Update colocalization-by-cross-correlation.md

Author: andmccall

_pages/plugins/colocalization-by-cross-correlation.md

@@ -41,7 +41,7 @@ Additionally, the images (particularly 3D) need to be correctly scaled (Image >
 
 ### Run the plugin
 {% include img align="right" name="Colocalization by correlation options" src="colocbycorrelateoptions"%}
-The plugin can be found in the **Analyze > Colocalization** menu after it has been installed. At the dialog menu, select the two images and the analysis mask to be used. If the possible localizations for your dye/stain encompasses the entire image, you can check the no mask box instead. The plugin can also calculate what signal within each input image contributed to the result by checking the "Generate contriubtion images" checkbox. This process does use more memory, so should be disabled if an out of memory error message is received. If the "Show intermediate images" box is checked, the plugin will open images showing the cross-correlation images, both before and after subtraction of the low spatial frequency component. This can be useful for understanding the function of the plugin, or for visualizing the direction of the correlation if your sample has a polarized axis. More details on the contribution and intermediate images can be found below.
+The plugin can be found in the **Analyze > Colocalization** menu after it has been installed. At the dialog menu, select the two images and the analysis mask to be used. If the possible localizations for your dye/stain encompasses the entire image, you can check the no mask box instead. The plugin can also calculate what signal within each input image contributed to the result by checking the "Generate contriubtion images" checkbox. This process does use more memory, so should be disabled if an out of memory error message is received. A multiple term sum-of-Gaussians curve can be optionally fit to the data by setting the "Number of Gaussians to fit" to 2 or more (discussed below). If the "Show intermediate images" box is checked, the plugin will open images showing the cross-correlation images, both before and after subtraction of the low spatial frequency component. This can be useful for understanding the function of the plugin, or for visualizing the direction of the correlation if your sample has a polarized axis. More details on the contribution and intermediate images can be found below.
 
 ## Citing CCC
 - A. McCall, (2024) Colocalization by cross-correlation, a new method of colocalization suited for super-resolution microscopy. *BMC Bioinformatics*
@@ -53,16 +53,16 @@ To help describe the results, we will use the simple, idealized example shown be
 {% include gallery content=
 "
 /media/plugins/colocbycorrelate-originalslides.jpg | Composite of images analyzed
-/media/plugins/colocbycorrelate-correlationplot.jpg | Radial profile
+/media/plugins/colocbycorrelate-correlationplot.jpg | Correlogram
 /media/plugins/colocbycorrelate-gaussfit.jpg | Gaussian fit result
 /media/plugins/colocbycorrelate-contributionslide1.jpg | Composit image of Gaussian fit contributions
 "
 %}
 
 Here's a detailed description of each of the result windows:
 
-### Correlation plot 
-A radial profile plot will be displayed, it contains the radial profile of the original cross-correlation image (blue circles), the radial profile of the cross-correlation after subtraction of low spatial frequency component (green circles), and a Gaussian curve fit to the subtracted profile (magenta filled circles). The distance between the blue and the green is a visual indicator of the confidence value described below. The Y-axis is the average of the cross-correlation function. While not technically arbitrary, it is most easily viewed as a measure of relative cross-correlation. The range of the graph is set automatically to fit the Gaussian curve. If you wish to view all the data right click the plot and select Auto Range > Both Axes.
+### Correlogram plot 
+A radial profile plot will be displayed, it contains the radial profile of the original cross-correlation image (blue circles), the radial profile of the cross-correlation after subtraction of low spatial frequency component (green circles), and a Gaussian curve fit to the subtracted profile (magenta filled circles). The distance between the blue and the magenta is a visual indicator of the confidence value described below. The Y-axis is the average of the cross-correlation function. While not technically arbitrary, it is most easily viewed as a measure of relative cross-correlation. The range of the graph is set automatically to fit the Gaussian curve. If you wish to view all the data right click the plot and select Auto Range > Both Axes.
 
 ### Gaussian fit analysis 
 This table will contain (in scaled units), the mean distance for the measured correlation (µ), the standard deviation of that correlation (σ), and the peak height of the Gaussian fit. It also contains the statistical measures confidence and R-squared. Each parameter is explained below in detail, including limitations and methods to improve on that parameter.
@@ -74,7 +74,7 @@ Simply the average distance of the measured spatial correlation from the Gaussia
 The standard deviation of the measured spatial correlation. Generally speaking, this value can be improved by improving the input image resolution. However, the returned value could also be caused by true variability in the measured spatial correlation. Abnormally high values (_e.g._ σ values of ~7-10µm for an image of a single cell) are usually caused by an inappropriate mask or complete lack of mask when one is justified, or by the resolution being too low for the high molecular density in one or both of the images. 
 
 #### Confidence
-Confidence is a novel metric specific to CCC. It is determined by taking the area under the curve (AUC) of the subtracted correlation radial profile (in range of mean ± 3×sigma) divided by the AUC of the original correlation radial profile (in same range). Values closer to 1 indicate a strong likelihood of true correlation. Values near 0 indicate low to no correlation between the two images, or that more resolution is needed. I currently estimate that values of \~0.10 or greater indicate a reasonably likley correlation (within the range specified by the Gaussian curve), with values of 0.2 or greater indicating a likely true correlation. Ultimately, it is more important to have consistent results across experimetal repeats than a confidence above 0.2. 
+Confidence is a novel metric specific to CCC. It is determined by taking the area under the curve (AUC) of the Gaussian fit curve (in range of mean ± 3×sigma) divided by the AUC of the original correlation radial profile (in same range). Values closer to 1 indicate a strong likelihood of true correlation. Values near 0 indicate low to no correlation between the two images, or that more resolution is needed. I currently estimate that values of \~0.10 or greater indicate a reasonably likley correlation (within the range specified by the Gaussian curve), with values of 0.2 or greater indicating a likely true correlation. Ultimately, it is more important to have consistent results across experimetal repeats than a confidence above 0.2. 
 
 **The confidence is influenced by many image quality and spatial correlation parameters, including image resolution, molecular density, correlation distance, non-correlated particles, and image background.** Generally speaking, low confidence values can be increased by improving image resolution. However, this assumes a true spatial correlation exists, as low confidence can also simply indicate a lack of a true correlation. If your confidence is very low, make sure you are pre-processing your images correctly and subtracting image background on a 32-bit image.
 
@@ -87,6 +87,9 @@ The peak height can likely be ignored in most cases, but loosely reflects the re
 ### Contribution of each image to the Gaussian fit
 Two new images will be created that display the signal from each analyzed image that contributed to the cross-correlation and Gaussian fit result. **It is important to note that the data it contains will always be visible, even if you do NOT have a strong correlation between the two images.** Generally, the pixel intensity values should NOT be used as an indicator of overall correlation between the images, but the relative brightness within an image can be used as an approximate indicator of how strongly that particular signal contributed to the correlation result. This relative brightness indication can be easily seen in the example data above: In our original data, all the dots are of the same size and intensity, however, in the resulting contribution images, the dots that remain are varied in their brightness based on how much they contributed to the cross-correlation result (you'll notice that the brightest dots are all oriented in the same direction). 
 
+## Multi-Gaussian curve fitting
+As of v2.3.0, CCC now natively supports the fitting of multiple Gaussians to data as a sum-of-Gaussians curve. The number of Gaussian terms to attempt to fit is set at the dialog pop-up when running CCC. Mutli-term Gaussian curves can be useful if the spatial relation between your two images has multiple components, most often a broad low-frequency component and a narrow high-frequency component with similar mean values. The confidence value is calculated independently for each Gaussian term, thus over-fitting can result in reducing the confidence of each individual Gaussian term. Also, every additional Gaussian term in the fitting process adds additional computation time. 
+
 ## Working with time-series data:
 
 Working with time-series data is not that different than working with non-time-series data. Every frame of your data is analyzed individually, in the exact same manner that non-time-series data would be analyzed. Thus, all inputs (including the mask) must have the same number of frames. The output generated from the plugin has been changed to better suit time-series data:
@@ -156,6 +159,9 @@ I originally made this as I had someone who wanted to determine the average thic
 
 ## Major revisions
 
+### New confidence value calculation in 2.3
+With the release of the multi-Gaussian fitting in v2.3, the confidence calculation was changed to use the area under the curve (AUC) of the Gaussian fit curve in place of the subtracted correlogram data. This was changed so that each individual Gaussian of a multi-Gaussian fit would have its own confidence value. 
+
 ### Slightly different results in v2.1
 In v2.1 of CCC, the way that the low-frequency component of the data is removed from the cross-correlation was altered to allow creation of the "no confidence" command. Basically, instead of cross-correlating a low-frequency component of image 1 (mask with mean value image) with image 2, as described above in the how it works section, in v2.1 the mean pixel value within the mask is subtracted from every pixel of image 1 that is within the mask bounds before it is cross-correlated with image 2. This effectively subtracts the low-frequency component before the cross-correlation is performed, rather than after. During testing, this process generated either identical or very similar results to the version 2 method that is described above. I believe the reason it was not always identical was due to differences in rounding, since the new v2.1 method skips a couple rounding steps from v2. I made this change for both the No confidence command and the original CCC command as I wanted them to produce identical results, and because this method was more memory efficient.