9i/XSSKrSSKJr SSKJrJr /SQrS SjrS Sjr S Sjr S S jr g) N)pearsonr)check_shape_equalityas_binary_ndarray)pearson_corr_coeffmanders_coloc_coeffmanders_overlap_coeffintersection_coeffc.[R"U5n[R"U5nUb[USS9n[XU5 XnXnO-[X5 UR S5nUR S5n[ S[ X555$)u Calculate Pearson's Correlation Coefficient between pixel intensities in channels. Parameters ---------- image0 : (M, N) ndarray Image of channel A. image1 : (M, N) ndarray Image of channel 2 to be correlated with channel B. Must have same dimensions as `image0`. mask : (M, N) ndarray of dtype bool, optional Only `image0` and `image1` pixels within this region of interest mask are included in the calculation. Must have same dimensions as `image0`. Returns ------- pcc : float Pearson's correlation coefficient of the pixel intensities between the two images, within the mask if provided. p-value : float Two-tailed p-value. Notes ----- Pearson's Correlation Coefficient (PCC) measures the linear correlation between the pixel intensities of the two images. Its value ranges from -1 for perfect linear anti-correlation to +1 for perfect linear correlation. The calculation of the p-value assumes that the intensities of pixels in each input image are normally distributed. Scipy's implementation of Pearson's correlation coefficient is used. Please refer to it for further information and caveats [1]_. .. math:: r = \frac{\sum (A_i - m_A_i) (B_i - m_B_i)} {\sqrt{\sum (A_i - m_A_i)^2 \sum (B_i - m_B_i)^2}} where :math:`A_i` is the value of the :math:`i^{th}` pixel in `image0` :math:`B_i` is the value of the :math:`i^{th}` pixel in `image1`, :math:`m_A_i` is the mean of the pixel values in `image0` :math:`m_B_i` is the mean of the pixel values in `image1` A low PCC value does not necessarily mean that there is no correlation between the two channel intensities, just that there is no linear correlation. You may wish to plot the pixel intensities of each of the two channels in a 2D scatterplot and use Spearman's rank correlation if a non-linear correlation is visually identified [2]_. Also consider if you are interested in correlation or co-occurence, in which case a method involving segmentation masks (e.g. MCC or intersection coefficient) may be more suitable [3]_ [4]_. Providing the mask of only relevant sections of the image (e.g., cells, or particular cellular compartments) and removing noise is important as the PCC is sensitive to these measures [3]_ [4]_. References ---------- .. [1] https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.pearsonr.html .. [2] https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.spearmanr.html .. [3] Dunn, K. W., Kamocka, M. M., & McDonald, J. H. (2011). A practical guide to evaluating colocalization in biological microscopy. American journal of physiology. Cell physiology, 300(4), C723–C742. https://doi.org/10.1152/ajpcell.00462.2010 .. [4] Bolte, S. and Cordelières, F.P. (2006), A guided tour into subcellular colocalization analysis in light microscopy. Journal of Microscopy, 224: 213-232. https://doi.org/10.1111/j.1365-2818.2006.01706.x mask variable_namec38# UHn[U5v M g7fN)float).0vs _/var/www/html/land-doc-ocr/venv/lib/python3.13/site-packages/skimage/measure/_colocalization.py %pearson_corr_coeff..as<#;aq#;s)npasarrayrrreshapetupler)image0image1r s rrrsLZZ F ZZ F  V<VT2V,## <8F#;< <<cJ[R"U5n[USS9nUb[USS9n[XU5 XnXnO [X5 UR 5S:a [ S5e[R "U5nUS:Xag[R "X-5U- $)uJ Manders' colocalization coefficient between two channels. Parameters ---------- image0 : (M, N) ndarray Image of channel A. All pixel values should be non-negative. image1_mask : (M, N) ndarray of dtype bool Binary mask with segmented regions of interest in channel B. Must have same dimensions as `image0`. mask : (M, N) ndarray of dtype bool, optional Only `image0` pixel values within this region of interest mask are included in the calculation. Must have same dimensions as `image0`. Returns ------- mcc : float Manders' colocalization coefficient. Notes ----- Manders' Colocalization Coefficient (MCC) is the fraction of total intensity of a certain channel (channel A) that is within the segmented region of a second channel (channel B) [1]_. It ranges from 0 for no colocalisation to 1 for complete colocalization. It is also referred to as M1 and M2. MCC is commonly used to measure the colocalization of a particular protein in a subceullar compartment. Typically a segmentation mask for channel B is generated by setting a threshold that the pixel values must be above to be included in the MCC calculation. In this implementation, the channel B mask is provided as the argument `image1_mask`, allowing the exact segmentation method to be decided by the user beforehand. The implemented equation is: .. math:: r = \frac{\sum A_{i,coloc}}{\sum A_i} where :math:`A_i` is the value of the :math:`i^{th}` pixel in `image0` :math:`A_{i,coloc} = A_i` if :math:`Bmask_i > 0` :math:`Bmask_i` is the value of the :math:`i^{th}` pixel in `mask` MCC is sensitive to noise, with diffuse signal in the first channel inflating its value. Images should be processed to remove out of focus and background light before the MCC is calculated [2]_. References ---------- .. [1] Manders, 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: 375-382. https://doi.org/10.1111/j.1365-2818.1993.tb03313.x https://imagej.net/media/manders.pdf .. [2] Dunn, K. W., Kamocka, M. M., & McDonald, J. H. (2011). A practical guide to evaluating colocalization in biological microscopy. American journal of physiology. Cell physiology, 300(4), C723–C742. https://doi.org/10.1152/ajpcell.00462.2010 image1_maskr r rzimage contains negative values)rrrrmin ValueErrorsum)rr r r#s rrrds~ZZ F#K}MK  V<V$7!' V1 zz|a9:: &&.C ax 66&& '# --rc:[R"U5n[R"U5nUb[USS9n[XU5 XnXnO [X5 UR 5S:a [ S5eUR 5S:a [ S5e[R "[R"U55[R "[R"U55-S-n[R "[R"X55U- $)u Manders' overlap coefficient Parameters ---------- image0 : (M, N) ndarray Image of channel A. All pixel values should be non-negative. image1 : (M, N) ndarray Image of channel B. All pixel values should be non-negative. Must have same dimensions as `image0` mask : (M, N) ndarray of dtype bool, optional Only `image0` and `image1` pixel values within this region of interest mask are included in the calculation. Must have ♣same dimensions as `image0`. Returns ------- moc: float Manders' Overlap Coefficient of pixel intensities between the two images. Notes ----- Manders' Overlap Coefficient (MOC) is given by the equation [1]_: .. math:: r = \frac{\sum A_i B_i}{\sqrt{\sum A_i^2 \sum B_i^2}} where :math:`A_i` is the value of the :math:`i^{th}` pixel in `image0` :math:`B_i` is the value of the :math:`i^{th}` pixel in `image1` It ranges between 0 for no colocalization and 1 for complete colocalization of all pixels. MOC does not take into account pixel intensities, just the fraction of pixels that have positive values for both channels[2]_ [3]_. Its usefulness has been criticized as it changes in response to differences in both co-occurence and correlation and so a particular MOC value could indicate a wide range of colocalization patterns [4]_ [5]_. References ---------- .. [1] Manders, 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: 375-382. https://doi.org/10.1111/j.1365-2818.1993.tb03313.x https://imagej.net/media/manders.pdf .. [2] Dunn, K. W., Kamocka, M. M., & McDonald, J. H. (2011). A practical guide to evaluating colocalization in biological microscopy. American journal of physiology. Cell physiology, 300(4), C723–C742. https://doi.org/10.1152/ajpcell.00462.2010 .. [3] Bolte, S. and Cordelières, F.P. (2006), A guided tour into subcellular colocalization analysis in light microscopy. Journal of Microscopy, 224: 213-232. https://doi.org/10.1111/j.1365-2818.2006.01 .. [4] Adler J, Parmryd I. (2010), Quantifying colocalization by correlation: the Pearson correlation coefficient is superior to the Mander's overlap coefficient. Cytometry A. Aug;77(8):733-42.https://doi.org/10.1002/cyto.a.20896 .. [5] Adler, J, Parmryd, I. Quantifying colocalization: The case for discarding the Manders overlap coefficient. Cytometry. 2021; 99: 910– 920. https://doi.org/10.1002/cyto.a.24336 r r rzimage0 contains negative valueszimage1 contains negative valuesg?) rrrrr!r"r#squaremultiply)rrr denoms rr r sBZZ F ZZ F  V<VT2V,zz|a:;; zz|a:;; VVBIIf% &"&&61B*C D LE 66"++f- . 66rc[USS9n[USS9nUb[USS9n[XU5 XnXnO [X5 [R"U5nUS:Xag[R"[R"X55nXC- $)aFraction of a channel's segmented binary mask that overlaps with a second channel's segmented binary mask. Parameters ---------- image0_mask : (M, N) ndarray of dtype bool Image mask of channel A. image1_mask : (M, N) ndarray of dtype bool Image mask of channel B. Must have same dimensions as `image0_mask`. mask : (M, N) ndarray of dtype bool, optional Only `image0_mask` and `image1_mask` pixels within this region of interest mask are included in the calculation. Must have same dimensions as `image0_mask`. Returns ------- Intersection coefficient, float Fraction of `image0_mask` that overlaps with `image1_mask`. image0_maskr r r r)rrr count_nonzero logical_and)r)r r nonzero_image0 nonzero_joints rr r s.$K}MK#K}MK  V<[t<!' !' [6%%k2N$$R^^K%MNM  ))rr) numpyr scipy.statsr _shared.utilsrr__all__rrr r rrr3s/ C S=lO.dR7j%*r