JIRA [IMG-695] MeasureCorrelation: Measure Mander's correlation coefficients + Spectral angle approach

[thouis]

Measure Mander's overlap and M1& M2 coefficients along with Pearson's. For extra credit, implement the spectral angle method found in: Gavrilovic M, Wählby C. Quantification of colocalization and cross-talk based on spectral angles. J Microsc. 2009 Jun;234(3):311-2

Original reporter: mbray Jira link: https://jira.broadinstitute.org/browse/IMG-695 (Original JIRA has attachments.) Assignee: carolina

Comment from leek on Mon, 18 Oct 2010 11:11:16 -0400: This is Vasanth's measurecorrelation code.

[ksokolnicki]

Also, this was a previous JIRA: Considering adding Pearson's Correlation Coeff http://www.ncbi.nlm.nih.gov/pubmed/20946701

Microsc Microanal. 2010 Dec;16(6):710-24. Epub 2010 Oct 15. Colocalization analysis in fluorescence micrographs: verification of a more accurate calculation of pearson's correlation coefficient.

Barlow AL, Macleod A, Noppen S, Sanderson J, Guérin CJ. PerkinElmer, Viscount Centre II, Millburn Hill Road, Warwick University Science Park, Coventry CV4 7HS, UK.

Abstract One of the most routine uses of fluorescence microscopy is colocalization, i.e., the demonstration of a relationship between pairs of biological molecules. Frequently this is presented simplistically by the use of overlays of red and green images, with areas of yellow indicating colocalization of the molecules. Colocalization data are rarely quantified and can be misleading. Our results from both synthetic and biological datasets demonstrate that the generation of Pearson's correlation coefficient between pairs of images can overestimate positive correlation and fail to demonstrate negative correlation. We have demonstrated that the calculation of a thresholded Pearson's correlation coefficient using only intensity values over a determined threshold in both channels produces numerical values that more accurately describe both synthetic datasets and biological examples. Its use will bring clarity and accuracy to colocalization studies using fluorescent microscopy.

PMID: 20946701 [PubMed - indexed for MEDLINE]

[dlogan]

Another Forum request for Manders' coefficients in MeasureCorrelation: http://cellprofiler.org/forum/viewtopic.php?f=17&t=1402&p=10178#p10178

http://www.ncbi.nlm.nih.gov/pubmed/1478975

[LeeKamentsky]

Let me put this on the top of the queue post-release.

[LeeKamentsky]

This is the Manders paper that describes practical calculation of the Manders coefficients: http://fiji.sc/images/2/24/Manders.pdf The Manders coefficients depend on knowing which pixels in each of the two channels "are equal to zero". If i are the indexes of the object, S1_i and S2_i are the intensities in channels 1 and 2 and j1 and j2 are the indices where S1_i=0 and S2_i=0, then M1 = ∑_j2S1_j2 / ∑_iS1_i and M2 = ∑_j1S2_j1 / ∑_iS2_i

So there's a heuristic that's necessary: how to evaluate whether S1_i=0? The paper uses a noise reduction filter (the mean in a 3x3 neighborhood), a top-hat like filter (subtract the mean in a 31x31 neighborhood, set all pixels with values below zero to zero) and an estimation and reduction of crosstalk between fluorescence channels (after doing the above, find all pixels with values of zero and fit a line to the scattergram of their original values versus the value in the other channel). Clearly, both the size of the blurring filter and the top-hat filter are choices that can be tuned. Also, if the cells auto-fluoresce, the adjusted intensities near the edges will be artificially high because the filters are including pixels near the border or outside of the cells. I'm inclined to use the median intensity in each cell as the background estimation or to give the users a choice.

Topics for discussion:

• Do we use a noise reduction filter and, if so, how do we select or provide for user selection of the kernel?
• How do we estimate the local background?
• Should we use the authors' method for color deconvolution (which assumes that the background pixels have been correctly chosen) or should we use a more robust model e.g. for measured intensities I₁ and I₂ solve

I₁ = (1 - α)S₁ + βS₂ + δ₁ I₂ = αS₁ + (1 - β)S₂ + δ₂

Once we make a couple of choices, coding is pretty simple.