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Ayman F. Habib Photogrammetric & LiDAR Mapping 
1 
Principles of Photogrammetric Mapping 
Chapter 1 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
2 
Overview 
• Photogrammetry: Definition and Applications 
• Photogrammetric Tools: 
– Rotation matrices 
– Photogrammetric orientation: interior and exterior 
orientation 
– Collinearity equations/conditions 
• Photogrammetric Bundle Adjustment 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
3 
Photogrammetry 
• Classical Definitions: 
– The art and science of determining the position and 
shape of objects from photography 
– The process of reconstructing objects without touching 
them 
– Non-contact positioning method 
• Contemporary Definition: 
– The art and science of tool development for automatic 
generation of spatial and descriptive information from 
multi-sensory data and/or systems 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
4 
Data Acquisition Systems 
Traditional Mapping Cameras 
Large Format Imaging Systems 
Low-Cost Digital Cameras 
Medium and Small Format Digital Imaging Systems 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
5 
Terrestrial (Close Range) Imagery 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
6 
Terrestrial (Close Range) Imagery 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
7 
Input Stereo-Imagery 
Terrestrial (Close Range) Imagery 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
8 
Output Three-Dimensional Model 
Terrestrial (Close Range) Imagery 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
9 
• Experiments: 
 
 
 
• Results: 
 
Green: Reference 
Blue: Matches 
Red: Non-matches 
Test 1 
Terrestrial (Close Range) Imagery 
Test Descriptions 
1 Subject 1: Time 1 & Time 2 
2 Subject 1: No Smile & Smile 
3 Subject 2 & Subject 3 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
10 
• Experiments: 
 
 
 
• Results: 
 
Test Descriptions 
1 Subject 1: Time 1 & Time 2 
2 Subject 1: No Smile & Smile 
3 Subject 2 & Subject 3 
Green: Reference 
Blue: Matches 
Red: Non-matches 
Test 2 
Terrestrial (Close Range) Imagery 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
11 
• Experiments: 
 
 
 
• Results: 
 
Green: Reference 
Blue: Matches 
Red: Non-matches 
Test 3 
Terrestrial (Close Range) Imagery 
Test Descriptions 
1 Subject 1: Time 1 & Time 2 
2 Subject 1: No Smile & Smile 
3 Subject 2 & Subject 3 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
12 
Terrestrial (Close Range) Imagery 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
• 3D deformity of the human spine 
 
• Affects 2-3% of the population 
 
• Impacts the quality of life 
 
• Early detection is vital 
http://www.nlm.nih.gov/MEDLINEPLUS/ency/images/ency/fullsize/19466.jpg 
www.rad.washington.edu/mskbook/scoliosis.html 
13 
www.nlm.nih.gov/MEDLINEPLUS/ency/images/ency/fullsize/19466.jpg 
www.rad.washington.edu/mskbook/scoliosis.html 
Terrestrial (Close Range) Imagery 
Scoliosis 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
Traditional method: 
• Full-length spinal x-ray 
 in a standing position 
 
Consequences: 
• Frequent exposure to radiation 
 (4-5 times a year, for 3-5 years) 
• Increased risk of cancer 
 http://medicineworld.org/images/blogs/6-2007/scoliosis-2020.jpg 
14 
http://www.e-radiography.net/radpath/c/cobb-angle.jpg 
α 
Cobb Angle 
Terrestrial (Close Range) Imagery 
Scoliosis Detection & Monitoring 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
15 
Terrestrial (Close Range) Imagery 
 Cameras, projectors, frame, target board, computer(s), 
remote control 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
16 
I 
II 
III 
IV Object 
 Four point clouds in four different 
reference frames → necessity for a 
registration to a common reference frame 
Terrestrial (Close Range) Imagery 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
Multiple surface registration: complete 3D torso model 
17 
 Qualitative assessment 
Terrestrial (Close Range) Imagery 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
18 
Terrestrial (Close Range) Imagery 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
19 
Mobile Mapping Systems (MMS) 
Terrestrial (Close Range) Imagery 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
20 
The Ohio State University 
Terrestrial (Close Range) Imagery 
Mobile Mapping Systems (MMS) 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
21 
University of Calgary 
Terrestrial (Close Range) Imagery 
Mobile Mapping Systems (MMS) 
http://www.amsvisat.com/VISAT Van 2006 Shadow.jpg
Ayman F. Habib Photogrammetric & LiDAR Mapping 
22 
Sign Type 
Height above Pavement 
Offset from Road Edge 
Coordinate Locations 
Size of Sign 
Terrestrial (Close Range) Imagery 
Mobile Mapping Systems (MMS) 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
23 
Collecting Inventories 
On-going Maintenance 
Database Integration 
Terrestrial (Close Range) Imagery 
Mobile Mapping Systems (MMS) 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
24 
Aerial Imagery 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
25 
Photogrammetric Mapping 
Aerial Imagery 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
26 
Aerial Imagery 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
27 
Satellite Imagery 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
28 
IKONOS QUICKBIRD 
Satellite Imagery 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
29 
Photography 
A 
a 
C 
c 
B 
b 
D 
d 
Lens (Perspective Center) 
Image Space 
Object Space 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
30 30 
Object Point (A) 
Conjugate Points 
• The interior orientation parameters of the involved cameras have to be known. 
• The position and the orientation of the camera stations have to be known. 
a a´ 
Camera Calibration (IOP) Geo-referencing (EOP) 
Photogrammetry 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
31 
xa 
ya 
a 
xc 
zc 
yc Perspective Center 
Xm 
Zm 
Ym 
A 
XA 
YA 
ZA 
),,,,(
),,,,(
EOPIOPZYXfy
EOPIOPZYXfx
AAAya
AAAxa


Photogrammetry 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
32 
Overlap 
Photogrammetry 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
33 
Photogrammetry 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
34 
Photogrammetry 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
35 
• Rotation matrices: 
– Express the mathematical relationship between two 
coordinate systems 
– In a three-dimensional space, a rotation matrix involves 
at most three independent rotation angles. 
• Photogrammetric orientation: 
– Internal characteristics: Interior Orientation Parameters 
(IOP) 
– External characteristics: Exterior Orientation Parameters 
(EOP) 
• Collinearity condition: 
– The general mathematical model relating the image and 
ground coordinates of corresponding points 
Photogrammetry: Necessary Tools 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
Notations 
36 
Stands for the coordinates of point a relative to 
point b – this vector is defined relative to the 
coordinate system associated with point b. 
b
ar
Stands for the rotation matrix that transforms a 
vector defined relative to the coordinate system 
denoted by a into a vector defined relative to the 
coordinate system denoted by b. 
b
aR
Vectors will be represented by a lower case ''r'' 
Rotation matrices will be represented by an 
upper case ''R'' 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
b
ar
b 
a 
b
aR
37 
Notations 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
Rotation Matrix 
• A rotation matrix transforms a vector from one 
coordinate system to another. 
 
38 
Xm 
Zm 
Ym 
I 
J 
K 
c
a
m
c
m
a rRr 











333231
232221
131211
rrr
rrr
rrr
R
m
c
Ayman F. Habib Photogrammetric & LiDAR Mapping 
39 
Rotation Matrix 
c
a
m
c
m
a rRr 
• Let’s consider the transformation of a unit vector 
along the x-axis of the camera coordinatesystem 





















0
0
1
31
21
11
m
cR
r
r
r
• The first column of the rotation matrix represents 
the components of a unit vector along the x-axis of 
the camera coordinate system w.r.t. the mapping 
reference frame. 
• The norm of the first column is unity. 
1
2
31
2
21
2
11  rrr 1 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
40 
Rotation Matrix 
c
a
m
c
m
a rRr 
• Let’s consider the transformation of a unit vector 
along the y-axis of the camera coordinate system 





















0
1
0
32
22
12
m
cR
r
r
r
• The second column of the rotation matrix 
represents the components of a unit vector along 
the y-axis of the camera coordinate system w.r.t. 
the mapping reference frame. 
• The norm of the second column is unity. 
1
2
32
2
22
2
12  rrr 2 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
41 
Rotation Matrix 
c
a
m
c
m
a rRr 
• Let’s consider the transformation of a unit vector 
along the z-axis of the camera coordinate system 





















1
0
0
33
23
13
m
cR
r
r
r
• The third column of the rotation matrix represents 
the components of a unit vector along the z-axis of 
the camera coordinate system w.r.t. the mapping 
reference frame. 
• The norm of the third column is unity. 
1
2
33
2
23
2
13  rrr 3 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
42 
Rotation Matrix 
• Since the x and y axes of the camera coordinate 
system are orthogonal to each other, then 
0
32
22
12
31
21
11






















r
r
r
r
r
r
0323122211211  rrrrrr
• Since the x and z axes of the camera coordinate 
system are orthogonal to each other, then 
0
33
23
13
31
21
11






















r
r
r
r
r
r
0333123211311  rrrrrr
4 
5 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
43 
Rotation Matrix 
• Since the y and z axes of the camera coordinate 
system are orthogonal to each other, then 
0
33
23
13
32
22
12






















r
r
r
r
r
r
0333223221312  rrrrrr
• Since the nine elements of a rotation matrix must 
satisfy six constraints (orthogonality constraints), a 
3D rotation matrix is defined by a maximum of 
three independent parameters/rotation angles. 
• In photogrammetry, the rotation matrix is defined 
by the angles (w, f, and k). 
6 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
44 
Positive Rotation Angles 
(Right Handed System) 
y 
x 
z 
+ve f 
+ve k 
+ve w 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
45 
z 
x 
y 
Z 
X 
Y 
z 
x 
y 
Y 
X 
Z 
x 
Y 
X Z 
y 
w 
f 
k 
z 
w ≈ 90° k ≈ 0° f ≈ -20° 
Rotation Angles (w, f, k) 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
46 
Rotation Angles (Azimuth, Pitch, Roll) 
Azimuth ≡ Yaw 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
47 
Interior Orientation Parameters 
• Interior Orientation Parameters (IOP) describe the 
internal characteristics of the implemented camera. 
– IOP include the principal distance, principal point 
coordinates, and distortion parameters. 
– IOP are determined using a calibration procedure. 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
48 
• Alternative procedures for camera calibration are 
well established. 
– Laboratory camera calibration (Multi-collimators) 
– Indoor camera calibration 
– In-situ camera calibration 
Interior Orientation Parameters 
Analytical Camera 
Calibration 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
49 
Laboratory Calibration: Multi-Collimators 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
50 
Indoor Camera Calibration 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
51 
In-Situ Camera Calibration 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
52 
x 
y 
z 
pc (xp, yp, c) 
• IOP together with the image coordinates of selected 
features define a bundle of light rays (image bundle). 
Interior Orientation Parameters 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
53 
• Target function of the Interior Orientation: 
– The defined bundle by the IOP should be as similar as possible to 
the incident bundle onto the camera at the moment of exposure. 
Interior Orientation Parameters 
≡ 
A 
a 
C 
c 
B 
b 
D 
d 
Lens 
Image Space 
Object Space 
Photography 
a c b d 
Lens 
Image Space 
Establishing IO 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
54 
• Exterior Orientation Parameters (EOP) – geo-
referencing parameters – define the position and 
the attitude of the image bundle relative to the 
ground coordinate system. 
– The position of the bundle is defined by (Xo, Yo, Zo). 
– The attitude of the bundle (camera/image coordinate 
system) relative to the ground coordinate system is 
defined by the rotation angles (w, f, k). 
• EOP can be either: 
– Indirectly estimated using Ground Control Points 
(GCP), or 
– Directly measured using GNSS/INS units onboard the 
imaging platform. 
Exterior Orientation Parameters 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
55 
XG 
YG 
ZG 
x 
y z 
),,( kfwR
Xo 
Zo 
Yo 
pc 
• EOP: 
– Indirectly estimated (indirect geo-referencing), or 
– Directly measured (direct geo-referencing) 
Exterior Orientation Parameters 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
56 
Ground Control Points 
Tie Points 
Indirect Geo-Referencing 
Exterior Orientation Parameters 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
57 
Signalized Targets 
Indirect Geo-Referencing 
Exterior Orientation Parameters 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
58 
Natural Targets 
Indirect Geo-Referencing 
Exterior Orientation Parameters 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
59 
Direct Geo-Referencing 
Exterior Orientation Parameters 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
60 
Direct Geo-Referencing 
Exterior Orientation Parameters 
GNSS Antenna 
Camera 
INS PC 
Two Base Stations 
GNSS Receiver 
Direct geo-referencing in practice 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
61 
Direct Geo-Referencing 
Exterior Orientation Parameters 
 
Digital camera 
 
GNSS antenna 
 
INS 
Direct geo-referencing in practice 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
62 
Collinearity Equations 
• Objective: 
– Mathematically represent the general relationship 
between image and ground coordinates 
• Concept: 
– Image Point, Object Point, and the Perspective Center 
are collinear 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
63 
(A) Object Point 
(a) Image Point 
Perspective Center 
Straight Line 
Collinearity Equations 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
64 
o 
a 
A 
oa = l oA 
These vectors should be defined w.r.t. 
the same coordinate system 
Collinearity Equations 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
65 
Frame Camera 
Diapositive 
Foot Print 
Negative 
Perspective Center 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
66 
Negative Versus Diapositive Films 
Negative Film 
Diapositive 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
67 
Oi 
xi 
yi zi 
A 
XA 
YA 
ZA 
a 
+ 
(xa, ya) 
R( , , )w f k
XG 
YG 
ZG 
OG 
pp 
+ 
c 
(Perspective Center) 
Xo 
Zo 
Yo 
Collinearity Equations 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
68 
The Vector Connecting the Perspective 
Center to the Image Point 






































c
distyy
distxx
c
y
x
disty
distx
rv ypa
xpa
p
p
ya
xa
c
oai
0

w.r.t. the image coordinate system 
o 
a 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
69 
The Vector Connecting the Perspective 
Center to the Object Point 



































oA
oA
oA
o
o
o
A
A
A
m
oAo
ZZ
YY
XX
Z
Y
X
Z
Y
X
rV

w.r.t. the ground coordinate system 
o 
A 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
70 






































oA
oA
oA
ypa
xpa
c
oA
c
mO
c
oai
ZZ
YY
XX
mmm
mmm
mmm
c
distyy
distxx
rRVMrv
333231
232221
131211
),,(
l
lkfwl

Where: l is a scale factor 
Collinearity Equations 
• Questions: 
– Can you come up with an average estimate of λ? 
– Is λ constant for a given image? Why? 
oAoa l
Ayman F. Habib Photogrammetric & LiDAR Mapping 
71 
Collinearity Equations 
y
oAoAoA
oAoAoA
pa
x
oAoAoA
oAoAoA
pa
dist
ZZrYYrXXr
ZZrYYrXXr
cyy
dist
ZZrYYrXXr
ZZrYYrXXr
cxx








)()()(
)()()(
)()()(
)()()(
332313
322212
332313
312111
m
cRR 
y
oAoAoA
oAoAoA
pa
x
oAoAoA
oAoAoA
pa
dist
ZZmYYmXXm
ZZmYYmXXm
cyy
dist
ZZmYYmXXm
ZZmYYmXXm
cxx








)()()(
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Ayman F. Habib Photogrammetric & LiDAR Mapping 
72 
• Involved parameters: 
– Image coordinates (xa, ya) 
– Ground coordinates (XA, YA, ZA) 
– Exterior Orientation Parameters (Xo, Yo, Zo, w, f, k) 
– Interior Orientation Parameters (xp, yp, c, distx, disty) 
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Collinearity Equations 
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Ayman F. Habib Photogrammetric & LiDAR Mapping 
73 
 
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Frame
2. Image Coordinate System
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Vector Summation Procedure 
Collinearity Equations 
Ayman F. Habib Photogrammetric & LiDAR Mapping 

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74 
Vector Summation Procedure 
Collinearity Equations 
c
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Ayman F. Habib Photogrammetric & LiDAR Mapping 
75 
Bundle Block Adjustment 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
76 
60% overlap and 20% side lap 
Bundle Block Adjustment 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
77 
Bundle Block Adjustment 
• Direct relationship between image and ground 
coordinates 
• We measure the image coordinates in the images 
of the block. 
• Using the collinearity equations, we can relate the 
image coordinates, corresponding ground 
coordinates, IOP, and EOP. 
• Using a simultaneous least squares adjustment, we 
can solve for the: 
– The ground coordinates of the tie points, 
– The EOP, and 
– The IOP (Camera Calibration Procedure). 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
78 
• The image coordinate measurements and the IOP 
define a bundle of light rays. 
• The EOP define the position and the attitude of the 
bundles in space. 
• During the adjustment: The bundles are rotated 
(w, f, k) and shifted (Xo, Yo, Zo) until: 
– Conjugate light rays intersect as well as possible at the 
locations of object space tie points. 
– Light rays corresponding to ground control points pass 
through the object points as close as possible. 
Bundle Block Adjustment: Concept 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
79 
Bundle Block Adjustment: Concept 
Ground Control Points 
Tie Points 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
80 
Advantages of Bundle Block Adjustment 
• Most accurate triangulation technique since we have direct 
transformation between image and ground coordinates. 
• Straight forward to include parameters that compensate for 
various deviations from the collinearity model. 
• Straight forward to include additional observations: 
– GNSS/INS observations at the exposure stations 
– Object space distances 
• Can be used for normal, convergent, aerial, and close range 
imagery 
• After the adjustment, the EOP can be set on analogue and 
analytical plotters for compilation purposes. 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
81 
Photogrammetric Compilation 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
82 
Disadvantages of Bundle Block Adjustment 
• Model is non linear: approximations as well as 
partial derivatives are needed. 
• Requires computer intensive computations. 
• Analogue instruments cannot be used (they cannot 
measure image coordinate measurements). 
• The adjustment cannot be separated into 
planimetric and vertical adjustment. 
Ayman F. Habib Photogrammetric & LiDAR Mapping 
83