Stereo vision, 3D video capture and scene representations - 3D Video Processing and Transmission - page 27

Under the assumption that the world coordinate system equals the camera coordinate
system of the first camera, the two perspective projection equations will be;

~

~

x  AP n X
~ ~
Equation 2.2

x ʹ  A ʹ P n H f X
Equation 2.3

Wherexandx`symbolizetwo2Dimagepointswithrespecttothe3DspacepointXinho-
mogeneous notation.Thesymbol denotesthe'equalityuptoanon-zeroscale-factor' [22]
[23]. The4×4matrix H f contains the transform matrix which converts the 3D space point
from world coordinate system into
thecameracoordinatesystemofthesecondview.TheH f consistsoftwotransformcomponents
namely
rotation R and translation T. The 3 × 3 matrices A and A` defines the intrinsic parameters
of the first and second cameras respectively. The normalized perspective projection matrix
is denoted by the 3 × 4 identity matrix P n .

The3Dspacepoint X isstilldependentonitsdepthvalue Z .Hence,Equation2.2canberear-
rangedinto;

X  ZA

1 ~
m

Equation 2.4