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Prévia do material em texto

Ayman F. Habib MMT 2013 – Summer School (Taiwan) 
QA/QC of Photogrammetric and LiDAR 
Mapping 
Chapter 4 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
2 
Overview 
• Motivation 
• Quality Assurance (QA) and Quality Control (QC) 
– Introduction 
– Prerequisites 
• Photogrammetric Principles 
• QA/QC of Photogrammetric Mapping 
• LiDAR Principles 
• QA/QC of LiDAR Mapping 
• Concluding Remarks 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
3 
Motivation 
• There has been a significant advancement in the 
remote sensing and mapping technology. 
– Digital cameras provide an alternative to conventional 
large format analogue cameras for rapid data collection. 
– Direct geo-referencing is providing the means for an 
almost control-free mapping environment. 
– LiDAR provides a dense point cloud representing the object 
space surface, and thus offers a fast and accurate way of 
obtaining a Digital Surface Model (DSM). 
• Effective utilization of these advances mandates the 
development of reliable, practical, and standardized 
procedures for the Quality Assurance (QA) and 
Quality Control (QC) of the mapping process. 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
4 
• Quality Assurance and Quality Control are important 
concepts, yet we might have only a vague understanding of 
the meanings and the differences between these terms. 
• Quality Assurance (QA) refers to the process used to 
create the deliverables. 
– QA includes process checklists for project audits. 
– If a process is audited, an auditor might not be able to tell if the 
specific deliverable is acceptable (QC). 
– However, the auditor should be able to tell if the deliverable seems 
acceptable based on the process used to create it (QA). 
• Quality Control (QC) refers to activities associated with 
the evaluation of project deliverables. 
– QC is used to verify that the deliverables are of acceptable quality 
and that they are complete and correct. 
Quality Assurance & Quality Control 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
5 5 
• Quality Assurance (pre-mission): 
– Management activities to ensure that a process, item, or 
service is of the quality needed by the user 
– It deals with creating management controls that cover 
planning, implementation, and review of data collection 
activities. 
– Key activity in QA is the calibration procedure. 
• Quality Control (post-mission): 
– Provide routines and consistent checks to ensure data 
integrity, correctness, and completeness 
– Check whether the desired quality has been achieved 
Quality Assurance & Quality Control 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
6 
• To develop effective QA/QC procedures, we need 
to understand the mechanism of the mapping 
process including: 
– Data acquisition systems, 
– Error sources (random and systematic), 
– How to mitigate the impact of these error sources, 
– Nature of available data, 
– Data processing algorithms, and 
– Nature of delivered product. 
Quality Assurance & Quality Control 
Ayman F. Habib MMT 2013 – Summer School (Taiwan) 
Photogrammetric Mapping 
7 
http://earth.google.com/
Photogrammetric & LiDAR Mapping Ayman F. Habib 
8 
Frame Cameras 
Applanix DSS 439 SONY 717 
RC30 
Kodak 14n Canon EOS 1D 
DMC 
IKONOS/GeoEye 
Line Cameras 
ADS 80 
Medium-Format Digital Cameras 
Photogrammetric Data Acquisition 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
9 
Multi-Camera Systems 
A rigid-relationship among the cameras 
Photogrammetric Data Acquisition 
Airborne Mobile Mapping System 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
10 
Multi-Camera Systems 
A rigid-relationship among the cameras 
Photogrammetric Data Acquisition 
Airborne Mobile Mapping System 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
11 
Photogrammetric Data Acquisition 
Multi-Camera Systems 
A rigid-relationship among the cameras 
Terrestrial Mobile Mapping System 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
12 
Photogrammetric Data Acquisition 
Multi-Camera Systems 
A rigid-relationship among the cameras 
Portable Panoramic Image Mapping System 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
13 
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´ 
Photogrammetric Point Positioning 
Camera Calibration (IOP) Geo-referencing (EOP) 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
Objective: Determine the Interior 
Orientation Parameters (IOP) of the camera 
The defined bundle by the IOP should be as 
similar as possible to the incident bundle onto 
the camera at the moment of exposure. 
Principal Point Coordinates 
Principal Distance 
Distortion Parameters 
Image 
Point 
Perspective 
Centre 
Principal Distance c 
xp yp 
Principal Point Coordinates 
Distortions 
Photogrammetric Camera Calibration 
14 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
15 
• Exterior Orientation Parameters (EOP) 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 (image/camera coordinate 
system) relative to the ground/mapping 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 GPS/INS units onboard the 
imaging platform. 
Photogrammetric Geo-Referencing 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
16 
Ground Control Points 
Tie Points 
Photogrammetric Geo-Referencing 
Indirect Geo-Referencing 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
17 
Photogrammetric Geo-Referencing 
Indirect Geo-Referencing 
Signalized Targets 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
18 
Photogrammetric Geo-Referencing 
Indirect Geo-Referencing 
Natural Targets 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
19 
Direct Geo-Referencing 
Photogrammetric Geo-Referencing 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
20 
 
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1. Mapping Reference 
Frame
2. Image Coordinate System
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Photogrammetric Positioning 
Indirect Geo-Referencing 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
21 
GP

xb
yb
zb
XG
ZG
YG Object point (I)
2. IMU body frame
1. Mapping Reference Frame
3. Image Coordinate System
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Photogrammetric Positioning 
Direct Geo-Referencing – ISO 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
• Photogrammetric quality assurance includes: 
– Percentage of overlap 
– Percentage of side lap 
– Flying height 
– Base-height ratio 
– Number/distribution of tie points 
– Number/distribution of GCP 
– Scanning resolution (analog images) 
– Geo-referencing procedure 
– Camera calibration 
– System calibration 
Photogrammetric Quality Assurance 
22 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
23 
• Camera Calibration. 
– Laboratory calibration 
– Indoor calibration 
– In-situ calibration 
• Total System Calibration 
– Camera calibration, and 
– Mounting parameters: spatial and rotational offsets 
between various system components 
• The DPRG has been investigating: 
– Automated procedures for indoor camera calibration 
– Flight configuration with minimum control 
requirements for camera and mounting parameter 
estimation 
Photogrammetric Quality Assurance 
Analytical 
calibration 
Photogrammetric & LiDAR MappingAyman F. Habib 
24 
Traditional Versus Proposed Indoor Test Field 
Traditional test field 
Test field proposed by the 
DPRG 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
25 
Linear Features & Camera Calibration 
• Deviations from straightness in the image space are 
attributed to various distortions. 
• Incorporating linear features in the adjustment 
procedure would allow for the calibration of the 
implemented camera. 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
26 
After Calibration 
• When compared to traditional point-based 
calibration approaches, linear features proved to be 
more effective in distortion removal from imagery 
captured by cameras with significant lens distortion. 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
27 
Stability Analysis: Problem Statement 
• Some mapping activities utilize imaging systems not 
intended for mapping applications. 
• For these systems, we need to investigate whether the 
estimated interior orientation parameters from 
temporal calibration sessions are compatible or not. 
• Statistical testing focuses on testing the changes in the 
numerical values of the IOP without investigating 
their impact on the reconstructed object space. 
• We should develop procedures that investigate the 
impact of changes in the IOP on the reconstructed 
object space: Bundle similarity for stability analysis. 
 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
28 
cI 
cII 
P.C.I 
P.C.II 
Original Image Grid Points 
Distortion-free Grid Points using IOPI 
Bundle I 
Bundle II 
Distortion-free Grid Points using IOPII 
Side View Top View 
Stability Analysis: New Approach 
≡ 
? 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
29 
• The degree of similarity between the bundles from 
two sets of IOP (RMSE offset) is evaluated in terms of 
average image space deviation (pixel units). 
• The RMSE offset is compared to expected image noise. 
• We have different approaches for the RMSE offset 
estimation that are commensurate with the utilized 
geo-referencing technique (e.g., indirect, ISO). 
• The cameras must meet the following specifications to 
be deemed stable. 
– RMSE offset (Tier I mapping) < 1 Pixel 
– RMSE offset (Tier II mapping) < 1.5 Pixels 
 
Stability Analysis: New Approach 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
GP

xb
yb
zb
XG
ZG
YG Object point (I)
2. IMU body frame
1. Mapping Reference Frame
3. Image Coordinate System
x
y
z
)t(r
m
b
)t(R
m
b
b
c
r
 
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
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30 
Mounting Parameters Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
31 
xb 
yb 
zb 
Xm 
Object point I 
)t(r
m
b
)t(R
m
b
b
c
r
b
c
R
1. Mapping reference frame 
Ym 
Zm 
2. IMU body 
frame 
 
m
I
r
m
I
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x. 
y 
z 
Image point i 
3. Camera 
 Coordinate System 
 
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r 
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c
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GPS/INS-assisted Photogrammetric System 
c
i
b
c
m
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c
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I rRtRSrtRtrr )()()( 
System Calibration 
Photogrammetric System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
Conjugate Points 
a´ 
32 
a 
Object Point (A) 
• Conceptual Basis: If the system is properly calibrated and 
geo-referenced, conjugate light rays should intersect at 
the true position of the corresponding object point 
(regardless of the flight direction/configuration). 
Photogrammetric System Calibration 
System Calibration: IOP + Mounting Parameters 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
33 
I. Check whether inaccurate/biased parameters would lead to Y-parallax 
between conjugate light rays from directly geo-referenced stereo-imagery 
II. Check whether inaccurate/biased parameters would lead to biases in the 
derived object points, whose magnitudes and directions depend on the flight 
configuration 
III. If some of the system parameters under investigation do not introduce Y-
parallax between conjugate light rays or discrepancies between derived 
points from overlapping imagery in a given flight configuration, control 
points will be required to derive such parameters 
System Calibration: Mounting and camera parameters 
Photogrammetric System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
34 
I. Y-Parallax 
II. Discrepancies 
III. Control Information 
Reconstructed Object Space 
Flightline 1 
Reconstructed Object Space 
Flightline 2 
Reconstructed Object Space 
Control Surface 
System Calibration: Mounting and camera parameters 
• Analysis Concept: 
Photogrammetric System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
• To investigate whether biases in the system mounting 
parameters will introduce artificial parallax, we 
generate a pair of normalized images. 
35 
Photogrammetric System Calibration 
lb
x
lb
y
lb
z
lx
ly
lz
rx
ry
rz
ln
x
ln
y
ln
z
rn
x
rn
yrnz
IMU body 
frame
Left Image Right Image
Normalized image pair
cncn
cc
OrOl
rb
x
rb
y
rb
z
IMU body 
frame
Object point (I)
ln
i
x
ln
i
y
rn
i
y
rn
i
x
• Conjugate points in the 
normalized images will not 
have y-parallax. 
• For the analysis, we introduce 
systematic errors in the system 
calibration parameters and 
investigate whether they will 
lead to x- or y-parallax in the 
normalized image coordinates. 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
36 
ni
pi
x



rn
y
rn
y
ln
y
rn
x
ln
x
ni
pi
x



1
2
3
4
6
7
1
2
3
4
6
7
Bias in the xp component of the camera parameters 
Impact of Camera Parameters Errors on the Normalized Images 
Photogrammetric System Calibration 
No artificial parallax 
neither in the X-direction nor in the Y-direction 
Such finding reveals the fact that it is not 
possible to estimate the bias in the xp 
component of the camera parameters from a 
control-free stereo pair. 
 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
37 
Bias in the yp component of the camera parameters 
Impact of Camera Parameters Errors on the Normalized Images 
Photogrammetric System Calibration 
ni
pi
y



ni
pi
y



rn
y
ln
y
rn
x
ln
x
1
2
3
4
6
7
1
2
3
4
6
7
No artificial parallax 
neither in the X-direction nor in the Y-direction 
Such finding reveals the fact that it is not 
possible to estimate the bias in the yp 
component of the camera parameters from a 
control-free stereo pair. 
 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
38 
rn
y
ln
y
rn
x
ln
x
c
c
y
nni
l
nii



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c
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nii
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c
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nni
l
nii
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c
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nii

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

1
2
3
4
6
7
1
2
3
4
6
7
 
artificial parallax in the X-direction 
 
Such finding reveals the fact that it is not 
possible to estimate the bias in the camera’s 
principal distance from a control-free stereo 
pair. 
 
Bias in the principal distance of the camera 
Impact of Camera Parameters Errors on the Normalized Images 
Photogrammetric System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
1 2 
5 6 
3 4 
1 2 
5 6 
3 4 
No artificial parallax 
neither in the X-direction nor in the Y-direction 
Bias in the X component of the lever-arm offset vector 
39 
Impact of Mounting Parameters Errors on the Normalized Images 
Such finding reveals the fact that it is not 
possible to estimate the bias in the X 
component of the lever-arm offset vector 
from a control-free stereo pair. 
 
Photogrammetric System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
40 
Impact of Mounting Parameters Errors on the Normalized Images 
Bias in the Y component of the lever-arm offset vector 
1 2 
5 6 
3 4 
1 2 
5 6 
3 4 
No artificial parallax 
neither in the X-direction nor in the Y-direction 
Such finding reveals the fact that itis not 
possible to estimate the bias in the Y 
component of the lever-arm offset vector 
from a control-free stereo pair. 
 
Photogrammetric System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
1 2 
5 6 
3 4 
1 2 
5 6 
3 4 
41 
 
artificial parallax in the X-direction 
 
Impact of Mounting Parameters Errors on the Normalized Images 
Bias in the vertical component of the lever-arm offset vector 
Such finding reveals the fact that it is not 
possible to estimate the bias in the vertical 
component of the lever-arm offset vector 
from a control-free stereo pair. 
 
Photogrammetric System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
1 2 
5 6 
3 4 
1 2 
5 6 
3 4 
42 
 
artificial parallax in the X-direction 
 
Bias in the boresight roll angle 
Impact of Mounting Parameters Errors on the Normalized Images 
Such finding reveals the fact that it is not 
possible to estimate the bias in the boresight 
roll angle from a control-free stereo pair. 
 
Photogrammetric System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
1 2 
5 6 
3 4 
1 2 
5 6 
3 4 
43 
 
artificial parallax in the X-direction and in 
the Y-direction 
 
Bias in the boresight pitch angle 
Such finding reveals the possibility of estimating 
the bias in the boresight pitch angle using a 
control-free stereo pair. 
 
Impact of Mounting Parameters Errors on the Normalized Images 
Photogrammetric System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
1 2 
5 6 
3 4 
1 2 
5 6 
3 4 
44 
 
artificial parallax in the Y-direction 
 
Bias in the boresight yaw angle 
Impact of Mounting Parameters Errors on the Normalized Images 
Such finding reveals the possibility of estimating 
the bias in the boresight yaw angle using a 
control-free stereo pair. 
 
Photogrammetric System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
45 45 
Lever-Arm Offset Bias (δΔX) 
Lever-Arm Offset Bias (δΔY) 
Lever-Arm Offset Bias (δΔZ) 
Impact of Mounting Parameters Errors on Reconstructed Object Space 
Photogrammetric System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
DX DY 
DZ 
46 
0
100
200
300
350
-500
-300
-100
100
300
500
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
X axis (m)Y axis (m)
D
if
f.
 X
 (
m
)
Forward
Backward
0
100
200
300
350
-500
-300
-100
100
300
500
-1
-0.75
-0.5
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if
f.
 Y
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
0
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-300
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D
if
f.
 Z
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
Differences between the bias-contaminated and true object-space in the X , Y, 
and Z directions, after the introduction of a bias in the xp component of the 
camera parameters (1000m flight height). 
Such finding reveals the possibility of estimating 
the bias in the xp of the camera parameters by 
having flight lines in opposite directions. 
 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
DX DY 
DZ 
47 
-200
0
200
400
600
-500
0
500
-1.5
-1
-0.5
0
0.5
1
1.5
X axis (m)Y axis (m)
D
if
f.
 X
 (
m
)
Forward
Backward
-200
0
200
400
600
-500
0
500
-1.5
-1
-0.5
0
0.5
1
1.5
D
if
f.
 Y
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
-200
0
200
400
600
-500
0
500
-1.5
-1
-0.5
0
0.5
1
1.5
D
if
f.
 Z
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
Differences between the bias-contaminated and true object-space in the X , Y, 
and Z directions, after the introduction of a bias in the xp component of the 
camera parameters (1800m flight height). 
The impact of the bias in the xp of the camera 
parameters is flying-height dependent. 
 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
DX DY 
DZ 
48 
0
100
200
300
350
-500
-300
-100
100
300
500
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
D
if
f.
 X
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
0
100
200
300
350
-500
-300
-100
100
300
500
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
X axis (m)Y axis (m)
D
if
f.
 Y
 (
m
)
Forward
Backward
0
100
200
300
350
-500
-300
-100
100
300
500
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
D
if
f.
 Z
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
Such finding reveals the possibility of estimating 
the bias in the yp of the camera parameters by 
having flight lines in opposite directions. 
 
Differences between the bias-contaminated and true object-space in the X , Y, 
and Z directions, after the introduction of a bias in the yp component of the 
camera parameters (1000m flight height). 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
DX DY 
DZ 
49 
-200
0
200
400
600
-500
0
500
-1.5
-1
-0.5
0
0.5
1
1.5
D
if
f.
 X
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
-200
0
200
400
600
-500
0
500
-1.5
-1
-0.5
0
0.5
1
1.5
X axis (m)Y axis (m)
D
if
f.
 Y
 (
m
)
Forward
Backward
-200
0
200
400
600
-500
0
500
-1.5
-1
-0.5
0
0.5
1
1.5
D
if
f.
 Z
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
Differences between the bias-contaminated and true object-space in the X , Y, 
and Z directions, after the introduction of a bias in the yp component of the 
camera parameters (1800m flight height). 
The impact of the bias in the yp of the camera 
parameters is flying-height dependent. 
 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
DX DY 
DZ 
50 
0
100
200
300
350
-500
-300
-100
100
300
500
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
D
if
f.
 X
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
0
100
200
300
350
-500
-300
-100
100
300
500
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
D
if
f.
 Y
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
0
100
200
300
350
-500
-300
-100
100
300
500
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
X axis (m)Y axis (m)
D
if
f.
 Z
 (
m
)
Forward
Backward
Differences between the bias-contaminated and true object-space in the X , Y, 
and Z directions, after the introduction of a bias in the camera’s principal 
distance (1000m fling height) 
Such finding reveals the fact that it is not possible to 
estimate the bias in camera’s principal distance by 
having flight lines in opposite directions. 
 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
DX DY 
DZ 
51 
Differences between the bias-contaminated and true object-space in the X , Y, 
and Z directions, after the introduction of a bias in the camera’s principal 
distance (1800m fling height) 
-200
0
200
400
600
-500
0
500
-1.5
-1
-0.5
0
0.5
1
1.5
D
if
f.
 X
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
-200
0
200
400
600
-500
0
500
-1.5
-1
-0.5
0
0.5
1
1.5
D
if
f.
 Y
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
-200
0
200
400
600
-500
0
500
-1.5
-1
-0.5
0
0.5
1
1.5
D
if
f.
 Z
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
The impact of the bias in the camera’s principal 
distance is flying-height dependent. 
 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
52 
0
100
200
300
-500
-300
-100
100
300
500
-0.1
-0.05
0
0.05
0.1
0.15
 
X axis (m)Y axis (m)
 
D
iff
. 
X
 (
m
)
Forward
Backward
0
100
200
300
-500
-300
-100
100
300
500
-0.1
-0.05
0
0.05
0.1
0.15
 
 
D
iff
. 
Y
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
0
100
200
300
-500
-300
-100
100
300
500
-0.1
-0.05
0
0.05
0.1
0.15
 
 
D
iff
. 
Z
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
Differences between the bias-contaminated and true object-space in the X , Y, 
and Z directions, after the introduction of a bias in the X component of the lever-
arm offset (1000m fling height). 
DX DY 
DZ 
Such finding reveals the possibility of estimating 
the bias in the X component of the lever-arm 
offset by having flight lines in opposite directions. 
 
Photogrammetric & LiDAR Mapping Ayman F.Habib 
DZ 
DX DY 
53 
-200
0
200
400
600
-500
0
500
-0.1
-0.05
0
0.05
0.1
0.15
D
if
f.
 X
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
-200
0
200
400
600
-500
0
500
-0.1
-0.05
0
0.05
0.1
0.15
D
if
f.
Y
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
-200
0
200
400
600
-500
0
500
-0.1
-0.05
0
0.05
0.1
0.15
D
if
f.
Z
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
Differences between the bias-contaminated and true object-space in the X , Y, 
and Z directions, after the introduction of a bias in the X component of the lever-
arm offset (1800m fling height). 
The impact of the bias in the X component of the 
lever arm offset is flying-height independent. 
 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
54 
0
100
200
300
-500
-300
-100
100
300
500
-0.1
-0.05
0
0.05
0.1
0.15
 
 
D
iff
. 
X
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
0
100
200
300
-500
-300
-100
100
300
500
-0.1
-0.05
0
0.05
0.1
0.15
 
 
D
iff
. 
Z
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
DX DY 
DZ 
Differences between the bias-contaminated and true object-space in the X , Y, 
and Z directions, after the introduction of a bias in the Y component of the lever-
arm offset (1000m fling height). 
Such finding reveals the possibility of estimating 
the bias in the Y component of the lever-arm 
offset by having flight lines in opposite directions. 
 
0
100
200
300
-500
-300
-100
100
300
500
-0.1
-0.05
0
0.05
0.1
0.15
 
X axis (m)Y axis (m)
 
D
iff
. Y
 (m
)
Forward
Backward
Photogrammetric & LiDAR Mapping Ayman F. Habib 
DX DY 
DZ 
55 
-200
0
200
400
600
-500
0
500
-0.1
-0.05
0
0.05
0.1
0.15
D
if
f.
 X
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
-200
0
200
400
600
-500
0
500
-0.1
-0.05
0
0.05
0.1
0.15
D
if
f.
 Y
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
-200
0
200
400
600
-500
0
500
-0.1
-0.05
0
0.05
0.1
0.15
D
if
f.
Z
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
Differences between the bias-contaminated and true object-space in the X , Y, 
and Z directions, after the introduction of a bias in the Y component of the lever-
arm offset (1800m fling height). 
The impact of the bias in the Y component of the 
lever arm offset is flying-height independent. 
 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
56 
0
100
200
300
-500
-300
-100
100
300
500
-0.1
-0.05
0
0.05
0.1
0.15
 
 
D
iff
. 
X
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
0
100
200
300
-500
-300
-100
100
300
500
-0.1
-0.05
0
0.05
0.1
0.15
 
 
D
iff
. 
Y
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
0
100
200
300
-500
-300
-100
100
300
500
-0.1
-0.05
0
0.05
0.1
0.15
 
 
D
iff
. 
Z
 (
m
)
Y axis (m) X axis (m)
Forward
Backward
Differences between the bias-contaminated and true object-space in the X , Y, 
and Z directions, after the introduction of a bias in the Z component of the lever-
arm offset (1000m fling height). 
DX DY 
DZ 
Such finding reveals the fact that it is not possible to 
estimate the bias in the Z component of the lever-
arm offset by having flight lines in opposite 
directions. 
 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
DX DY 
DZ 
57 
-200
0
200
400
600
-500
0
500
-0.1
-0.05
0
0.05
0.1
0.15
D
if
f.
 X
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
-200
0
200
400
600
-500
0
500
-0.1
-0.05
0
0.05
0.1
0.15
D
if
f.
Y
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
-200
0
200
400
600
-500
0
500
-0.1
-0.05
0
0.05
0.1
0.15
D
if
f.
 Z
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
Differences between the bias-contaminated and true object-space in the X , Y, 
and Z directions, after the introduction of a bias in the Z component of the lever-
arm offset (1800m fling height). 
The impact of the bias in the Z component of the 
lever arm offset is flying-height independent. 
 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
58 
0
100
200
300
-500
-300
-100
100
300
500
-0.1
-0.05
0
0.05
0.1
0.15
 
 
D
if
f.
 X
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
0
100
200
300
350
-500
-300
-100
100
300
500
-3
-2
-1
0
1
2
3
 
X axis (m)Y axis (m)
 
D
if
f.
 Y
 (
m
)
Forward
Backward
0
100
200
300
350
-500
-300
-100
100
300
500
-2
-1
0
1
2
 
X axis (m)
Y axis (m)
 
D
if
f.
 Z
 (
m
)
Forward
BackwardDX DY 
DZ 
Differences between the bias-contaminated and true object-space in the X , Y, 
and Z directions, after the introduction of a bias in the boresight roll angle. 
Such finding reveals the possibility of estimating 
the bias in the boresight roll angle by having 
flight lines in opposite directions. 
 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
59 
0
100
200
300
350
-500
-300
-100
100
300
500
-4
-2
0
2
4
 
X axis (m)Y axis (m)
 
D
if
f.
 X
 (
m
)
Forward
Backward
0
100
200
300
350
-500
-300
-100
100
300
500
-4
-2
0
2
4
 
X axis (m)Y axis (m)
 
D
if
f.
 X
 (
m
)
Forward
Backward
0
100
200
300
350
-500
-300
-100
100
300
500
-0.1
-0.05
0
0.05
0.1
0.15
 
X axis (m)
Y axis (m)
 
D
if
f.
 Y
 (
m
)
Forward
Backward
0
100
200
300
350
-500
-300
-100
100
300
500
-1
-0.5
0
0.5
1
 
X axis (m)
Y axis (m)
 
D
if
f.
 Z
 (
m
)
Forward
Backward
Differences between the bias-contaminated and true object-space in the X , Y, 
and Z directions, after the introduction of a bias in the boresight pitch angle. 
DX DY 
DZ 
Such finding reveals the possibility of estimating 
the bias in the boresight pitch angle by having 
flight lines in opposite directions. 
 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
60 
0
50
100
150
200
250
300
350
-500
-300
-100
100
300
500
-2
-1
0
1
2
 
X axis (m)Y axis (m)
 
D
if
f.
 X
 (
m
)
Forward
Backward
0
100
200
300
350
-500
-300
-100
100
300
500
-1
-0.5
0
0.5
1
 
X axis (m)Y axis (m)
 
D
if
f.
 Y
 (
m
)
Forward
Backward
0
100
200
300
-500
-300
-100
100
300
500
-0.1
-0.05
0
0.05
0.1
0.15
 
 
D
if
f.
 Z
 (
m
)
X axis (m)Y axis (m)
Forward
Backward
DX DY 
DZ 
Such finding reveals the fact that flight lines in 
opposite directions would not lead to 
additional information for the estimation of the 
bias in the boresight yaw angle. 
 
Differences between the bias-contaminated and true object-space in the X , Y, 
and Z directions, after the introduction of a bias in the boresight yaw angle. 
However, parallel flight lines with some side lap 
would lead to additional information for the 
estimation of the bias in the boresight yaw angle. 
 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
350
400
450
500
550
600
650
-500
-300
-100
100
300
500
700
9001000
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
 
X axis (m)
Y axis (m)
 
D
if
f.
 X
 (
m
)
Flightline 1
Flightline 2
350
400
450
500
550
600
650 -500
-300
-100
100
300
500
700
900
1000-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
 
Y axis (m)
X axis (m)
 
D
if
f.
 Y
 (
m
)
Flightline 1
Flightline 2
350
400
450
500
550
600
650 -500
-300
-100
100
300
500
700
900
1000-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
 
Y axis (m)
X axis (m)
 
D
if
f.
 Z
 (
m
)
Flightline 1
Flightline 2
Differences between the bias-contaminated and true object-space in the X , Y, 
and Z directions, after the introduction of a bias in the boresight yaw angle. 
Parallel flight lines with some side lap would lead 
to additional information for the estimation of the 
bias in the boresight yaw angle. 
 
61 
DX 
DY 
DZ 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
62 
Parameter y-parallax 
Discrepancies: 
Flying Direction/ 
Flying Height/ 
Point Coord. Dependent 
Control 
Requirement 
planimetric 
lever arm offset components 
No Yes/No/No No 
verticallever arm offset component 
No No/No/No Yes 
boresight roll No Yes/Yes/Yes No 
boresight Pitch Yes Yes/Yes/Yes No 
boresight yaw Yes No/Yes/Yes No 
principal point 
coordinates 
No Yes/Yes/No No 
principal distance No No/Yes/No No 
Summary 
Photogrammetric System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
63 
Parameter Y-parallax 
Discrepancies: 
Flying Direction/ 
Flying Height 
Dependent 
Control 
Requirement 
Optimum 
Configuration 
Planimetric 
Lever-arm 
components 
No Yes/No No 
Opposite flight lines 100% 
overlap 
Vertical 
Lever-arm 
component 
No No/No Yes 1 vertical GCP 
Boresight Pitch Yes Yes/Yes No 
Opposite flight lines 100% 
overlap 
Boresight yaw Yes Yes/Yes No 
Parallel flight lines with 
minimum side lap 
Boresight roll No Yes/Yes No 
Opposite flight lines 100% 
overlap 
Principal Point 
Coordinates 
No Yes/Yes No 
Opposite flight lines 100% 
overlap 
Principal Distance No No/Yes No Flight lines at diff. flying height 
Summary 
Photogrammetric System Calibration 
 
At Different Flying Heights 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
Optimum Flight Configuration for the 
Estimation of the Mounting Parameters 
64 
Photogrammetric System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
65 
Optimum Flight Configuration for the System 
Calibration (Mounting Parameters, xp, yp, c) 
Photogrammetric System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
• So far, we assumed that we are dealing with a 
single-camera system. 
• For each image, we have a set of exterior 
orientation parameters. 
• Modern mobile mapping systems can utilize 
multi-camera imaging system. 
• The direct incorporation of the GPS/INS-derived 
position and orientation information in the 
collinearity equations is the optimum way of 
dealing with such systems. 
– Modified collinearity equations 
 66 
Photogrammetric System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
67 
Airborne Mobile Mapping System 
Lever arm and boresight angles 
between the different 
cameras 
Mounting Parameters Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
68 
Lever arm and boresight angles 
between the different 
cameras 
Terrestrial Mobile Mapping System 
Mounting Parameters Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
69 
Lever arm and boresight angles 
between the different 
cameras 
Terrestrial Mobile Mapping System 
Mounting Parameters Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
70 
For Multi-Camera System 
Mounting Parameters Calibration 
x 
y 
z 
x 
y 
z 
x 
y 
z 
x 
y 
z 
x 
z 
y 
x b y b 
z b 
Camera “0” 
Camera “1” 
Camera “2” 
Camera “3” 
Camera “j” 
IMU Body Frame 
X G 
Y G 
Z G 
• Lever arm and boresight angles between the different cameras 
• Lever arm and boresight angles between the IMU body frame 
and the cameras 
•These parameters are not independent. 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
71 
XG 
x 
y 
z 
x 
y 
z 
x 
y 
z 
x 
y 
z 
x 
z 
y Camera “0” 
Camera “1” 
Camera “2” 
Camera “3” 
Camera “j” 
YG 
ZG )(0 tR
m
c
)(0 tr
m
c )(tR
m
cj
)(tr
m
cj
0
1
c
c
R
0
1
c
c
r
0c
cjR0c
cjr
# Unknowns = N_cam * N_epoch * 6 
For Multi-Camera System 
Mounting Parameters Calibration 
Indirect Geo-Referencing for Multi-Camera Systems with Additional ROC 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
72 
• If we have N_cam cameras capturing imagery for N_epoch: 
)()()()(
)()()()(
)()()()(
)()()()(
)()()()(
)()()()(
)()()()(
)()()()(
)()()()(
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3311
3311
3311
2211
2211
2211
_
1
_
11
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3
1
3
11
3
2
1
2
11
2
_
1
_
11
_
3
1
3
11
3
2
1
2
11
2
_
1
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11
_
3
1
3
11
3
2
1
2
11
2
epochN
m
cepochN
c
m
m
c
c
m
c
c
epochN
m
cepochN
c
m
m
c
c
m
c
c
epochN
m
cepochN
c
m
m
c
c
m
c
c
m
c
c
m
m
c
c
m
c
c
m
c
c
m
m
c
c
m
c
c
m
c
c
m
m
c
c
m
c
c
m
c
c
m
m
c
c
m
c
c
m
c
c
m
m
c
c
m
c
c
m
c
c
m
m
c
c
m
c
c
tRtRtRtRR
tRtRtRtRR
tRtRtRtRR
tRtRtRtRR
tRtRtRtRR
tRtRtRtRR
tRtRtRtRR
tRtRtRtRR
tRtRtRtRR
camNcamNcamN
camNcamNcamN
camNcamNcamN






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11
3
12
1
12
11
2
epochN
m
cepochN
m
cepochN
c
m
m
c
m
c
c
m
c
c
epochN
m
cepochN
m
cepochN
c
m
m
c
m
c
c
m
c
c
epochN
m
cepochN
m
cepochN
c
m
m
c
m
c
c
m
c
c
m
c
m
c
c
m
m
c
m
c
c
m
c
c
m
c
m
c
c
m
m
c
m
c
c
m
c
c
m
c
m
c
c
m
m
c
m
c
c
m
c
c
m
c
m
c
c
m
m
c
m
c
c
m
c
c
m
c
m
c
c
m
m
c
m
c
c
m
c
c
m
c
m
c
c
m
m
c
m
c
c
m
c
c
trtrtRtrtrtRr
trtrtRtrtrtRr
trtrtRtrtrtRr
trtrtRtrtrtRr
trtrtRtrtrtRr
trtrtRtrtrtRr
trtrtRtrtrtRr
trtrtRtrtrtRr
trtrtRtrtrtRr
camNcamNcamN
camNcamNcamN
camNcamNcamN













For Multi-Camera System 
Mounting Parameters Calibration 
Indirect Geo-Referencing for Multi-Camera Systems with Additional ROC 
Relative relationship between the different cameras and 
the reference one are constant at epochs t1, t2, …, tN_epoch 
Total Number of Constraints: 6 (N_epoch – 1) (N_cam -1) 
• Total number of EOP: 6 * N_cam* N_epoch 
• Total number of constraints: 6 * (N_cam – 1) * (N_epoch – 1) 
• Total number of independent EOP: 6 * N_epoch + 6 * (N_cam – 1) 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
x 
y 
z 
x 
y 
z 
x 
y 
z 
x 
y 
z 
x 
z 
y Camera “0” 
Camera “1” 
Camera “2” 
Camera “3” 
Camera “j” 
XG 
YG 
ZG 
)(0 tR
m
c
)(0 tr
m
c
)(tR
m
cj
)(tr
m
cj
xb 
yb 
zb 
IMU Body Frame 
b
c
r
0
b
c
R
0
b
cj
r
b
cj
R
)(tR
m
b )(tr
m
b
73 
For Multi-Camera System 
Traditional ISO (collinearity equations + GPS/INS observations) 
Mounting Parameters Calibration 
# of Add. Obs. = N_epoch * N_cam * 6 (Some Repeated Observations) 
# Unknowns = N_cam * N_epoch * 6 + N_cam * 6 
camNjrtRtrjtr
cj
b
m
cj
m
cj
m
b _1:)()(}){( 
camNjRtRjtR
cj
b
m
cj
m
b _1:),,()(}{)(  kfw
j
j
j
j
c
i
m
c
c
i
m
c
m
I rtRStrr )()( 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
74 
GP

xb
yb
zb
XG
ZG
YG Object point (I)
2. IMU body frame
1. Mapping Reference Frame
3. Image Coordinate System
x
y
z
)t(r
m
b
)t(R
m
b
b
c
r
 














c
distyy
distxx
ypi
xpi
c
i
r
c
ii
rS
b
c
R
m
I
r
Image point (i)
c
i
b
c
m
bi
b
c
m
b
m
b
m
I rRtRSrtRtrr )()()( 
Photogrammetric Positioning: New Model 
New ISO Model (Direct Incorporation of GPS/INS observations): Single-Camera System 
)()()( / t
e
e
e
t
Z
Y
X
t
Z
Y
X
m
bZ
Y
X
m
b
INSGPS
m
b
































)()()( / t
e
e
e
tt
m
b
m
b
INSGPS
m
b
































k

w
k

w
k

w
Mounting Parameters 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
x 
y 
z 
x 
y 
z 
x 
y 
z 
x 
y 
z 
x 
z 
y Camera “0” 
Camera “1” 
Camera “2” 
Camera “3” 
Camera “j” 
Xm 
Ym 
Zm 
xb 
yb 
zb 
IMU Body Frame 
b
c
r
0
b
c
R
0
)t(r
m
b
)t(R
m
b
b
cj
r
b
cj
R
 )( )()( j
j
j
j
c
i
b
c
m
b
c
i
b
c
m
b
m
b
m
I rRtRSrtRtrr 
75 
For Multi-Camera System 
Mounting Parameters Calibration 
New ISO Model (Direct Incorporation of GPS/INS observations ):Multi-Camera System 
)()()( / t
e
e
e
t
Z
Y
X
t
Z
Y
X
m
bZ
Y
X
m
b
INSGPS
m
b
































)()()( / t
e
e
e
tt
m
b
m
b
INSGPS
m
b
































k

w
k

w
k

w
# of Add. Obs. = N_epoch * 6 
# Unknowns = N_epoch * 6 + N_cam * 6 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
76 
Mounting Parameters Calibration 
x 
y 
z 
x 
y 
z 
x 
y 
z 
x 
y 
z 
x 
z 
y Camera “0” 
Camera “1” 
Camera “2” 
Camera “3” 
Camera “j” 
XG 
YG 
ZG )(0 tR
m
c
)(0 tr
m
c
0
1
c
c
R
0
1
c
c
r
0c
cj
R0c
cj
r
For Multi-Camera System 
Indirect Geo-Referencing with Built-in Relative Orientation Constraints 
xb 
yb 
zlb 
Virtual 
IMU Body 
Frame 
j
j
j
j
c
i
b
c
m
b
c
i
b
c
m
b
m
b
m
I rRtRSrtRtrr )()()( 
)()()( / t
e
e
e
t
Z
Y
X
t
Z
Y
X
m
bZ
Y
X
m
b
INSGPS
m
b
































)()()( / t
e
e
e
tt
m
b
m
b
INSGPS
m
b
































k

w
k

w
k

w
























0
0
0
b
cr
Z
Y
X
























0
0
0
b
cr
k

w
Do not exist Do not exist 
Treated as 
constant 
 )( )()( jr
jr
jr
jrr
c
i
c
c
m
c
c
i
c
c
m
c
m
c
m
I rRtRSrtRtrr 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
77 
For Multi-Camera System 
General Model: Incorporation of prior information on the 
ROP among the cameras 
x y 
z 
x 
y 
z x 
y 
z 
x 
y 
z 
x 
z 
y Camera “0” 
Camera “1” 
Camera “2” 
Camera “3” 
Camera “j” 
0
1
c
c
r
0
1
c
c
R
0c
cj
R xb yb 
zb 
IMU Body 
Frame 
b
c
R
0
XG 
YG 
ZG 
)(tr
m
b
b
c
r
0
0c
cj
r
)t(R
m
b
 )( )( )()( jr
jr
jr
jrr
c
i
c
c
b
c
m
b
c
i
c
c
b
c
m
b
b
c
m
b
m
b
m
I rRRtRSrRtRrtRtrr 
)()()( / t
e
e
e
t
Z
Y
X
t
Z
Y
X
m
bZ
Y
X
m
b
INSGPS
m
b
































)()()( / t
e
e
e
tt
m
b
m
b
INSGPS
m
b
































k

w
k

w
k

w
cr
cjZ
Y
X
cr
cj
cr
cj
e
e
e
Z
Y
X
)prior(
Z
Y
X









































cr
cj
cr
cj
cr
cj
e
e
e
)prior(
































k

w
k

w
k

w
b
crZ
Y
X
b
cr
b
cr
e
e
e
Z
Y
X
)prior(
Z
Y
X









































b
cr
b
cr
b
cr
e
e
e
)prior(
































k

w
k

w
k

w
Photogrammetric Positioning: General Model 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
x 
y 
z 
x 
y 
z 
x 
y 
z 
x 
y 
z 
x 
z 
y Camera “0” 
Camera “1” 
Camera “2” 
Camera “3” 
Camera “j” 
XG 
YG 
ZG )(0 tR
m
c
)(0 tr
m
c
0
1
c
c
R
0
1
c
c
r
0c
cj
R0c
cj
r
78 
For Multi-Camera System 
Special case of the general model: 
Indirect Geo-Referencing with Built-in Relative Orientation Constraints 
 )( )()( jr
jr
jr
jrr
c
i
c
c
m
c
c
i
c
c
m
c
m
c
m
I rRtRSrtRtrr 
Mounting Parameters Calibration 
xb 
yb 
zlb 
Virtual 
IMU Body 
Frame 
 )( )( )()( jr
jr
jr
jrr
c
i
c
c
b
c
m
b
c
i
c
c
b
c
m
b
b
c
m
b
m
b
m
I rRRtRSrRtRrtRtrr 
General Model 
)()()( / t
e
e
e
t
Z
Y
X
t
Z
Y
X
m
bZ
Y
X
m
b
INSGPS
m
b
































)()()( / t
e
e
e
tt
m
b
m
b
INSGPS
m
b
































k

w
k

w
k

w
cr
cjZ
Y
X
cr
cj
cr
cj
e
e
e
Z
Y
X
)prior(
Z
Y
X









































cr
cj
cr
cj
cr
cj
e
e
e
)prior(
































k

w
k

w
k

w





















0
0
0
)prior(
Z
Y
X
b
cr
























0
0
0
)prior(
b
cr
k

w
Treated as 
constant 
Do not exist Do not exist 
Might exist Might exist 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
x 
y 
z 
x 
y 
z 
x 
y 
z 
x 
y 
z 
x 
z 
y Camera “0” 
Camera “1” 
Camera “2” 
Camera “3” 
Camera “j” 
XG 
YG 
ZG 
xb 
yb 
zb 
IMU Body Frame 
b
c
r
0
b
c
R
0
)(tr
m
b
)(tR
m
b
b
cj
r
b
cj
R
79 
For Multi-Camera System 
Special case of the general model: 
ISO Model without ROP Prior Information 
 )( )()( j
j
j
j
c
i
b
c
m
b
c
i
b
c
m
b
m
b
m
I rRtRSrtRtrr 
Mounting Parameters Calibration 
 )( )( )()( jr
jr
jr
jrr
c
i
c
c
b
c
m
b
c
i
c
c
b
c
m
b
b
c
m
b
m
b
m
I rRRtRSrRtRrtRtrr 
General Model 
x 
y 
z Virtual Reference 
Camera 
cr
cjZ
Y
X
cr
cj
cr
cj
e
e
e
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Photogrammetric & LiDAR Mapping Ayman F. Habib 
80 
• Photogrammetric reconstruction is based on redundant 
measurements. 
• Results from the photogrammetric triangulation gives 
quantitative measures of the precision of the 
reconstruction outcome. 
– Variance component (overall measure of the quality of fit between 
the observed quantities and the used model) 
– Variance-covariance matrix for the derived object coordinates 
– These values can be compared with expected nominal values 
• Independent measure for accuracy verification can be 
established using check point analysis. 
– Photogrammetric coordinates are compared with independently 
measured coordinates (e.g., GPS survey)  RMSE analysis. 
Photogrammetric Quality Control 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
81 
• Precision of a single model: If we have 
– Bundle block adjustment with additional parameters 
that compensate for various distortions 
– Regular blocks with 60% overlap and 20% side lap 
– Signalized targets 
space image in thegiven are valuesprecision These
cameras)(SWA distance principalcameratheof%004.0
cameras) WA and(NA distance principalcameratheof%003.0
3

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Z
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XY m

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Precision of Photogrammetric Reconstruction 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
82 
Check Point Analysis 
Accuracy of Photogrammetric Reconstruction 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
83 
40 m
40 m
15 m
10 m10 m10 m10 m
10 m
10 m
10 m
10 m
10 m
10 m
15 m
1 2 3
456
7
8
9 10
11
12
wall
w
al
l
w
al
l
wall
YG
ZG
Results from Simulated Data 
Configuration 
used for the 
estimation of 
the ROP 
among the 
camerasMounting Parameters Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
84 
400 m
400 m
150 m
100 m100 m100 m100 m
100 m
100 m
100 m
100 m
100 m
100 m
150 m
1 2 3
456
7
8
9 10
11
12
wall
w
al
l
w
al
l
wall
YG
ZG
Results from Simulated Data 
Mounting Parameters Calibration 
Configuration 
used for the 
ISO 
with/without 
prior 
information 
on the ROP 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
85 
ROP among the Cameras 
Reference Camera: Camera “0” 
Mounting Parameters Calibration 
Δω 
(o±″) 
diff 
(″) 
Δφ 
(o±″) 
diff 
(″) 
Δκ 
(o±″) 
diff 
(″) 
ΔX 
(m±m) 
diff 
(m) 
ΔY 
(m±m) 
diff 
(m) 
ΔZ 
(m±m) 
diff 
(m) 
“1” 
1.00726 
±24.8 
26.1 
-0.51046 
±25.2 
-37.6 
-1.99529 
±17.9 
17.0 
-0.05 
±0.0011 
0.00 
-1.45 
±0.0024 
0.00 
0.05 
±0.0028 
0.00 
“2” 
-40.99046 
±31.2 
34.3 
-0.20617 
±34.8 
-22.2 
-0.98933 
±45.4 
38.4 
-0.05 
±0.0025 
0.00 
-1.50 
±0.0036 
0.00 
0.60 
±0.0040 
0.00 
“3” 
-88.99505 
±45.3 
17.8 
1.97783 
±54.5 
-79.8 
-0.68205 
±59.8 
64.6 
-0.05 
±0.0034 
0.00 
-1.51 
±0.0051 
-0.01 
1.69 
±0.0052 
-0.01 
“4” 
-127.99759 
±41.6 
8.7 
0.47521 
±84.1 
-89.3 
-0.39339 
±49.3 
23.8 
-0.05 
±0.0039 
0.00 
-1.46 
±0.0063 
-0.01 
2.44 
±0.0051 
-0.01 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
86 
ISO 
Mounting Parameters Calibration 
Scenario I: good distribution of the points in the imagery 
Δω 
(deg± sec) 
Diff (sec) 
Δφ 
(deg± sec) 
Diff (sec) 
Δκ 
(deg± sec) 
Diff (sec) 
ΔX 
(m± m) 
Diff. (m) 
ΔY 
(m± m) 
Diff. (m) 
ΔZ 
(m± m) 
Diff. (m) 
ISO without ROP Prior Information 
“0” 
-1.02037 
±50.0 
-73.3 
-0.52277 
±52.1 
-82.0 
1.29626 
±31.9 
-13.5 
0.09 
±0.0578 
-0.01 
0.51 
±0.0453 
0.01 
-1.48 
±0.0369 
0.07 
“1” 
1.01157 
±24.7 
41.6 
-0.50661 
±25.6 
-23.8 
-2.00714 
±19.5 
-25.7 
-0.04 
±0.0111 
0.01 
-1.46 
±0.0111 
-0.01 
0.03 
±0.0273 
-0.02 
“2” 
-40.98329 
±30.6 
60.2 
-0.19405 
±31.7 
21.4 
-0.99312 
±38.7 
24.8 
-0.01 
±0.0212 
0.04 
-1.53 
±0.0278 
-0.03 
0.55 
±0.0388 
-0.05 
“3” 
-88.96407 
±46.0 
129.3 
1.99550 
±48.0 
-16.2 
-0.68499 
±48.7 
54.1 
0.00 
±0.0318 
0.05 
-1.59 
±0.0454 
-0.09 
1.65 
±0.0473 
-0.05 
“4” 
-127.98520 
±41.4 
53.3 
0.49494 
±66.7 
-18.2 
-0.38421 
±41.8 
56.9 
0.03 
±0.0349 
0.08 
-1.49 
±0.0574 
-0.04 
2.37 
±0.0392 
-0.08 
Δω 
(deg± sec) 
Diff (sec) 
Δφ 
(deg± sec) 
Diff (sec) 
Δκ 
(deg± sec) 
Diff (sec) 
ΔX 
(m± m) 
Diff. (m) 
ΔY 
(m± m) 
Diff. (m) 
ΔZ 
(m± m) 
Diff. (m) 
ISO with ROP Prior Information 
“0” 
-0.99957 
±37.4 
1.5 
-0.50688 
±28.1 
-24.8 
1.29701 
±27.9 
-10.8 
0.16 
±0.0420 
0.06 
0.45 
±0.0281 
-0.05 
-1.53 
±0.0287 
0.02 
“1” 
1.00003 
±13.6 
0.1 
-0.50102 
±13.8 
-3.7 
-1.99915 
±12.6 
3.0 
-0.05 
±0.0066 
0.00 
-1.46 
±0.0067 
-0.01 
0.05 
±0.0083 
0.00 
“2” 
-40.99790 
±13.5 
7.6 
-0.19356 
±13.8 
23.2 
-1.00318 
±13.0 
-11.5 
-0.03 
±0.0076 
0.02 
-1.50 
±0.0080 
0.00 
0.61 
±0.0082 
0.01 
“3” 
-88.99617 
±14.4 
13.8 
1.99999 
±14.2 
0.0 
-0.69842 
±13.9 
5.7 
-0.05 
±0.0079 
0.00 
-1.51 
±0.0085 
-0.01 
1.70 
±0.0082 
0.00 
“4” 
-128.00221 
±14.7 
-8.0 
0.50729 
±15.0 
26.3 
-0.39904 
±14.0 
3.5 
-0.04 
±0.0081 
0.01 
-1.45 
±0.0085 
0.00 
2.47 
±0.0083 
0.02 
Slight improvements 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
87 
ISO 
Mounting Parameters Calibration 
Scenario II: poor distribution of the points in the imagery 
Δω 
(deg±sec) 
Diff.(sec) 
Δφ 
(deg±sec) 
Diff.(sec) 
Δκ 
(deg±sec) 
Diff.(sec) 
ΔX 
(m±m) 
Diff.(m) 
ΔY 
(m±m) 
Diff.(m) 
ΔZ 
(m±m) 
Diff.(m) 
ISO without ROP Prior Information 
“0” 
-1.01261 
±83.6 
-45.4 
-0.54072 
±79.1 
-146.6 
1.31125 
±140.7 
40.5 
-0.01 
±0.0810 
-0.11 
0.50 
±0.0851 
0.00 
-1.35 
±0.1327 
0.20 
“1” 
1.01825 
±44.9 
65.7 
-0.49631 
±46.5 
13.3 
-1.99811 
±136.7 
6.8 
0.00 
±0.0335 
0.05 
-1.47 
±0.0327 
-0.02 
-0.10 
±0.1049 
-0.15 
“2” 
-41.01139 
±131.3 
-41.0 
-0.19463 
±137.3 
19.3 
-1.01321 
±165.7 
-47.6 
0.01 
±0.1257 
0.06 
-1.34 
±0.2002 
0.16 
0.36 
±0.1942 
-0.24 
“3” 
-88.94687 
±135.5 
191.3 
2.03304 
±181.9 
118.9 
-0.67732 
±136.9 
81.6 
0.15 
±0.1126 
0.20 
-1.65 
±0.1533 
-0.15 
1.59 
±0.1923 
-0.11 
“4” 
-127.96319 
±126.3 
132.5 
0.48415 
±182.9 
-57.1 
-0.38947 
±154.4 
37.9 
0.08 
±0.1135 
0.13 
-1.72 
±0.1663 
-0.27 
2.44 
±0.1849 
-0.01 
Δω 
(deg±sec) 
Diff.(sec) 
Δφ 
(deg±sec) 
Diff.(sec) 
Δκ 
(deg±sec) 
Diff.(sec) 
ΔX 
(m± m) 
Diff.(m) 
ΔY 
(m± m) 
Diff.(m) 
ΔZ 
(m± m) 
Diff.(m) 
 
ISO with ROP Prior Information 
“0” 
-0.98192 
±45.6 
65.1 
-0.51156 
±32.5 
-41.6 
1.30811 
±42.2 
29.2 
0.10 
±0.0437 
0.00 
0.41 
±0.0356 
-0.09 
-1.53 
±0.0481 
0.02 
“1” 
0.99956 
±13.5 
-1.6 
-0.50046 
±13.5 
-1.7 
-1.99199 
±15.5 
28.8 
-0.05 
±0.0073 
0.00 
-1.46 
±0.0073 
-0.01 
0.05 
±0.0078 
0.00 
“2” 
-40.99696 
±14.4 
10.9 
-0.19499 
±14.1 
18.0 
-1.00202 
±15.4 
-7.3 
-0.03 
±0.0077 
0.02 
-1.49 
±0.0078 
0.01 
0.61 
±0.0078 
0.01 
“3” 
-89.00064 
±14.8 
-2.3 
2.00299 
±14.1 
10.8 
-0.69806 
±15.5 
7.0 
-0.05 
±0.0076 
0.00 
-1.50 
±0.0078 
0.00 
1.70 
±0.0077 
0.00 
“4” 
-128.00085 
±15.2 
-3.1 
0.50711 
±14.9 
25.6 
-0.39812 
±15.5 
6.8 
-0.04 
±0.0077 
0.01 
-1.45 
±0.0078 
0.00 
2.47 
±0.0078 
0.02 
0.20 0.02 
0.00 
0.01 -0.24 0.16 0.01 
0.20 
-0.15 
191.3 118.9 -0.15 -2.3 10.8 0.00 0.00 
0.00 -3.1 -0.27 132.5 
Significant improvements 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
88 
Concluding Remarks 
• QA/QC procedures are essential for any spatial 
data acquisition system. 
• QA/QC are well established for photogrammetric 
mapping systems. 
– More attention should be given to medium-format 
digital imaging systems (specifically, stability analysis). 
– In-situ calibration of GPS/INS-assisted 
photogrammetric systems 
• Camera parameters (principal point coordinates & principal 
distance) 
• Mounting parameters 
– Multi-camera systems require special attention 
(Relative Orientation Constraint among the cameras) 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
Concluding Remarks 
• The work has introduced a general mathematical 
model with the following characteristics: 
– Capable of handling any number of cameras onboard the 
mapping platform (in the absence or presence of GPS/INS 
information), and 
– Allows for the incorporation of prior information about the 
ROP among the cameras in the ISO. 
• Special cases can be derived from the general model: 
– Indirect geo-referencing with built-in Relative Orientation 
Constraints (ROC) among the cameras 
– ISO for multi-camera system without prior information 
about the ROC among the cameras 
 
89 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
• Conducted experiments have demonstrated that: 
– In the presence of a reasonable imaging geometry and good tying 
among the images, the use of prior ROP information leads to 
slight improvements in the accuracy of the estimated parameters. 
– On the other hand, under the scenario where a poor tying among 
the images is present, significant improvements are observed (this 
might happen in terrestrial mobile mapping systems – fewer 
identifiable features in open areas). 
• Thus, in addition to the simplification of the mathematical 
model and the ability to handle several scenarios as special 
cases, the proposed model has significant advantages when 
faced with weaker geometric configuration. 
• Future work will focus on more testing using real datasets 
from terrestrial and airborne mobile mapping systems. 
90 
Concluding Remarks 
Ayman F. Habib MMT 2013 – Summer School(Taiwan) 
Airborne LiDAR Mapping 
91 
Laser scanner 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
92 
ALS 60 (Leica Geosystems) 
Operational LiDAR Systems 
OPTECH ALTM GEMINI 
long-range RIEGL LMS-Q680i 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
93 
LiDAR Principles 
Three Measurement Systems 
1. GNSS 
2. IMU 
3. Laser scanner emits laser 
beams with high 
frequency and collects the 
reflections. 
INS 
GNSS 
GNSS 
IMU 
Direct acquisition of high 
density and accurate 
topographic data 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
94 
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LiDAR Principles 
m
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Photogrammetric & LiDAR Mapping Ayman F. Habib 
95 
• QA activities/measures include: 
– Optimum mission time 
– Distance to GNSS base station 
– Flying height 
– Pulse repetition rate 
– Beam divergence angle 
– Scan angle 
– Percentage of overlap 
– System calibration 
LiDAR Quality Assurance 
Laser scanner 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
96 
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LiDAR QA: System Calibration 
m
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Photogrammetric & LiDAR Mapping Ayman F. Habib 
97 
• Laboratory Calibration (conducted 
by the system manufacturer) 
– Calibration of individual system 
components, 
– Mirror to IMU misalignment, 
– Mirror to IMU lever arm, and 
– Mirror to reference point 
 
 
• Platform Calibration 
– Reference point to GPS antenna 
LiDAR QA: System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
98 
• In-Flight Calibration (refines the 
estimated parameters during the 
laboratory & platform calibration): 
– Utilizes a calibration test field composed of 
control surfaces for the estimation of biases 
in the LiDAR system parameters 
– The observed discrepancies between the 
LiDAR and control surfaces are used to 
determine the biases in the system 
parameters (e.g., boresighting roll and pitch 
angles and scale parameters). 
laser point 
firing point 
d 
LiDAR QA: System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
99 
• Status of current calibration methods: 
– There is lack of a commonly accepted calibration 
methodology. 
– System raw measurements are required. 
– Estimated parameters are limited. 
– Manual and empirical approaches are utilized. 
– Calibration sites with control targets are required. 
• For example, buildings and runways 
– Calibration is not possible for end-users using point cloud 
coordinates in overlapping strips. 
LiDAR QA: System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
100 
I. Y-Parallax 
II. Discrepancies 
III. Control Information 
Reconstructed Object Space 
Flightline 1 
Reconstructed Object Space 
Flightline 2 
Reconstructed Object Space 
Control Surface 
System Calibration: Mounting and laser scanner parameters 
• Analysis Concept: 
LiDAR QA: System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
101 
• Conceptual Basis: Estimate the system parameters that minimize 
discrepancies between derived surfaces from multiple flight 
lines while reducing ground control requirements 
• This process requires establishing the optimal flight configuration 
that maximizes the impact of biases in the system parameters. 
LiDAR QA: System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
f
Opposite directions with 100% overlap ratio 
Biases in 
system parameters 
Lever-arm δΔX 
Lever-arm δΔY 
Lever-arm δΔZ 
Boresight δΔω 
Boresight δΔφ 
Boresight δΔκ 
Range bias δρ 
Scale bias of S.A. δS 
X
Y
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δΔX
δΔY
δΔω
δΔφ
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Ground Coordinate 
System
S
trip
 A
S
trip
 B
Z
Y
X
Ba
ck
wa
rd
Fo
rw
ard
102 
LiDAR QA: System Calibration 
Optimum Flight Configuration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
f
Biases in 
system parameters 
Lever-arm δΔX 
Lever-arm δΔY 
Lever-arm δΔZ 
Boresight δΔω 
Boresight δΔφ 
Boresight δΔκ 
Range bias δρ 
Scale bias of S.A. δS 
Sk

δΔκ δΔκ
δΔφ δΔφ
βT
βT
δSβT δSβT
δρ δρ
D
x
YG
ZG
XG
Ground Coordinate 
System
S
trip
 A
S
trip
 BZ
Y
X
Fo
rw
ard
Fo
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103 
Same direction with some sidelap 
LiDAR QA: System Calibration 
Optimum Flight Configuration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
104 
Parameter 
Discrepancies: 
Flying Direction/ Flying Height/ 
Scan Angle Dependent 
Control 
Requirement 
planimetric lever arm offset components Yes/No/No No 
vertical lever arm offset component No/No/No Yes 
boresight roll Yes/Yes/Yes No 
boresight pitch Yes/Yes/No No 
boresight yaw No/No/Yes No 
range bias No/Yes-No*/Yes Yes 
mirror scan angle scale No/Yes/Yes No 
Optimum Flight Configuration 
LiDAR QA: System Calibration 
* The impact is flying height dependent for conjugate points (small discrepancies are generated among 
conjugate point) and independent when considering points mapped using the same scan angle. 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
105 
Optimum Flight Configuration 
LiDAR QA: System Calibration 
Impact of the range bias on strips captured at different flying heights 
21 HH XZXZ    


21 HH XZXZ    
H1 
H2 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
106 
Parameter 
Discrepancies: 
Flying Direction/ 
Flying Height/ 
Scan Angle dependent? 
Control 
Required? 
Optimum Requirement 
Lever arm 
offset 
across flight direction ΔX Yes/No/No No Two flight lines in opposite directions with 100% side lap 
along flight direction ΔY Yes/No/No No 
Two flight lines in opposite directions with 100% side lap 
(flying height H1) 
vertical ΔZ* No/No/No Yes One vertical control point 
Boresight pitch 
 angle Δω 
Yes/Yes/No No 
Two flight lines in opposite directions with 100% side lap 
(flying height H2) 
Boresight roll 
angle Δφ 
Yes/Yes/Yes No Two flight lines in opposite directions with 100% side lap 
Boresight yaw 
angle Δκ 
No/No/Yes No Two flight lines in the same direction with minimum side lap 
Range bias Δρ* No/No/Yes Yes One vertical control point 
Mirror scan angle scale S No/Yes/Yes No Two flight lines in the same direction with minimum side lap 
*The vertical lever arm offset component and the range bias cannot be simultaneously estimated. 
Optimum Flight Configuration 
LiDAR QA: System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
107 
Optimum Flight Configuration 
LiDAR QA: System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
• The DPRG has developed several LiDAR system 
calibration techniques that are commensurate with the 
nature of available data. 
–Simplified Calibration: With some constraints on the flight 
configuration and ground coverage, we can conduct the calibration 
using only the point cloud coordinates. 
–Quasi-Rigorous Calibration: Using the trajectory data and time-
tagged point cloud coordinates, we can estimate the system 
parameters with fewer constraints on the flight configuration. 
–Rigorous Calibration: With the availability of raw measurements, 
the calibration can be conducted without any assumptions regarding 
the flight configuration and ground coverage. 
108 
LiDAR QA: System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
Overlapping strips 
Discrepancies 
3D Transformation 
Rotation 
Shifts 
CalibrationParameters 
• LiDAR Data in Overlapping Parallel Strips 
 Point cloud coordinates 
 Raw measurements are not necessarily available 
Simplified Calibration 
LiDAR QA: System Calibration 
109 
• Assumptions: 
o Linear scanner, 
o Vertical scanner, 
o Parallel flight lines, 
o Terrain-height variations are minimal compared to 
the flying height, and 
o Small biases in the boresight angles 
• Can handle any type of terrain coverage 
• Cannot handle control points 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
Quasi-Rigorous Calibration 
110 
• LiDAR Data in Overlapping Strips 
 Point cloud coordinates with the time tag 
 Time-tagged trajectory 
LiDAR QA: System Calibration 
• Assumptions: 
o Vertical scanner, 
o Small biases in the boresight angles 
• Can handle cross strips 
• Can handle any type of terrain coverage 
• Can handle control points 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
Rigorous Calibration 
111 
• LiDAR Data in Overlapping Strips 
 Point cloud coordinates together with the system raw 
measurements (position and the attitude of each 
pulse as well as the measured scan angles and ranges) 
LiDAR QA: System Calibration 
• Assumptions: 
o None 
• Can handle cross strips 
• Can handle any type of terrain coverage 
• Can handle control points 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
112 
Rigorous Quasi-Rigorous 
LiDAR Geometric 
Model 
Data Requirements 
Rigorous 
LiDAR Equation 
Simplified 
LiDAR Equation 
Raw measurements Time-tagged LiDAR 
point cloud and 
trajectory position 
LiDAR QA: System Calibration 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
113 
Quasi-Rigorous Approach 
Assumptions 
Linear Scanner Vertical LiDAR unit 
(steady platform) 
Relatively small 
boresight angles 
Simplified LiDAR Equation 
 
  

































 




















 

)Scos(
)Ssin(
cossin
sincos
Z
Y
X
cossin
sincos
)t(rr
m
b
m
I


w
wk
k
kk
kk



kk
kk
0
1
1
1
100
0
0
100
0
0
),(
lb
I)S(
lu
lb),,(
b
lu
m
b)Z,Y,X(
b
lu
m
b
m
b
m
I
rRRRrR)t(rr
kwkk )()(
 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
Trajectory points between (t-Δt) to (t+Δt)
Estimated position at time t
114 
Quasi-Rigorous Approach 
















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













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 




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

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


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




 

z
x
cossin
sincos
Z
Y
X
cossin
sincos
)t(rr
m
b
m
I
0
1
1
1
100
0
0
100
0
0
w
wk
k
kk
kk



kk
kk
Estimated trajectory 
point at time t
Fitted trajectory line
LiDAR point 
captured at time t
x
z
YG
κ
β
XG
ZG
Ground Coordinate System
Estimated 
encoder angle
(Xt, Yt, Zt)
(Xot, Yot, Hot)
 For each LiDAR point, we compute: 
– The heading of the trajectory (κ), 
– The flying height above that point (-z), 
– The lateral distance (x) between the 
LiDAR point and the trajectory, and 
– The mirror scan angle () using (x, z). 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
115 
Rigorous Approach 
No Assumptions 
Can handle linear 
and elliptical scanners 
Can handle steady and 
unsteady platforms 
Small/large 
boresight angles 
Rigorous LiDAR Equation 
),(
lb
I)S,S(
lu
lb),,(
b
lu
m
b)Z,Y,X(
b
lu
m
b
m
b
m
I
rRR)t(Rr)t(R)t(rr
kw
 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
LSA: Observation Equations 
(Quasi-rigorous) 
116 
0XX
B
True
A
True


For conjugate points in 
overlapping strips we have: 
 
nfG
l,xf)True(X 

 
nbBiased
l,xfX 

 elxxfX nbTrue  ,

    0,, 
BnbAnb
elxxfelxxf 
Linearization: 
 
  0)(/)(/, 
)(/)(/,
,,
,,


BlxlxBnb
AlxlxAnb
elfxxflxf
elfxxflxf
BnbB
nb
AnbAnb

   ,0~eexAy


Photogrammetric & LiDAR Mapping Ayman F. Habib 
117 
0)(X)(X
BGAG
 TrueTrue

For conjugate points in 
overlapping strips we have: 
 
nfG
l,xf)(X True

 
noG
l,xf)(X Predicted

 el,xxf)(X
noG
 True

    0el,xxfel,xxf
BnoAno
 
Linearization: 
 
  0)e(l/fxx/fl,xf
)e(l/fxx/fl,xf
B
Bn
l,
o
x
B
nl,o
xBno
A
An
l,
o
x
An
l,
o
xAno




 
LSA: Observation Equations 
(Rigorous) 
  ,0~eexAy


Photogrammetric & LiDAR Mapping Ayman F. Habib 
118 
Blue: Matched Points 
Red: Non-matched Points 
Surface 1 Surface 2 
Matching 
Primitives & Matching Procedure 
Point/Patch Pairs: Closest Patch Procedure 
Conditions: 
• Closest patch (within a threshold) 
• Point located within the patch 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
119 
Closest-patch procedure provides conjugate point/patch pairs 
that satisfy the following conditions. 
We will have conjugate point-patch pairs only whenever the TIN 
patches represent the physical surface. 
Non-matches 
• Closest patch 
• Normal distance < threshold 
• Point located within the patch 
Primitives & Matching Procedure 
Point/Patch Pairs: Closest Patch Procedure 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
120 
Surface 1: 44,156 points Surface 2: 45,520 patches 
Match 
Primitives & Matching Procedure 
Point/Patch Pairs: Closest Patch Procedure 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
121 
Green: Reference Surface 
Blue: Matches 
Red: Non-matches 
Primitives & Matching Procedure 
Point/Patch Pairs: Closest Patch Procedure 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
122 
Non-matches are typically along 
edges of buildings and around 
areas with vegetations 
Primitives & Matching Procedure 
Point/Patch Pairs: Closest Patch Procedure 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
123 
Conjugate patch to a 
given point 
0
)()(


TrueB
j
TrueA
i XX
Assuming that A & B are conjugate points 
Conditions: 
• Closest patch (within a 
threshold) 
• Point located within the 
patch 
Primitives & Matching Procedure 
Point/Patch Pairs: Closest Patch Procedure 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
124 
Point-based Observation 
Equations 
Modified Least Squares 
Adjustment 
 
d

Pseudo-conjugate points 
CorrectedP
Corrected
c
Corrected
b
Corrected
a
exAy

 Assuming the availability of 
conjugate points 
edxAy

 
Modification of the stochastic 
properties of the random noise 
vector 
0d'P

 ,~e 0

12 
 P
o

Primitives & Matching Procedure 
Point-Based Adjustment 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
125 
• Once the corrections to the system parameters have been 
estimated, the corrected ground coordinates of the LiDAR 
points are reconstructed using the estimated parameters: 
 
• Quasi-rigorous Approach: 
 
 
 
 
 
• Rigorous Approach: 
• LiDAR rigorous equation 
 
LiDAR Point Cloud Reconstruction 
),,,,,,( estestestestestestest SYX kfw 
 
 
  














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

































estest
estestest
estestest
est
estestestest
estestestest
Biased
Biased
Biased
Corrected
Corrected
Corrected
SxS
SzsSx
SzcSx
x
zzcYX
zzYX
Z
Y
X
Z
Y
X

kkkk
kkkk
f
fkwkkk
fkwkkk
 cos
 in sinsin cos
 os sincos sin
 
sin os cossin
cos sin sincos
~
~
~
~
~
~
Photogrammetric & LiDAR Mapping Ayman F. Habib 
126 126 
• Quality control is a post-mission procedure to 
ensure/verify the quality of collected data. 
• Quality control procedures can be divided into two 
main categories: 
– External/absolute QC measures: the LiDAR point 
cloud is compared with an independently collected 
surface. 
• Check point analysis 
– Internal/relative QC measures:the LiDAR point 
cloud from different flight lines is compared with each 
other to ensure data coherence, integrity, and 
correctness. 
LiDAR Quality Control 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
127 127 
Csanyi, N., Toth, C. (2004). On using LiDAR-specific ground targets. ASPRS 
Annual Conference, Denver, CO, May 23-28. CD-ROM. 
EQC: LiDAR Control Targets 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
128 128 
Range Data Intensity Data 
• One should implement a segmentation procedure to 
derive the LiDAR coordinates of the target. 
EQC: LiDAR Control Targets 
Csanyi, N., Toth, C. (2004). On using LiDAR-specific ground targets. ASPRS 
Annual Conference, Denver, CO, May 23-28. CD-ROM. 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
129 
• Surface reconstruction from LiDAR does not have 
redundancy. 
– Therefore, we do not have explicit measures in the derived 
surfaces to assess the quality of LiDAR coordinates. 
• DPRG Concept: Evaluate the degree of consistency 
among the LiDAR footprints in overlapping strips. 
Strip 2 Strip 3 Strip 4 
IQC: LiDAR Quality Control 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
130 130 
Overlapping strips with common features 
IQC: LiDAR Quality Control 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
131 131 
Check for the presence of biases 
IQC: LiDAR Quality Control 
•Derive quantitative estimate of the necessary 
transformation parameters (shifts & rotations) for the co-
alignment of the captured data from different flight lines. 
• For a well-calibrated system and with accurate navigation 
information, the transformation parameters should be very close 
to zero. 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
132 
Conditions: 
• Closest patch 
• Normal distance < threshold 
• Point located within the 
patch 
0
1
1
1
1


ccc
bbb
aaa
iii
ppp
ppp
ppp
qqq
ZYX
ZYX
ZYX
ZYX



































i
i
i
i
i
i
q
q
q
T
T
T
q
q
q
Z
Y
X
RS
Z
Y
X
Z
Y
X
Where: 
XT, YT, ZT, S, Ω, 
Φ,Κ 
),,,,,,( SZYX TTT
Point/Patch Pairs: Iterative Closest Patch (ICPatch) 
IQC: LiDAR Quality Control 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
133 
Surface 1: 44,156 points Surface 2: 45,520 patches 
Register 
XT (mm) YT (mm) ZT (mm) S Ω °) Φ °) Κ °) 
Optimal Para.* 0.000 0.000 0.000 1.000 0.000 0.000 0.000 
Estimated -0.660 -0.367 0.007 1.001 -0.017 0.002 0.003 
Estimated Variance Component 0.122 
Average Normal Distance 0.142 m 
* Assuming the LiDAR data has no biases 
Point/Patch Pairs: Iterative Closest Patch (ICPatch) 
IQC: LiDAR Quality Control 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
Strip Number Flying Height Direction 
1 1150 m N-S 
2 1150 m S-N 
3 539 m E-W 
4 539 m W-E 
5 539 m E-W 
6 539 m E-W 
Strip 1
Strip 2
Strip 3
Strip 4
Strip 5
Strip 6
Strip 1
Strip 2
Strip 3
Strip 4
Strip 5
Strip 6
Overlapping 
Strips Cases 
% 
of Overlap 
Direction 
Strips 1&2 80% Opposite directions 
Strips 3&4 25% Opposite directions 
Strips 4&5 75% Opposite directions 
Strips 5&6 50% Same direction 
134 
LiDAR QA/QC: Experimental Results (I) 
Dataset Description 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
135 
Method δΔX(m) δΔY(m) δΔω(°) δΔφ(°) δΔκ(°) Δρ(m) δS 
Simplified 0.03 -0.01 -26 -91 -19 0.18 0.000046 
Quasi-rigorous -0.01 0.02 -40.2 -90.9 -4.58 0.26 -0.000096 
Estimated system biases using the Simplified and the Quasi-rigorous methods 
LiDAR QA: Experimental Results (I) 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
136 
Intensity Image (Before) 
 
Intensity Image (After) 
Qualitative Evaluation 
LiDAR QC: Experimental Results (I) 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
137 
1m1m
Original Point Cloud 
LiDAR QC: Experimental Results (I) 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
138 
1m1m
Adjusted Point Cloud 
Relative Accuracy Evaluation 
LiDAR QC: Experimental Results (I) 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
Before Calibration After Calibration 
Strips 1&2 Strips 1&2 
XT (m) YT (m) ZT (m) XT (m) YT (m) ZT (m) 
1.10 -0.32 -0.01 0.11 0.07 -0.05 
w (deg) φ (deg) κ (deg) w (deg) φ (deg) κ (deg) 
0.0001 -0.052 -0.002 0.0012 -0.0016 -0.0051 
Strips 3&4 Strips 3&4 
XT (m) YT (m) ZT (m) XT (m) YT (m) ZT (m) 
0.18 0.41 -0.01 -0.01 -0.01 0.01 
w (deg) φ (deg) κ (deg) w (deg) φ (deg) κ (deg) 
0.0484 -0.0005 -0.0011 0.0052 0.0008 -0.0045 
Compatibility between overlapping strips before and after the calibration procedure 
139 
Relative Accuracy Evaluation 
LiDAR QC: Experimental Results (I) 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
140 
 Before Calibration After Calibration 
Mean ΔX (m) -0.36 -0.10 
Mean ΔY (m) 0.67 0.24 
Mean ΔZ (m) -0.05 -0.015 
σX (m) 0.40 0.11 
σY (m) 0.29 0.06 
σZ (m) 0.24 0.13 
RMSEX (m) 0.53 0.14 
RMSEY (m) 0.72 0.24 
RMSEZ (m) 0.25 0.20 
RMSETOTAL (m) 0.93 0.35 
RMSE analysis of the photogrammetric check points using extracted control planar 
features from the LiDAR data before and after the calibration procedure 
Absolute Accuracy Evaluation 
LiDAR QC: Experimental Results (I) 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
141 
Source: http://www.isprs.org/publications/related/semana_geomatica05/front/abstracts/Dimecres9/F01.pdf 
LiDAR QA/QC: Experimental Results (II) 
Dataset Description 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
142 
Dataset captured by a compact LiDAR system built at EPFL 
operated from the side of a helicopter 
LiDAR QA/QC: Experimental Results (II) 
Dataset Description 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
143 
Platform attitude variation 
Flight line 
ω (o) 
min/max 
φ (o) 
min/max 
1 -3.0 / 4.2 6.4 / 9.1 
2 -9.4 / -3.0 -4.0 / 1.6 
4 6.8 / 8.7 0.6 / 1.4 
5 0.0 / 7.5 4.7 / 10.7 
6 -11.4 / -3.0 0.4 / 5.0 
7 -4.2 / 8.8 -12.9 / -7.4 
9 -9.9 / -2.2 1.6 / 23.2 
LiDAR QA/QC: Experimental Results (II) 
Dataset Description 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
144 
LiDAR QA/QC: Experimental Results (II) 
Dataset Description 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
145 
Strip pairs Flying Direction 
Rigorous 1&9; 2&4; 5&6; 5&7 
Quasi-rigorous 1&9; 2&4; 5&6; 5&7 
Simplified 1&9; 2&4; 5&7 
Strip pairs Flying Direction % Overlap 
Average 
Lateral Distance D 
(m) 
Average 
Flying Height H 
(m) 
1&9 approx. parallel 75 66 130 
2&4 approx. opposite 70 160 130 
5&6 cross - - 230 
5&7 approx. opposite 75 10 230 
LiDAR QA/QC: Experimental Results (II) 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
146 
1&9 
~Parallel Direction 
2&4 
~Opposite Direction 
5&6 
~Cross Direction 
5&7 
~Opposite Direction 
Dataset Description 
LiDAR QA/QC: Experimental Results (II) 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
147 
Method δΔω(o) δΔφ(o) δΔκ(
o) S/δS 
Simplified 0.039 0.092 -0.029 -0.00028204 
Quasi-rigorous 0.038 0.093 -0.044 -0.00000514 
Rigorous -0.094 0.032 90.064 1.00017 
Please, note that the estimated parameters are not compatible since 
different coordinate systems definition are utilized in the two 
calibration approaches. 
yb 
xb 
zb 
xlu 
ylu 
zlu 
xb 
yb 
zb 
xlu 
zlu 
ylu 
Flight direction 
Flight direction 
Simplified/Quasi-Rigorous Rigorous 
LiDAR QA/QC: Experimental Results (II) 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
148 
Before Calibration 
After Calibration: Rigorous Approach 
1m 
After Calibration: Quasi-Rigorous Approach 
1m 
Qualitative QC 
1m 
LiDAR QA/QC: Experimental Results (II) 
Photogrammetric & LiDAR Mapping Ayman F. Habib 
149 
Before Calibration 
After Calibration 
Rigorous Quasi-Rigorous Simplified 
1&9 
XT’(m) YT’(m) ZT’(m) XT’(m) YT’(m) ZT’(m) XT’(m) YT’(m) ZT’(m) XT’(m) YT’(m) ZT’(m) 
0.00 -0.21 -0.07 0.01 -0.01 0.01 0.03 -0.11 0.01 0.04 -0.13 0.00 
Ω’(o) Φ’ (o) Κ’(o) Ω’(o) Φ’ (o) Κ’(o) Ω’(o) Φ’ (o) Κ’(o) Ω’(o)