Image Processing Reference
In-Depth Information
P
O
′
O
O
′′
P
′
Fig. 13.1. An illustration of the pinhole camera, also known as the perspective camera
world points
P
and
Q
the notation
−−
PQ
will be used. The primed points represent
mapped versions of the corresponding points to a plane.
The axis
−−→
OO
is known as the
optical axis
of the camera. The image is formed
in the plane orthogonal to the optical axis, shown in green in Fig. 13.1. Exploiting
the congruency between the triangles
1
of the pinhole camera, an equivalent geometry
for points mapped through the camera can be obtained (Fig. 13.2). The points that
have the same labels correspond logically to each other when compared to those
in Fig. 13.1. The image plane is again shown in green. Note that the focal plane
or the image plane is now placed between “the pinhole” and the object, whereas
in its physical realization it is the pinhole that is between the object and the image
plane. Use of this geometry as a reference model for the
projective camera
is mostly
adopted in computer vision studies, and it is equivalent to the physical model shown
in Fig. 13.1. One advantage is that the image of an object is not turned upside down.
The parameters that depend on the hardware and the design of the camera are
called
intrinsic parameters
. Referring to Fig. 13.2, the distance
−−→
OO
=
f
(13.1)
called the
focal length
,
2
is the foremost one. Because digital images are used in
the practice of computer vision, there are more parameters that are intrinsic. The
parameters
s
x
,s
y
, representing the size of 1 pixel in the length unit, e.g., meter, are
the most obvious. In a CCD sensor, for example, these are determined by how many
pixels there are in horizontal and vertical directions and how large the total width and
1
If two triangles have the same angles, then they are said to be congruent.
2
The tiny hole in the pinhole camera is effectively replaced by a lens in practice. This has
the advantage that the camera can receive more light since the lens is larger than the tiny
hole, allowing imaging with less light. Also, a lens effectively captures one plane of the
world and focuses it on the image plane, allowing us to map objects that are at a certain
distance, only.
