(3.3.5) — Xg=(x!/2")=[ X/Z + XY/Z2 = w(1+X2/z2) + xY/Z 1; 
Ygs(yV z0sE Y/Z * 9 (1*Y2/Z22) - wXY/Z2 - xX/Z J. 
3.4 Displacement vector extraction 
The left part of (3.3.5) represents the components of the 
displacement vector, and must be determined as a result of the 
measurement, 
To compute the displacement we use the phase correlation 
technique, described by Kuglin and Hines (Kuglin and Hines,1975). 
The phase correlation method uses the fact that the information 
pertaining to the displacement of two images resides in the phase 
of the cross power spectrum. The phase correlation function is 
obtained by first computing the discrete two-dimensional Fourier 
transforms, and extracting the phase of the cross-power spectrum 
of two images, Gy and Go: 
* 
G1G» 
! Gio," | 
and then computing the inverse Fourier transform of the phase 
array 
d = Pl 1 olf}. 
The last equation yields a sharp peak located at 
corresponding to the displacement vector. 
This method is relatively scene-independent, exibits an extremely 
narrow correlation peak, and is insensitive to narrow bandwidth 
noise. However, in the digital implementation used, only integer 
pixel displacement are used, so that displacement to only the 
nearest pixel is available. 
4, Simulation 
4,1 Lookpoint model and image extraction 
et 
he position 
For the purpose of this simulation, the displacement vector 
components are determined from the comparison of the time- 
sequential subimages, extracted from a LANDSAT Thematic Mapper 
frame. 
The square detector array not parallel to the ground will 
generally image a trapezoidal area. To extract the portion of the 
TM scene as "seen" by our níne arrays, we first compute the 
location of the corners and the centers of the nine array