Although high altitude frequencies effects are removed at the time of basic image generation, low altitude (Yaw) effects are still present in form of affinity/angular affinity. They are effectively removed by additional parameters. Bundle block adjustment based on properly weighted ephemeris/altitude quaternions (BBABEQ) are not enough to remove the systematic effect. Moreover, due to the narrow FOV of the HRSI, position and altitude are highly correlated making it almost impossible to separate and remove their systematic effects without extending the geometric model (Self-Calib.) The systematic effects gets evident on the increase of accuracy (in terms of RMSE at GCPs) for looser and relaxed ground control at the expense of large and strong block deformation with large residuals at check points. Systematic errors are most freely distributed and their effects propagated all over the block

Passini, Richardo M.

NASA Technical Reports Server

ACCURACY ANALYSIS ON LARGE BLOCKS 
OF HIGH RESOLUTION IMAGES
Dr. Ing. Ricardo M. Passini
BAE SYSTEMS ADR
https://ntrs.nasa.gov/search.jsp?R=20070038229 2019-08-29T18:36:00+00:00Z
Document number- 2
•INTRODUCTION
•SHORT DESCRIPTION OF THE 
ORIENTATION MODELS
•EXPERIMENTAL TESTS
•ANALYSIS OF THE RESULTS
•CONCLUSIONS
•RECOMMENDATIONS
Accuracy Analysis on Large Blocks of High Resolution Images
Document number- 3
Accuracy Analysis on Large Blocks of High Resolution Images
INTRODUCTION
“TODAY EXISTING HIGH RESOLUTION 
IMAGES ARE ENTERING INTO 
COMPETITION WITH AERIAL 
PHOTOGRAPHY FOR REGIONAL 
MAPPING PROGRAMS AND OTHER 
EXTENSIVE MAPPING APPLICATIONS 
WHERE HIGH RESOLUTION IS 
REQUIRED”
OUR STUDY IS CONCENTRATED MAINLY ON 
QUICKBIRD IMAGES
Document number- 4
Accuracy Analysis on Large Blocks of High Resolution Images
INTRODUCTION
Mapping, Risk Management, Forest, Geology, Regional Planning, Utlity Corridor 
Planning,  Mapping for E911 applications, Defense Mapping, etc.
1. Information contents
Rule of thumb: for topographic maps 0.05 – 0.1 mm pixel size in map required
based on 1m     pixel size    Æ map 1 : 10 000 (~ 1“=800‘)
based on  0,6m pixel size    Æ map 1 : 6000       (1“=500‘)
For orthoimages  8 pixel / mm (0.125 m pixel size)
based on 1m pixel size     Æ orthoimage 1 : 8000 (~1“=667‘)
based on 0,6m pixel size  Æ orthoimage 1 : 4800   (1“=400‘)
2. Accuracy
Required accuracy of x, y- coordinates: ~ 0,25mm in map,  in orthoimage ~ 0,3mm
Æ required ground accuracy    2,5m  /  1,5m (0.25 mm at above map scales)
Image orientation must be better because of additional error components
USE OF VERY HIGH RESOLUTION IMAGES
Document number- 5
Accuracy Analysis on Large Blocks of High Resolution Images
Introduction
ACCURACY DEPENDS ON:
 Orientation Model used
 GCPs (Number, Distribution, Geometric & Radiometric Quality, etc.)
 For Orthos (DTM accuracy, Resolution, Fidelity of Terrain Reconstruction, etc)
 Others
USED ORIENTATION MODELS IN THE INVESTIGATION:
• SIMULTANEOUS BUNDLE BLOCK ADJUSTMENT (using ephemeris & 
quaternion algebra)
• RATIONAL POLINOMIAL COEFFICIENTS (+image correction functions)
USED IMAGE:
 A block of 40 QB Basic images with limited overlap (hilly, equatorial, jungle 
zone)
GROUND CONTROL:
Manually Transferred from existing oriented aerial photography (1:20,000) 
Document number- 6
Bundle Orientation using ephemeris and quaternion algebra
)()()(
)()()(0
333231
131211
jjjjjj
jjjjjj
ZoZpaYoYpaXoXpa
ZoZpaYoYpaXoXpac −+−+−
−+−+−−=
)()()(
)()()(
333231
232221
jjjjjj
jjjjjj
ZoZpaYoYpaXoXpa
ZoZpaYoYpaXoXpac −+−+−
−+−+−−
),(
→= vaq
p
z image
y image
x image
(orbit direction)
γo
λp
Northing or y
Easting or x
Z
ξp
y =
ξp = γo + λp or
P
It is possible to use quaternion multiplication to perform a rotation about an 
arbitrary unit axis m by an angle Θ. The quaternion that computes the rotation is:
)v(a,q
→= Where a = cos(Θ/2) , v=sin(Θ/2). 
Then q1=μxsin(Θ/2), A point in 3D 
q2 = μy sin(Θ/2)                is rotated by
q3 = μz sin(Θ/2)
q4 = cos(Θ/2)
)P(0,p
→=
Protated=q*p*q-1
q=a+bi+cj+dk
2222
2222
2222
2222
2222
2222
dcbacdabacbd
abcddcbabcad
bdacadbcdcba
+−−+−
−−+−+
+−−−+
The orthogonal rotation matrix corresponding to a 
rotation by the unit quaternion p=a+bi+cj+dk is given 
by q*q-1 = 
q*q-1 =
Assuming smooth stable paths (that generally is), then no 
ephemeris corrections are applied, only attitude corrections are
computed in the adjustment.
Document number- 7
Bundle Orientation using ephemeris and quaternion algebra
The QB Camera Sensor Model includes the Coordinate Systems:
ECEF Spacecraft Coord. System
Camera Coord. 
System
Image Coord. System
Detector Coord. System
qsE(t)
qCS (Fixed)
1 to 1 relation. No 
image distortion in 
Level 1B
Rotation + Shift 
(α, ShX, ShY)
Document number- 8
Bundle Orientation using ephemeris and quaternion algebra
Derivation of the co-linearity equations
As the Level 1B product is sampled at a constant rate, the corresponding time (t)= t=r/ avgLineRate + firstLineTime 
One point on the imaging ray is the perspective centre of the virtual camera at time t. The coordinates of the perspective centre in the spacecraft 
coordinate systems are constant and given data. In matrix notation: CS = (CX, CY, CZ)T (from *.geo file)
It is possible to locate the origin of the spacecraft coordinate system in the ECF system at a time t by interpolating the position time series in the 
ephemeris file. Let us call this position SE(t). Likewise, we can find the attitude of the spacecraft coordinate system at a time (t) in the ECF system 
by interpolating the quaternion time series in the attitude file. This quaternion, qSE(t), represents the rotation from the ECF system to the spacecraft 
body system at time t. Then using quaternion algebra, the position of the perspective centre at time t in the ECF coordinate system is:
CE(t) = (qES(t))-1 CS qES(t) + SE(t), or 
CE(t) = qSE(t) CS (qSE(t))-1 + SE(t) or CE(t) = RES(t) CS + SE(t) This is the Projection Center if ECEF
Any point that we measure (c,r) is expressed in the detector system as 
XD=0, YD=-c*detPitch (detPitch: Calibrated distance between pixels)
In the camera system is XC = cos(α)∗ XD – sin(α)∗ YD + ShX; 
YC = sin(α)∗ XD + cos(α)∗ YD + ShY; ZC = C (Nominal Principal Distance)
As Level 1B images do not have lens distortion the image point is identical to the measured image point, hence:XC’=XC, YC’=YC, ZC’=ZC. 
The unit vector wC that is parallel to the external ray in the camera coordinate system is just the position of (XC’, YC’, ZC’) relative to the 
perspective centre at (0, 0, 0), normalized by its length. In matrix notation, this vector is: WC = (X C’ , Y C’ , Z C’ )T & w C = W C / || W C ||
It is possible to convert this vector first to the spacecraft coordinate system and then to the ECF system. The unit quaternion for the attitude of the 
camera coordinate system, i.e., the quaternion for the rotation of spacecraft frame into the camera frame qCS, is in the geometric calibration file 
(*.geo). Then, using quaternion algebra:
wE = qES(t) -1 qSC-1 wC qSC qES(t) or wE = qS E(t) qCS wC (qSE (t) qCS) -1 or using matrix algebra, wE = RES(t) RSC wC
Hence, the co-linearity equation will be: 
wC = [RES(t) RSC ] or wC = (qSE (t) qCS) -1 wE [qSE(t) qCS]T
Document number- 9
Bundle Orientation using ephemeris and quaternion algebra
Ephemeris and Quaternion data. Variance-Co-variance Matrix
– Ephemeris File: Sample mean and covariance estimates of the position of the 
spacecraft system relative to the ECEF system. These data are produced for a continuous 
image period, e.g., an image strip, and spans the period from at least 4 seconds before 
start of imaging to at least four seconds after the end of imaging
– Attitude File: Contains Sample mean and covariance estimates of the attitude of the 
spacecraft system relative to the ECEF system. These data are also produced for a 
continuous image period, e.g., an image strip, and spans the period from at least 4 seconds 
before start of imaging to at least four seconds after the end of imaging
– Sampling rate (timeInterval): Each 0.02 seconds. For intermediate position only linear 
interpolation  is required
– Possibility to implement a weighting schema based on:
2
4
43
2
3
4232
2
2
413121
2
1
2
o
oo
2
o
oooo
2
o
q
qqq
qqqqq
qqqqqqq
Z
ZYY
ZXYXX
σ
σσ
σσσ
σσσσ
σ
σσ
σσσ
                                 
Document number- 10
Block Adjustment using RPC + image correction functions
{Image Space (Line, Sample)}  FUNCTIONAL RELATION {Object Space (φ, λ, h)}
LAT_SCALE
LAT_OFF-P ϕ=
LONG_SCALE
LONG_OFFλL −=
LEHEIGHT_SCA
HEIGHT_OFFhH −=
y=Line = g(φ, λ, h) = 
Bb
Aa
H)L,(P,DEN
H)L,(P,NUM
T
T
L
L = x = Sample =h(φ,λ,h)= Ad
Ac
H)L,(P,DEN
H)L,(P,NUM
T
T
S
S =
AaHaHPaHLaPHaPaPLaLHaLPaLaPLHa
HaPaLaPHaLHaLPaHaPaLaaH)L,(P,NUM
T3
20
2
19
2
18
2
17
3
16
2
15
2
14
2
13
3
1211
2
10
2
9
2
87654321l
=+++++++++
++++++++++=
AbHbHPbHLbPHbPbPLbLHbLPbLbPLHb
HbPbLbPHbLHbLPbHbPbLbbH)L,(P,DEN
T3
20
2
19
2
18
2
17
3
16
2
15
2
14
2
13
3
1211
2
10
2
9
2
87654321l
=+++++++++
++++++++++=
The de-normalized image space coordinates (Line, Sample), can also be computed from:
Line = y. LINE_SCALE + LINE_OFF Sample = x. SAMP_SCALE + SAMP_OFF
Computed de-normalized image coordinates (Line, Sample)
≠ Observed image Coordinates (Line, Sample)
Document number- 11
Block Adjustment using RPC + image correction functions
Li
(j)
sss
(j)(j)
i dξ)h,λ,(ξLine ∇++ϕ= Si(j)sss(j)(j)i dρ)h,λ,(ρSample ∇++ϕ=
With: Linei j and Samplei j measured image coordinates of a TP or GCP s with coordinates (φs, λs, hs )
ξ(j)(φs, λs, hs ) and ρ(j) (φs, λs, hs ) computed de-normalized image coordinates of the GCP or tie point s
dξ(j)  and dρ(j) Correction Functions to account for the difference between measured and computed coordinates
NablaLi and NablaSi are random errors. Or:
g(φ, λ, h) . LINE_SCALE + LINE_OFF =ϕ )h,λ,(ξ sss(j) )h,λ,(ρ sss
(j) ϕ =h(φ,λ,h) . SAMPLE_SCALE + SAMPLE_OFF 
_____
l
________
so Line.rSample.rrdξ ++=
_____
L
_______
so LinesSamplessdρ ++=
(j)
Sis
s
Si
s
s
Si
s
s
Si(j)
L(j)
L
Si(j)
s(j)
s
Si(j)
o(j)
o
Si
Si
(j)
Lis
s
Li
s
s
Li
s
s
Li(j)
L(j)
L
Li(j)
s(j)
s
Li(j)
o(j)
o
Li
Li
vdh
h
φdλ
λ
φdφφds
s
φds
s
φds
s
φ
φ
vdh
h
φdλ
λ
φdφφdr
r
φdr
r
φdr
r
φ
φ
o
o
=∂
∂+∂
∂+ϕ∂
∂+∂
∂+∂
∂+∂
∂+
=∂
∂+∂
∂+ϕ∂
∂+∂
∂+∂
∂+∂
∂+
PL)(APA)(AX T1T −=
Document number- 12
Experimental Tests. Block of 40 QB Basic images
Full Control 
Distribution (Case A)
Perimeter Control and randomly distributed GCPs in the center of
the Block. (Case B)
Document number- 13
Experimental Tests. Block of 40 QB Basic images
Perimeter control only. 
(Case C)
Relaxed perimeter control. 
(Case D)
Control only in the corners of the 
block. (Case E)
Document number- 14
Experimental Tests. Block of 40 QB Basic images
Case #GCPs RMSEp #ChKPts RMSEp
A 89 0.74
B 33 0.63 56 3.13
C 25 0.50 64 3.34
D 9 0.47 80 5.42
E 5 0.35 84 8.71
Bundle Adjustment with Ephemeris & 
Quaternion. Accuracies in GCPs & Check 
Points
Bundle Adj with Ephemeris & Quaternions
0
1
2
3
4
5
6
7
8
9
10
Case A (89) Case B (33) Case C (25) Case D (9) Case E (5)
R
M
S
E
p
 
(
F
e
e
t
)
RMSEp (CGPs) RMSEp (CHK)
Max Errors on GCPs & CHK Pts
0
5
10
15
20
25
30
Case A (89) Case B (33) Case C (25) Case D (9) Case E (5)
M
a
x
 
E
r
r
o
r
s
 
(
m
)
MAX Error on GCPs MAX Error on CHKPts
Case #GCPs Max Err #ChKPts Max Err
A 89 3.27
B 33 1.87 56 8.61
C 25 1.58 64 10.01
D 9 1.45 80 19.01
E 5 0.81 84 26.49
Bundle Adjustment with Ephemeris & 
Quaternion. Max Errors on GCPs & Check 
Points
Document number- 15
Experimental Tests. Block of 40 QB Basic images
Block Adj with RPCs + Affine image Correction
0
1
2
3
4
5
6
7
Case A (89) Case B (33) Case C (25) Case D (9) Case E (5)
R
M
S
E
p
 
(
m
)
RMSEp @ GCPs
RMSEp @             Chk Pts
Case #GCPs RMSEp #ChKPts RMSEp
A
B
C
D
E
0.9889
33
25
9
1.07 56 2.21
1.41 64 2.93
1.57 80 4.16
5 1.70 84 5.97
Block Adjustment with RPCs + Affine Image 
Correction
RMSD [m] Max Errors [m]
Sx Sy Δxmax Δymax
A 89 0.21 0.25 2.53 4.93
B 33 0.19 0.23 2.51 4.56
C 25 0.16 0.22 2.48 1.50
D 9 0.16 0.21 2.45 1.48
E 5 0.15 0.20 2.06 1.35
Case Num 
GCPs
RMSD [m] Max Errors [m]
Sx Sy Δxmax Δymax
A 89 0.29 0.32 1.83 2.57
B 33 0.65 0.74 2.01 3.34
C 25 0.81 0.88 2.49 2.25
D 9 0.88 0.97 2.85 2.98
E 5 0.91 1.12 3.08 3.36
Case Num 
GCPs
Internal Accuracy. Statistics on TPs. Bundle Adj 
with Ephemeris & Quaternions
Internal Accuracy. Statistics on TPs. Block Adj 
with RPCs + Affine Image Correction
Document number- 16
Analysis of the results
Accuaracy Comparison
0
2
4
6
8
10
Case A
(89)
Case B
(33)
Case C
(25)
Case D (9) Case E (5)R
M
S
E
 
@
 
G
C
P
s
 
&
 
C
h
k
 
P
t
s
 
[
m
]
Ephem. + Quarter RMSE @ GCPs
Ephem. + Quarter RMSE @ Chk Pts
RPCs + Affine RMSE @ GCPs
RPCs + Affine RMSE @ Chk Pts
Ephem. + Quarter. RPCs + Affine
RMSE@
GCPs
RMSE@
Chk Pts
RMSE@
GCPs
RMSE@
Chk Pts
A(89) 0.74 0.98
B(33) 0.63 3.13 1.07 2.21
C(25) 0.50 3.34 1.41 2.93
D(9) 0.47 5.42 1.57 4.16
E(5) 0.35 8.71 1.70 5.97
CASE
#GCPs
Accuracy Comparison. Bundle Adjustment using 
ephemeris + quaternion vs. Block Adjustment 
based on RPC and affine image correction
RMS Errors at GCPs and Check Points
Document number- 17
Self-calibration through Additional Parameters
param add
)Zo(Zpa)Yo(Ypa)Xo(Xpa
)Zo(Zpa)Yo(Ypa)Xo(Xpac0 jjj
jjj
j
33
j
32
j
31
j
13
j
12
j
11 +−+−+−
−+−+−−=
param add
)jZo(Zpja)jYo(Ypja)jXo(Xpja
)jZo(Zpja)jYo(Ypja)jXo(Xpjacy
333231
232221 +
−+−+−
−+−+−−=
y=y+P1*y y=y+P12*COS (y*0.01600)
x=x+P2*y x=x+P13*SIN (y*0.03100)
x=x+P3*x*y x=x+P14*COS (y*0.03100)
y=y+P4*x*y x=x+P15*SIN (y*0.01600)
y=y+P5*SIN (y*0.12566)     x=x+P16*COS (y*0.01600)
y=y+P6*COS (y*0.12566)   x=x+P17*SIN (x*0.11)
y=y+P7*SIN (y*0.06283) *SIN (y*0.03)
y=y+P8*COS (y*0.06283 x=x+P18*x*y*COS(K) 
y=y+P9*SIN (y*0.03100)     y=y+P18*x*y*SIN(K)
y=y+P10*COS (y*0.03100) y=y+P19*x*y
y=y+P11*SIN (y*0.01600) x=x+P20*y*y
ADDITIONAL PARAMETERS IMPLEMENTED IN 
THE UNIVERSITY OF HANNOVER PROGRAM 
BLASPO
To avoid over-parameterization the AP are automatically 
eliminated using a stochastical model:
1. For each AP compute:
ip
i
i σ
p
t = otherwise if reject   1,t.σ qσ i o,iiip ≥=
2. Compute cross-correlation coeffs. for the parameters
0.85R   ;
qq
qR ij
jj ii
ij
ij ≥= Then eliminate the parameter with smaller ti value
3. Compute B = I – (diag N * diag N-1)-1;   eliminate the AP  
that Bij > or = 0.85
Systematic image errors   QuickBird Atlantic City, NJ
left: overall effect    right: without dominating angular affinity
Document number- 18
Self-calibration through Additional Parameters
Digital Ortho. 0.5 m GSD QB Basic Image, ~0.6 GSD
a.  GCPs Manually and automatically transferred from existing 0.5 m  GSD Orthophoto
Height of the GCPs through interpolation on a existing ± 1.3 feet Accuracy DEM (1”=1600’)
Same DEM for production of Orthophoto
Document number- 19
Self-calibration through Additional Parameters
Accuracy at GCPs Accuracy at Check Pts
RMSEx RMSEy RMSEx RMSEy
Manual 174 11.2 0.71 0.66
Automatic 398 10.1 0.48 0.45
Automatic 25 12.3 0.52 0.71 0.69 0.72
Automatic 20 13.1 0.59 0.75 0.69 0.88
Automatic 15 13.8 0.61 0.78 0.78 1.04
Type of 
Observations
Number of 
GCPs
Standard 
Deviation 
[microns]
Bundle Orientation with automatic selection and elimination additional parameters. 
Basic QB Image. Area of Atlantic City, NJ
Document number- 20
CONCLUSIONS
– Although high attitude frequencies effects are removed at the time of basic image 
generation, low attitude (Yaw) effects are still present in form of affinity/angular affinity. 
They are effectively removed by additional parameters
– Bundle block adjustment based on properly weighted ephemeris / attitude quaternions 
(BBABEQ) are not enough to remove the systematic effects. Moreover, due to the narrow 
FOV of the HRSI, position and attitude are highly correlated making almost impossible 
to separate and remove their systematic effects without extending the geometric model 
(Self-Calib.)
– The systematic effects gets evident on the increase of accuracy (in terms of RMSE at 
GCPs) for loser and relaxed ground control at the expenses of large and strong block 
deformation with large residuals at check points. Systematic errors are more freely 
distributed and their effects propagated all over the block. [No functional model for SE]
– Block adjustment based on RPCs with systematic image correction functions remove 
significantly the affinity deformation of the basic QB images. Although relaxed ground 
control produces less accurate results (in terms of RMSE on GCPs) than BBABEQ, the 
remaining block deformations are much smaller. Increase of absolute accuracy between 
65 to 80% can be reported.
– The systematic effects are also noticeable in the internal accuracy of the Block (residuals 
at pass/tie points). These are smaller for relaxed ground control in the BBABEQ and 
opposite in the case of RPCs with affine image correction function.
Document number- 21
RECOMMENDATIONS
Further Studies need to be carried out to be more conclusive:
1. To conduct accuracy studies on large blocks of images with larger long overlap. 
This will allows a 3D accuracy study and to increase the reliability of the derived 
quantities.
2. To extend the model of the BBABEQ to include Self-calibration making use of the 
co-variance matrices of the Position and Attitude to build-up proper weighting 
matrix.
3. To include cross track image strips to study the combined effect of multi-rays 
points and self-calibration on the final accuracy.
4. To extend the RPC model with other image correction functions, including 
statistical test to ensures the validity of the image correction function parameters 
to avoid over-parameterization.
5. To test alternative orientation models such as those based on feature matching, 
i.e., matching of linear features existing on a land data base and extracted from 
the image space.
6. Others
ACCURACY ANALYSIS ON LARGE BLOCKS 
OF HIGH RESOLUTION IMAGES
Dr. Ing. Ricardo M. Passini
BAE SYSTEMS ADR
QUESTIONS..?


Accuracy Analysis on Large Blocks of High Resolution Images

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