ó voi(0ãóX•SSKrSSKJr SSKJrJr /SQrS SjrS Sjr S Sjr S S jr g) éN)Úpearsonré)Úcheck_shape_equalityÚas_binary_ndarray)Úpearson_corr_coeffÚmanders_coloc_coeffÚmanders_overlap_coeffÚintersection_coeffcó.•[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 Úmask©Ú variable_nameéÿÿÿÿc3ó8# •UHn[U5v• M g7f©N)Úfloat)Ú.0Úvs Ú[/var/www/html/land-ocr/venv/lib/python3.13/site-packages/skimage/measure/_colocalization.pyÚ Ú%pearson_corr_coeff..asé€Ð<Ò#;˜a”q—Ò#;ùs‚)ÚnpÚasarrayrrÚreshapeÚtupler)Úimage0Úimage1r s rrrs…€ôLZŠZ˜Ó €FÜ ZŠZ˜Ó €FØ ÑÜ  °VÑ<ˆÜ˜V¨TÔ2Ø‘ˆØ‘‰ä˜VÔ,à—‘ Ó#ˆØ—‘ Ó#ˆä Ñ<¤8¨FÔ#;Ó<Ó <Ð<ócóJ•[R"U5n[USS9nUb[USS9n[XU5 XnXnO [X5 UR 5S:a [ S5e[R "U5nUS:Xag[R "X-5U- $)u­ Manders' colocalization coefficient between two image channels. Parameters ---------- image0 : (M, N) ndarray Input image (first channel). All pixel values should be non-negative. image1_mask : (M, N) ndarray of dtype bool Binary image giving the regions of interest in the second channel. Must have same shape as `image0`. mask : (M, N) ndarray of dtype bool, optional Only `image0` pixel values within `mask` are included in the calculation. Must have same shape as `image0`. Returns ------- mcc : float Manders' colocalization coefficient. Notes ----- Manders' colocalization coefficient (MCC) was developed in the context of confocal biological microscopy, to measure the fraction of colocalizing objects in each component of a dual-channel image. Out of the total intensity of, say, channel A, how much is found within the features (objects) of, say, channel B [1]_? The measure thus ranges from 0 for no colocalization to 1 for complete colocalization. MCC is commonly used to measure the colocalization of a particular protein in a subcelullar compartment. Typically, the mask for channel B is obtained by thresholding, to segment the features from the background. In this implementation, channel B is passed directly as a mask (`image1_mask`), leaving the segmentation step to the user (upstream). The implemented equation is: .. math:: mcc = \frac{\sum_i A_{i,coloc}}{\sum_i A_i} where - :math:`A_i` is the value of the :math:`i^{th}` pixel in `image0`, and - :math:`A_{i, coloc} = A_i B_i`, considering that :math:`B_i` is the (``True`` or ``False``) value of the :math:`i^{th}` pixel in `image1_mask` cast into int or float (``1`` or ``0``, respectively). MCC is sensitive to noise, with diffuse signal in the first channel inflating its value. Therefore, images should be processed beforehand to remove out-of-focus and background light [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 Ú image1_maskr r rzimage contains negative values)rrrrÚminÚ ValueErrorÚsum)rr r r#s rrrdsš€ô@ZŠZ˜Ó €FÜ# K¸}ÑM€KØ ÑÜ  °VÑ<ˆÜ˜V°$Ô7Ø‘ˆØ!Ñ'‰ ä˜VÔ1à ‡zzƒ|aÓÜÐ9Ó:Ð:ä &Š&‹.€CØ ˆaƒxØÜ 6Š6&Ñ&Ó '¨#Ñ -Ð-rcó:•[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 valuesgà?) rrrrr!r"r#ÚsquareÚmultiply)rrr Údenoms rr r ·sÙ€ôBZŠZ˜Ó €FÜ ZŠZ˜Ó €FØ ÑÜ  °VÑ<ˆÜ˜V¨TÔ2Ø‘ˆØ‘‰ä˜VÔ,ð‡zzƒ|aÓÜÐ:Ó;Ð;Ø ‡zzƒ|aÓÜÐ:Ó;Ð;ä VŠV”B—I’I˜fÓ%Ó &¬"¯&ª&´·²¸6Ó1BÓ*CÑ DÈÑ L€EÜ 6Š6”"—+’+˜fÓ-Ó .°Ñ 6Ð6rcó•[USS9n[USS9nUb[USS9n[XU5 XnXnO [X5 [R"U5nUS:Xag[R"[R"X55nXC- $)aFraction of a channel's segmented binary mask that overlaps with a second channel's segmented binary mask. Parameters ---------- image0_mask : (M, N) ndarray of dtype bool Image mask of channel A. image1_mask : (M, N) ndarray of dtype bool Image mask of channel B. Must have same dimensions as `image0_mask`. mask : (M, N) ndarray of dtype bool, optional Only `image0_mask` and `image1_mask` pixels within this region of interest mask are included in the calculation. Must have same dimensions as `image0_mask`. Returns ------- Intersection coefficient, float Fraction of `image0_mask` that overlaps with `image1_mask`. Ú image0_maskr r r r)rrrÚ count_nonzeroÚ logical_and)r)r r Únonzero_image0Ú nonzero_joints rr r s€ô.$ K¸}ÑM€KÜ# K¸}ÑM€KØ ÑÜ  °VÑ<ˆÜ˜[°tÔ<Ø!Ñ'ˆ Ø!Ñ'‰ ä˜[Ô6ä×%Ò% kÓ2€NؘÓØÜ×$Ò$¤R§^¢^°KÓ%MÓN€MØ Ñ )Ð)rr) ÚnumpyrÚ scipy.statsrÚ _shared.utilsrrÚ__all__rrr r ©rrÚr3s/ðÛÝ çCò €ôS=ôlP.ôfR7õj%*r