Properties of Aerial Photography
Chapter 4
Properties of Aerial
Photography
4.1
Introduction
Aerial photography is the basic data source for making maps by photogrametric means.
The photograph is the end result of the data acquisition process discussed in the previous chapter. Actually, the net result of any photographic mission are the photographic
negatives. Of prime importance for measuring and interpretation are the positive reproductions from the negatives, called diapositives.
Many factors determine the quality of aerial photography, such as
• design and quality of lens system
• manufacturing the camera
• photographic material
• development process
• weather conditions and sun angle during photo flight
In this chapter we describe the types of aerial photographs, their geometrical properties and relationship to object space.
4.2
Classification of aerial photographs
Aerial photographs are usually classified according to the orientation of the camera axis,
the focal length of the camera, and the type of emulsion.
42
4.2.1
4 Properties of Aerial Photography
Orientation of camera axis
Here, we introduce the terminology used for classifying aerial photographs according
to the orientation of the camera axis. Fig. 4.1 illustrates the different cases.
true vertical photograph A photograph with the camera axis perfectly vertical (identical to plumb line through exposure center). Such photographs hardly exist in
reality.
near vertical photograph A photograph with the camera axis nearly vertical. The
deviation from the vertical is called tilt. It must not exceed mechanical limitations
of stereoplotter to accomodate it. Gyroscopically controlled mounts provide
stability of the camera so that the tilt is usually less than two to three degrees.
oblique photograph A photograph with the camera axis intentially tilted between the
vertical and horizontal. A high oblique photograph, depicted in Fig. 4.1(c) is
tilted so much that the horizon is visible on the photograph. A low oblique does
not show the horizon (Fig. 4.1(b)).
The total area photographed with obliques is much larger than that of vertical
photographs. The main application of oblique photographs is in reconnaissance.
Figure 4.1: Classification of photographs according to camera orientation. In (a) the
schematic diagram of a true vertical photograph is shown; (b) shows a low oblique and
(c) depicts a high oblique photograph.
4.2.2 Angular coverage
The angular coverage is a function of focal length and format size. Since the format size
is almost exclusively 9 × 9 the angular coverage depends on the focal length of the
camera only. Standard focal lengths and associated angular coverages are summarized
in Table 4.1.
4.3 Geometric properties of aerial photographs
43
Table 4.1: Summary of photographs with different angular coverage.
focal length [mm]
angular coverage [o]
4.2.3
superwide
85.
119.
wideangle
157.
82.
intermediate
210.
64.
normalangle
305.
46.
narrowangle
610.
24.
Emulsion type
The sensitivity range of the emulsion is used to classify photography into
panchromatic black and white This is most widely used type of emulsion for photogrammetric mapping.
color Color photography is mainly used for interpretation purposes. Recently, color is
increasingly being used for mapping applications.
infrared black and white Since infrared is less affected by haze it is used in applications where weather conditions may not be as favorable as for mapping missions
(e.g. intelligence).
false color This is particular useful for interpretation, mainly for analyzing vegetation
(e.g. crop desease) and water pollution.
4.3
Geometric properties of aerial photographs
We restrict the discussion about geometric properties to frame photography, that is,
photographs exposed in one instant. Furthermore, we assume central projection.
4.3.1
Definitions
Fig. 4.2 shows a diapositive in near vertical position. The following definitions apply:
perspective center C calibrated perspective center (see also camera calibration, interior orientation).
focal length c calibrated focal length (see also camera calibration, interior orientation).
principal point PP principal point of autocollimation (see also camera calibration,
interior orienttion).
camera axis C-PP axis defined by the projection center C and the principal point PP.
The camera axis represents the optical axis. It is perpendicular to the image plane
44
4 Properties of Aerial Photography
C
t
PP
ip
I
pl
N
s
Y
Z
α
O’
N’
X
Figure 4.2: Tilted photograph in diapositive position and ground control coordinate
system.
nadir point N also called photo nadir point, is the intersection of vertical (plumb line)
from perspective center with photograph.
ground nadir point N intersection of vertical from perspective center with the earth’s
surface.
tilt angle t angle between vertical and camera axis.
swing angle s is the angle at the principal point measured from the +y-axis counterclockwise to the nadir N .
azimut α is the angle at the ground nadir N measured from the +Y-axis in the ground
system counterclockwise to the intersection O of the camera axis with the ground
surface. It is the azimut of the trace of the principal plane in the XY -plane of the
ground system.
principal line pl intersection of plane defined by the vertical through perspective center
and camera axis with the photograph. Both, the nadir N and the principal point
4.3 Geometric properties of aerial photographs
45
PP are on the principal line. The principal line is oriented in the direction of
steepest inclination of of the tilted photograph.
isocenter I is the intersection of the bisector of angle t with the photograph. It is on
the principal line.
isometric parallel ip is in the plane of photograph and is perpendicular to the principal
line at the isocenter.
true horizon line intersection of a horizontal plane through persepective center with
photograph or its extension. The horizon line falls within the extent of the photograph only for high oblique photographs.
horizon point intersection of principal line with true horizon line.
4.3.2
Image and object space
The photograph is a perspective (central) projection. During the image formation
process, the physical projection center object side is the center of the entrance pupil
while the center of the exit pupil is the projection center image side (see also Fig. 4.3.
The two projection centers are separated by the nodal separation. The two projection
centers also separate the space into image space and object space as indicated in Fig. 4.3.
B’
A’
negative
image space
exit
pupil
entrance
object space
A
B
Figure 4.3: The concept of image and object space.
During the camera calibration process the projection center in image space is
changed to a new position, called the calibrated projection center. As discussed in
2.6, this is necessary to achieve close similarity between the image and object bundle.
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4.3.3
4 Properties of Aerial Photography
Photo scale
We use the representative fraction for scale expressions, in form of a ratio, e.g. 1 : 5,000.
As illustrated in Fig. 4.4 the scale of a near vertical photograph can be approximated by
c
(4.1)
H
where mb is the photograph scale number, c the calibrated focal length, and H the
flight height above mean ground elevation. Note that the flight height H refers to the
average ground elevation. If it is with respect to the datum, then it is called flight altitude
HA , with HA = H + h.
mb =
C
P’
HA
H
P
h
datum
Figure 4.4: Flight height, flight altitude and scale of aerial photograph.
The photograph scale varies from point to point. For example, the scale for point P
can easily be determined as the ratio of image distance CP to object distance CP by
mP
=
CP =
CP
CP CP
x2P + yP2 + c2
(XP − XC )2 + (YP − YC )2 + (ZP − ZC )2
=
(4.2)
(4.3)
(4.4)
4.3 Geometric properties of aerial photographs
47
where xP , yP are the photo-coordinates, XP , YP , ZP the ground coordinates of
point P, and XC , YC , ZC the coordinates of the projection center C in the ground
coordinate system. Clearly, above equation takes into account any tilt and topographic
variations of the surface (relief).
4.3.4
Relief displacement
The effect of relief does not only cause a change in the scale but can also be considered
as a component of image displacement. Fig. 4.5 illustrates this concept. Suppose point
T is on top of a building and point B at the bottom. On a map, both points have identical
X, Y coordinates; however, on the photograph they are imaged at different positions,
namely in T and B . The distance d between the two photo points is called relief
displacement because it is caused by the elevation difference ∆h between T and B.
C
rB
d
PP
H
rT
T
∆h
B
Figure 4.5: Relief displacement.
The magnitude of relief displacement for a true vertical photograph can be determined by the following equation
d=
r ∆h
r ∆h
=
H
H − ∆h
(4.5)
dH
r
(4.6)
2 , and ∆h the elevation difference of two
where r = x2T + yT2 , r = x2B + yB
points on a vertical. Eq. 4.5 can be used to determine the elevation ∆h of a vertical
object
h=
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4 Properties of Aerial Photography
The direction of relief displacement is radial with respect to the nadir point N ,
independent of camera tilt.
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