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Fig. 2 | BMC Bioinformatics

Fig. 2

From: Modified Pearson correlation coefficient for two-color imaging in spherocylindrical cells

Fig. 2

Scheme for calculating PCC and MPCC for two representative images R and G sampled from distributions that are perfectly anti-correlated in both 3D and 2D. a Heat maps of R and G with 200 nm pixels. Each image comprises ~ 10,000 molecules. Color scale indicates the number of molecules in each pixel. b Standard PCC calculation. Top: The 2D uniform reference distribution \( \overline{\mathrm{R}} \) or \( \overline{\mathrm{G}} \) that is subtracted from images R or G. Bottom: Normalized difference matrices \( \sim \left(\mathrm{R}-\overline{\mathrm{R}}\right) \) and \( \sim \left(\mathrm{G}-\overline{\mathrm{G}}\right) \) obtained after subtraction. The Frobenius inner product of these two difference matrices gives the PCC. c Modified PCC calculation. Top: Reference distribution \( {\overset{\sim }{\mathrm{U}}}^{\mathrm{R}} \) and \( {\overset{\sim }{\mathrm{U}}}^{\mathrm{G}} \), which are 2D projections of 3D random distributions of 100,000 molecules within the spherocylinder and normalized to have a total of 10,000 molecules. These are subtracted from images R and G, respectively. Bottom: Normalized difference matrices \( {\hat{\Delta}}^{\mathrm{R}} \) and \( {\hat{\Delta}}^{\mathrm{G}} \) obtained after subtraction. The Frobenius inner product of these two difference matrices gives the MPCC. d Scatter plot of individual normalized difference matrix elements for PCC (Red) and for MPCC (Black). The MPCC elements are negatively correlated within the noise level, while the PCC elements are not. The resulting MPCC and PCC values are − 0.99 and − 0.47, respectively

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