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the relative position and orientation of the two viewpoints and also the 3D coordi-
nates of the five points (in some arbitrary coordinate system). However, this the-
orem assumes the images come from an ideal perspective projection, which real
cameras do not provide. Photogrammetry in general has been actively studied in
other disciplines, such as computer vision. The process of stereophotogrammetry
consists of the following three steps: camera calibration stereo correspondence,
and stereo reconstruction.
5.1.1 Camera Calibration
The precise details of how a particular camera forms a 2D image of a 3D scene
depends on two things: how incoming light paths are focused by the camera op-
tics, and how the incident radiance is recorded in the image. The former is most
relevant in stereo geometry reconstruction; the latter is of interest when the cam-
era is used for physical light measurement. How 3D points are transformed to
points on the 2D camera sensor plane can be modeled as a mathematical projec-
tion. Ultimately stereo reconstruction depends on the inverse of this projection.
The projection is determined by the internal optics of the camera as well as its
position and orientation in space with respect to the scene. The camera optics,
e.g., the position of the sensor with respect to the lens and the optical properties
of the lenses, are
intrinsic parameters
of the camera. The
extrinsic parameters
describe where the camera is located in space and where it is pointed.
What exactly the intrinsic parameters are depends on the projection model.
Generally, intrinsic camera parameters include the focal length of the lens, the
size of the aperture (f-stop), and the field of view. More detailed information
such as the error between the center of projection and the center of the sensor
plane, lens aberration, etc., may also be needed for more precise reconstruction.
The general process of determining the intrinsic parameters is known as
camera
calibration
. Most commonly, calibration is done by capturing a series of images
of a known target.
A simple pinhole camera consists of a closed box with photosensitive film
placed on the inside of one side and a small “pinhole” aperture punched in the
center of the opposite side. Mathematically the pinhole aperture is assumed to be a
single point, so each point on the film records the radiance of the light ray coming
from the direction of the aperture. The pinhole camera projection is the standard
perspective projection
(
Figure 5.1(a)
)
. A lens camera uses a system of lenses
to focus incoming light onto the film plane. An ideal lens camera focuses light
rays coming from a specific
focal plane
in space onto the film plane so that each
point on the film plane corresponds to a unique point on the focal plane. The focal
plane thus appears perfectly in focus in the image. The position of the focal plane
