Correlation

Correlation

Purpose

This program allows you to calculate the similarity between (parts of) volumes or images. Four different similarity indices are provided:

Correlation	`co = 1/N*sum(x*y)`
Cross-correlation coefficient	`cc = 1/N*sum{(x-mean_x)__(y-mean_y)}/(stddev_x__stddev_y*n)`
Euclidian Distance	`eu = sqrt[sum{(x-y)*(x-y)}]`
Mutual Information	`mi = sum [ P(x,y)__log2{P(x,y)/(P(x)__P(y))} ]`

where sum is over all N pixels of images/volumes x and y.

The input images or volumes are compared to the reference one. Results are written to the output screen, or can be piped into an output file.

Usage

$ correlation -ref [reference file] -i [input file] ...

Parameters

• `` Either a volume or an image file
• `` Either a volume, an image file, or a selfile containing multiple volumes or images. The input files should have the same (square/cubic) dimensions as the reference file
• `` Restrict the similarity calculation to the region within the mask. By default, the program uses the entire image or volume.
• `` By default, the program calculates four different similarity indices. Use this to only calculate the correlation (i.e. signal product)
• `` To only calculate the cross-correlation coefficient
• `` To only calculate the euclidian distance
• `` To only calculate the mutual information

Examples and notes

To calculate the similarity within a mask region between a reference image and all the images in a selfile, type:

$ correlation -ref reference.xmp -i selfile.sel -mask circular.msk

For each image in the selfile the program will write out one line, containing it's cross-correlation coefficient, euclidian distance and mutual information with respect to the reference image.

--Main.AlfredoSolano - 17 Jan 2007