Update colocalization-by-cross-correlation.md

Author: andmccall

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

@@ -134,21 +134,35 @@ First, this plugin applies the provided mask to both images, setting any pixels
 "
 %}
 
-To remove the contribution from low spatial frequency structures/data (such as cells and nuclei), a second cross-correlation image generated from a low spatial frequency image is then subtracted from the original correlation 
-image. For this process, the mean intesity of all the pixels of the first input image within the mask is calculated, then a new image is created where all the pixels within the mask are set to this mean value. This image is an averaged low spatial frequency image of your first input image. This low-frequency image is then cross-correlated with the second input image, and the resulting cross-correlation image is the low-frequency component, which is  subtracted from the original cross-correlation image. The mean under the mask process is only applied to one image as applying it to both did not result in a significant difference in results and uses more time and memory. Then, we generate a radial profile of the subtracted data and fit a Gaussian curve to it. We also generate a radial profile for the original correlation data before subtraction, as this is needed to establish a measure of confidence. The confidence is calculated as the area under the curve (AUC) of the subtracted correlation radial profile (in the range of mean ± 3×sigma) divided by the AUC of the original correlation radial profile (in same range). The confidence value, along with the mean and sigma of the Gaussian fit are displayed in a log window. Higher values of confidence, closer to 1, indicate that two images likely have a true spatial correlation at the indicated distance.
+To remove the contribution from low spatial frequency structures/data (such as cells and nuclei), a second cross-correlation image generated from a low spatial frequency image is then subtracted from the original correlation image. For this process, the mean intesity of all the pixels of the first input image within the mask is calculated, then a new image is created where all the pixels within the mask are set to this mean value. This image is an averaged low spatial frequency image of your first input image. This low-frequency image is then cross-correlated with the second input image, and the resulting cross-correlation image is the low-frequency component, which is  subtracted from the original cross-correlation image. The mean under the mask process is only applied to one image as applying it to both did not result in a significant difference in results and uses more time and memory. Then, we generate a radial profile of the subtracted data and fit a Gaussian curve to it. We also generate a radial profile for the original correlation data before subtraction, as this is needed to establish a measure of confidence. The confidence is calculated as the area under the curve (AUC) of the subtracted correlation radial profile (in the range of mean ± 3×sigma) divided by the AUC of the original correlation radial profile (in same range). The confidence value, along with the mean and sigma of the Gaussian fit are displayed in a log window. Higher values of confidence, closer to 1, indicate that two images likely have a true spatial correlation at the indicated distance.
 
 To generate the contribution images, we further modify the subtracted cross-correlation image, by effectively multiplying it with the Gaussian fit in order to create a cross-correlation image that only retains the data within our Gaussian curve range. This Gaussian-modified cross-correlation image is then used to back-calculate the contribution images. Image1Contribution = (image2 ∗ gaussModifiedCorr) × image1. Image2Contribution = (image1 ★ gaussModifiedCorr) × image2. Key: ∗ -> convolve, ★ -> correlate.
 
-## Major revisions
+## Alternate commands
+
+These commands can be found with CCC under Analyze > Colocalization > Colocalization by Cross Correlation. Use of these is recommended only if the original CCC fails due to lack of memory (and no higher memory computer is available), or if you are generating the cross-correlation data for a purpose other than colocalization. 
+
+### CCC - No confidence
+
+The no confidence command of CCC is very similar to the original command described above, but it does not calculate the original cross-correlation. Instead, it is able to remove the low-frequency contribution prior to the first cross-correlation and generate the subtracted cross-correlation result without ever generating the original. The downside of this is that it is now unable to calculate the confidence value, as this requires the original cross-correlation data. The no confidence version is not meant for data that generates low confidence results. This is meant solely for very large datasets that are unable to be processed by the original CCC due to memory constraints. Even in these instances, the best practice would be to take a cropped region of the original dataset and perform CCC to get an approximation of the confidence value for the dataset.
+
+As a note: for time-lapse data, since the "best" frame cannot be evaluted using confidence, the frame with the smallest standard deviation is used instead. For this reason, the best frame can differ dramatically between the original version and the no-confidence version of CCC.
 
 ### Just Cross-correlation
 
-When you install CCC, you'll also find the "Just Cross Correlation" command under Analyze > Colocalization. This command simply cross-correlates the two input images, and calculates the radial profile. No Gaussian curve fitting or statistics are calculated. Just cross-correlation can be used if CCC fails due to insufficient memory, allowing you to at least see a cross-correlation curve, or it can be used for non-Gaussian relations such as the one desscribed below.
+The "Just Cross Correlation"  This command simply cross-correlates the two input images, and calculates the radial profile. No Gaussian curve fitting or statistics are calculated. Just cross-correlation can be used if CCC and CCC - No Confidence fail due to insufficient memory, allowing you to at least see a cross-correlation curve, or it can be used for non-Gaussian relations such as the one desscribed below.
 
 I originally made this as I had someone who wanted to determine the average thickness of a joint from a microCT scan. The cross-correlation of an edges only version of the two bones on either side of the joint generated an S-curve (that trailed down after the peak but too slowly for a Gaussian fit), after which they could extract the curve data and fit an S-curve to it using a separate application. 
 
+## Major revisions
+
+### 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.
+
+I am not changing the description for "How it works" above, as I feel that is a little easier to understand and the result is effectively the same. 
+
 ### Removing pixel randomization
-In version 2 of CCC, the repeating pixel randomization process (as described in the BMC Bioinformatics publication) was replaced by the mean within the mask method to remove the low spatial frequency component. This new process was faster, more memory efficient, and allows CCC to generate consistent results when provided the same input. While it seems very different on its face, this is in effect the same process and produces identical results if infinite repeats were used with v1. This is ultimately because the cross-correlation did not have to be done after each randomization with the overall result being averaged across repeats, but instead the randomization of the image could be repeated and averaged first, then the resulting image cross-correlated with the second image. Effectively:
+In v2 of CCC, the repeating pixel randomization process (as described in the BMC Bioinformatics publication) was replaced by the mean within the mask method to remove the low spatial frequency component. This new process was faster, more memory efficient, and allows CCC to generate consistent results when provided the same input. While it seems very different on its face, this is in effect the same process and produces identical results if infinite repeats were used with v1. This is ultimately because the cross-correlation did not have to be done after each randomization with the overall result being averaged across repeats, but instead the randomization of the image could be repeated and averaged first, then the resulting image cross-correlated with the second image. Effectively:
 
 $$\lim\limits_{n \to \infty} \left(\frac{\sum_{i=1}^n \left(rand(Img1)_i \star Img2\right)}{n}\right) = \lim\limits_{n \to \infty} \left(\left(\frac{\sum_{i=1}^n \left(rand(Img1)_i\right)}{n} \right)\star Img2\right)$$