# Subspace Identification Extension to the Phase Correlation Method (SIE-PCM) demo

This short bit of  Matlab code was the original implementation of the method described in
``A subspace identification extension to the phase correlation method,''
IEEE Trans. Medical Imaging, 22(2):277-280, Feb. 2003.
http://dx.doi.org/10.1109/TMI.2002.808359

Images from the original 5 test frame data are included as well.

# File List

    run_example.m - start here
    siepcm.m      - a function to estimate the row and column translation between two images

The images are from 5 different MRI acquisition of a grapefruit, with
the grapefruit at different locations within the field-of-view.  In
the table below, the coordinates of one corner of the field of view
are given.

     Image File | Source file |  dim1 loc    | dim2 loc
    ------------|-------------|--------------|------------
     img1.png   | P64512.7    | y = 8.30 cm  | z= 2.00 cm
     img2.png   | P00000.7    | y = 8.15 cm  | z= 2.25 cm
     img3.png   | P00512.7    | y = 8.00 cm  | z= 2.50 cm
     img4.png   | P01024.7    | y = 7.85 cm  | z= 2.27 cm
     img5.png   | P01536.7    | y = 7.85 cm  | z= 2.75 cm

To determine the expected translational shift between the images, use the
difference between the coordinates divided by the distance per pixel.

                     dy = (y2 - y1) / n  where n=0.0625

The original data was acquired on a GE Signa Lx 1.5T MR Scanner using
the following parameters:
 TR: 500  TE: 15   protocol: FSE  coil: HEAD

----------------------------------------------------------------------

FOV length : Image Size :: 160mm : 256 pixels; => 0.0625 mm/pixel

 compare images 1 and 2.  S: -2.5 mm, A: 1.5 mm
	expect z =  -4.0000,  y =  +2.4000

 compare images 1 and 3.  S: -5 mm, A: 3 mm
	expect z =  -8.0000,  y =  +4.8000

 compare images 1 and 4.  S: -2.7 mm, A: 4.5 mm
	expect z =  -4.3200,  y =  +7.2000

 compare images 1 and 5.  S: -7.5 mm, A: 4.5 mm
	expect z = -12.0000,  y =  +7.2000

 compare images 2 and 3.  S: -2.5 mm, A: 1.5 mm
	expect z =  -4.0000,  y =  +2.4000

 compare images 2 and 4.  S: -0.2 mm, A: 3 mm
	expect z =  -0.3200,  y =  +4.8000

 compare images 2 and 5.  S: -5 mm, A: 3 mm
	expect z =  -8.0000,  y =  +4.8000

 compare images 3 and 4.  S: 2.3 mm, A: 1.5 mm
	expect z =  +3.6800,  y =  +2.4000

 compare images 3 and 5.  S: -2.5 mm, A: 1.5 mm
	expect z =  -4.0000,  y =  +2.4000

 compare images 4 and 5.  S: -4.8 mm, A: 0 mm
	expect z =  -7.6800,  y =  +0.0000

----------------------------------------------------------------------

Copyright 2003, W. Scott Hoge (wsh032580 at proton dot me)

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