Praca Dyplomowa - Photogrammetry and Remote Sensing - AGH

THEORETICAL BACKGROUND
Figure 2.8 Exterior orientation for terrestrial photogrammetry (Luhmann et al., 2006)
Matrix R of rotation for exterior orientation is a set of combination of sinus and cosinus
functions of rotation angles mentioned before. Matrix X0 describes position of the camera.
2.2.9 Collinearity equations
These equations are the core in the photogrammetry. From these equations it is possible to get
object coordinates from image coordinates (exterior orientation). These equations are also
base for other computations, like Bundle Adjustment or Direct Linear Transformation.
Collinearity equations:
( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( )
Where:
x’, y’, z’ – image coordinates of corresponding points (measured on the picture)
z’ – is usually equal principle distance z’=-c
x’0, y’0 – coordinates of the principle point H’ in image coordinate system
∆x’, ∆y’ – correction terms of the image coordinates
X, Y, Z – object coordinates of corresponding points (measured on the picture)
X0, Y0, Z0 – object coordinates of principle point H
These equations describe the transformation of object coordinates (X, Y, Z) into corresponding
image coordinates (x’, y’) as functions of the interior parameters and exterior orientation
parameters of one image.
An alternative form may be given, if the object coordinate system is transformed by shift to
the perspective centre and orientation parallel to the image coordinate system.
These equations demonstrate clearly that each object point is projected into a unique image
point, if it is not occluded by other object points. The formulas effectively describe image
generation inside a camera by the geometry of a central projection.
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(2.8)