and LEE, A. (1917). On the distribution of the correlation coefficient in small samples. Biometrika, 11(4):328– 413.
- [Maanders et al., 1993] Maanders, E. M. M., VERBEEK, F. J., and ATEN, J. A. (1993). Measurement of co-localization of objects in dual-colour confocal images. Journal of Microscopy, 169(3):375–382.
- [Costes et al., 2004] Costes, S. V., Daelemans, D., Cho, E. H., Dobbin, Z., Pavlakis,G., and Lockett, S. (2004). Automatic and quantitative measurement of protein-protein colocalization in live cells. Biophysical Journal, 86(6):3993–4003.
- [Boutte, 2006] Boutte, Y. (2006). The plasma membrane recycling pathway and cell polarity in plants: studies on pin proteins. Journal of Cell Science, 119(7):1255– 1265.
- [Lachmanovich et al., 2003] Lachmanovich, E., Shvartsman, D. E., Malka, Y., Botvin, C., Henis, Y. I., and Weiss, A. M. (2003). Co-localization analysis of complex formation among membrane proteins by computerized fluorescence microscopy: application to immunofluorescence co-patching studies. Journal of Microscopy, 212(2):122–131.