Titled Photograph

1. © 2019 Dr. Sarhat M Adam
BSc in civil Engineering
Msc in Geodetic Surveying
PhD in Engineering Surveying & Space Geodesy
Note – Figures and materials in the slides may be the authors own work or
extracted from internet websites, Materials by Duhok or Nottingham
universities staff and their slides, author's own knowledge, or various internet
image sources and books example (Element of Photogrammetry by wolf).
Lecture 08: Tilted
Photographs

2. Introduction
 tilted photographs: unavoidable aircraft tilts cause photographs to be
exposed with the camera axis tilted slightly from vertical.
 The tilt is usually less than 1° and rarely exceeds 3°.
 In some cases, aerial photography is purposely angled away from vertical.
These types of images are classified as high oblique if the photograph
contains the horizon, and low oblique otherwise.
 Terrestrial photos are almost always taken from an oblique pose.
Horizontal terrestrial photos are obtained if the camera axis is horizontal
when the exposure is made.
 (EOPs) express the spatial position and angular orientation of a photograph
given by XL, YL, and ZL, 3D-coordinates of the exposure station in a
ground coordinate system.
 Three angles are sufficient to define angular orientation, two different
systems are described: (1) the tilt-swing-azimuth (t-s-α) system and (2) the
omega-phi-kappa (ω-φ-κ) system.

3. Introduction
Rotation around the
X-axis (omega)
Rotation around the
Y-axis (phi)
Rotation around the
Z-axis (kappa)
•Omega (ω) is the rotation around the Χ-axis.
•Phi (φ) is the rotation around the Y-axis.
•Kappa (κ) is the rotation around the Z-axis.
•The omega, phi, kappa are in degrees and can be positive or negative. This means,
for example, that the value 350 degrees can be expressed also as -10 [0-(360-350)].

4. Introduction
Yaw
•If yaw = 0° and the camera is looking to the ground (i.e. nadir), it means that the
top of the image’s points to the north.
•If yaw = 90° and the camera is looking nadir, it means that the top of the images
points to the east.
•If yaw = 270 and the camera is looking nadir, it means that the top of the images
points to the west.
Pitch
•If pitch = 0, it means that the camera is looking down (i.e. nadir).
•If pitch = 90, it means that the camera is looking forward.
Roll
•If using a gimbal, this value is usually 0.

5. Point Perspective
 perspective projection: is how 3D objects (the scene photographed) appear
when projected onto a 2D surface (film or CCD array).
 The collinearity equations mathematically describe the perspective
projection from 3D object space to 2D image space (later described).
 In PP, straight lines are preserved and lines that are parallel in object space
intersect in image plane @ vanishing points. Fig shows (1, 2, 3-point P)

6. Angular Orientation in t, s, & Azimuth
y
x
L
o
n
Ng
Nd
Pg
Pd
N
t
s
Principal
line
Vertical
Optical
axis
Datum Principal
Line
Pricipal
plane

7. Tilted photo Coordinate system
1. Rotation around principal point, rotate
(x,y) to (x”,y”) using s (swing).
2. By translation: ,move from (o) to (n)
x
y
y"
x"
u
s
n
o
a
ya
xa
y"a
x"a
x'
y'
y'a
ftan(t)sinθ = –sins and cosθ = –coss
ftan(t)
f
o
n
L

8. Tilted photo scale
1. Objects (a & b) are the same in the ground.
2. Object a appears bigger than b.
3. Tilt or relief variations cause change in
scale.
4. If tilt, swing, height, & elevation known.
The scale can be calculated at any point.
o
n
a b
a
b
Pg
ng
L

9. Tilted photo scale
 Scale of tilted Photograph
 S = the scale on a tilted photograph for
any point whose elevation is h above
datum.
 H= Flying height above datum
 f = the camera focal length;
 y′ = the coordinate of the point in the
auxiliary system according to
L
n
o
H
A
A'
hA
Datum
plane
K
K'
Nd
a"
k k'
a' a
x'
y'
x'a