TwoD Histogram (TwoD_HistogramTP)
 
Author: J. Anthony Parker, MD PhD ( J.A.Parker@IEEE.org
Dates: 2002/05/22: First version
Source: The source file, TwoD_HistogramTP.java , is also contained in Align Stacks.
Installation: Download TwoD_HistogramTP.class to the plugins or "plugins/Align Stacks" folder and restart ImageJ.
Description: This ImageJ PlugIn shows a histogram of the intensities in two images.  The x-axis represents the intensity in the first image.  The y-axis represents the intensity in the second image.  Several options for the displayed are defined:
1. Pdf = the value at point x,y in this joint histogram is the probability of pixel pairs in the source images where the value of Image1(x',y') = x and the value of Image2(x',y') = y.
2. -Joint Entropy = Pdf * log(Pdf).
3. Product = the product of one dimensional marginal histograms.
4. Mutual Information = Pdf * log(Pdf/Product).
5. -Conditional Entropy(1|2) = Pdf * log(Pdf/marginal Pdf for image 1)
6. -Conditional Entropy(2|1) = Pdf * log(Pdf/marginal Pdf for image 2)

Pdf = probability density function.  The sum of values in a Pdf is 1.  For display, the values have been multiplied by the number of pixels in the histogram, e.g. the average value in a pdf is 1.

This plugin may be interesting for visualizing similarity measures used in registration.
Zhu Y-M: Volume image registration by cross-entropy optimization. IEEE Trans Med Imaging 21:174-180, 2002.
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