Image Processing Reference
In-Depth Information
Fig. 13.2. The perspective camera model is illustrated by projection of a point P to its image
point P
the total height of the sensor is in the length unit. Next, is the less obvious parameter
set
−−→
O C =( c 0 ,r 0 ) T
(13.2)
which is the translation vector between the digital image center and the analog im-
age center, the image of the optical axis. For technical reasons, such as limitations
and constraints of mechanical construction and lens imperfections, the digital image
rectangle, shown in magenta in Fig. 13.2 is not centered around the optical axis but
around a point that is marked as C in the figure.
We can represent the world point P by the vector
−− OP =( X, Y, Z ) T
(13.3)
where the numerical values of the vector components are represented relative to the
camera basis, e X , e Y , and e Z . Likewise we can represent an image point P by the
vector
−−−→
O P =( x, y ) T
(13.4)
where the vector components are given relative to the (analog) image coordinates,
e x , e y with the frame origin placed at the image of the optical axis, the point O .
Using the congruency between the triangle OO P
and the triangle OO P ,wecan
write
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