mapping from space 3. sensor orientation
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Institut für Photogrammetrie und GeoInformation
Mapping from Space3. Sensor orientation
Dr. Karsten JacobsenInstitute of Photogrammetry and GeoInformation
Leibniz University Hannoverjacobsen@ipi.uni-hannover.de
Institut für Photogrammetrie und GeoInformation
3.1 Geometric handling of space imagesInner orientation – important for satellite companies, not for user – the user gets a
homogenous virtual image
Arrangement of IKONOS CCDs1. Color 2. backward scan
3. forward scan
QuickBird: 6 CCD elements in every lineGeometric reality
Merge of sub-images by theory only correct for one elevation one pixel
mismatch at ∆h:for IRS-1C/1D: 450mfor QuickBird: 2.8km
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3.1 Very high resolution systems - imaging
Integration of received energy over several pixels
reason: relative speed of satellite ~ 7km/sec 1m in 0.14msec – too short integration time for sufficient image quality
5m pixel size – 0.7 msec – just sufficient
Staggered arrays – 50% over-sampling e.g. OrbView-3: 2m projected pixel size on ground, but 1m ground sampling distance (GSD) = distance between neighboured pixel centres
Transfer delay and integration (TDI)
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3.1 actual GSD / projected pixel size
Incidence angle = ν
Pixel size on ground in view direction: pv= p/cos²νin orbit direction: po= p/cosν
e.g. n = 30°, for p=1m in nadir: pv = 1.33m po=1.15m but sampling rate not changed – line every 1m still1m GSD, 1.15m pixel size in orbit direction
- oversampling in orbit direction by 15%
GSD
GSD in orbit direction determined by sampling rate
pixel size
Pixel on ground
τ
pixel size on ground depending upon nadir angle τ
pixel size in view direction pv = p / cos² pixel size in orbit direction po = p / cos
ττ
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3.1 actual GSD / projected pixel size
0
0,5
1
1,5
2
2,5
0° 10° 20° 30° 40° 50° nadir angle
pixel size in view direction
pixel size across view direction
[m] for panfor ms
10m
8m
6m
4m
under sampling over sampling
IKONOS – pixel size in nadir = 0.82m
Standard distribution with 1m GSD
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3.1 Image OrientationImage orientation = relation ground position to image position
exact geometric reconstruction or approximate
Asynchronous mode
Slow down factor = b / a
original image = combination of sub-images improved by inner orientation
Reaction wheels,
Control moment gyros
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3.1 Mathematical Model of Scene Geometry
One straight CCD-line located in the focal plane with equal distance of pixels
Projection center
Object
Colinearity condition: image point, projection center, object point are located on a straight line
Refraction (influence of atmosphere) of space images limited size
γ= (Pi – Po)∗pixel_size / f
viewing angle F(pixel address, pixel size and focal length)
Inner orientation partially not published
γ
Calibration: determination of parameters describing the camera geometry
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3.1 Specification of vertical accuracy
Standard deviation: ²dz
SZn u
=−
∑
Condition: dz = differences in height normal distributed – random errors
also named root mean square error = RMSE or RMSZ = 1 sigma1 sigma
SZ =
1sigma
LE90LE95
Normal distribution = frequency of error distribution
discrepancies [SZ]
frequency
discrepancies < 3 ∗ SZ with 99.73% probability
frequency distribution of KOMPSAT-2 DEM
discrepancies
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3.1 Specification of horizontal accuracy
Standard deviation: ²dz
SZn u
=−
∑ 68% probability level
for horizontal accuracy: SX, SY = standard deviation of coordinate component
In USA also: CE90 = circular error with 90% probability level of normal distribution
CE = circular error
if SX identical to SY: CE90 = SX ∗ 2.3 or CE95 = SX ∗ 2.8
90 ² ² 1.65CE SX SY= + •
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3.1 Nadir angle – incidence angle
nadir angle
incidence anglecentre angle
incidence angle = nadir angle + centre angle
e.g. for IKONOS with nadir angle = 25°centre angle = 2.9°
Incidence angle = 27.9°
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3.1 Control points
Rule of thumb for mapping: ground sampling distance (GSD) ~ 0.1mm in map scale
- with 1m GSD mapping in scale 1 : 10 000, 0.6m GSD can be used for 1 : 5000
Required accuracy for mapping: not better than 0.2mm in map scale 2 GSD
Direct sensor orientation by IKONOS in range of +/-4m, QuickBird and OrbView-3 with standard deviation of 12m, but often problems with national datum
Control points required, but direct sensor orientation can be used for support of image orientation
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3.1 Definition of control points
Building corner used as control point – left: original image, right: contrast enhanced
shift of position by 1 pixel
grey value profile of edge
grey value profile of symmetric target
not optimal location at corner
better location in centre – even if more difficult during ground survey
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3.1 Well defined control-“points”
Kompsat-1 optimal IKONOS IKONOSpoint not well defined in detail corner point
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3.1 Control point reference with different resolution
Left: Cartosat-1 2.5m GSD
Right: ADS40 0.4m GSD
Resolution too different – identification of control points very difficult and not accurate
With such control points
SX, SY ~ 3.2m SZ ~ 3.8m
With better control points improved to SX, SY ~ 2.0m SZ ~ 2.5m
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3.1 Results of bundle adjustment with BLASPO – QuickBird Basic
[m]2,0
1,01,21,41,61,8
9 13 15 48/56 207 control points
SXSY
accuracy at independent check points as function of number of control points (2 scenes)
Sigma0 ~ 1.4 pixel
control points from digital orthoimages with 1m pixel size and accuracy of +/-1,03m
Control points from USGS ortho-map, 1m pixel
typical control point used at grey value corners – shift from bright to dark part - 25% less accurate like symmetric points e.g. centre of swimming pool (nadir angle 11°)
QB Basic Imagery, scenes 12450 and 12451
with symmetric points
with corner points
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3.1 control points Rio de Janeiro
Control points only in small area of the IKONOS scene
Possible only with the good pre-information about the IKONOS Geo-scenes
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3.1 control points Rio de Janeiro
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3.1 control points Rio de Janeiro
Precise definition of control points required for acceptable accuracy, but not simple
Discrepancies of orientation
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3.1 Type of available imagesOriginal image (only radiometric correction + inner sensor geometry) level 1A, Basic Imagery
projected images – level 1B type, IKONOS Geo, QuickBird OR Standard,OrbView-3 Geo(QB Standard Imagery – rough DEM)
dh
dL
imag
eprojection center
h
plane with constant height
reference surface
QuickBird Basic
OrbView-3 Basictype
Level 1B-type images – position influenced by ground elevation dh against reference height level causes discrepancy dL
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Orthoimage - rectification
Perspective image
terrain
Rectification plane = plane with constant height
Position in rectification
Correct object location
map
IKONOS Geo and QuickBird OR Standard correspond to a rectification
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Ortho-image
perspective image map / ortho-image
parallel projection
Ortho-image: geometry of map, contents of image
image
DEM
Ortho-image
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Ortho-imageGeometry of map, information contents of image
1. original projection shift of position depending upon height
2. Map projection = parallel projection
Projection of image pixel by pixel in the height level of the given height model to the map geometry
Required: image orientation, digital elevation model (DEM)
Remaining problems:
1. Objects with vertical lines (bridges, buildings) do have remaining problems
2. Geometry only correct for objects located in the height level of the DEM – for example roof tops shifted
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Principle of orthoimage
Orthophoto
Inhalt des Bildes,Geometrie der Karte
OberflächeKarte
Projektionszentrum
Bild
Gelände
Karte Entzerrung
Projection of image pixel by pixel to geometry of map
DLDZ
ν
DL = DZ ∗ tan ν
Projection centre
image
map rectification
terrain
Surface
map
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Ortho-image
Position X,Y fixed by specification of orthoimage, with X,Y Z interpolated in DEM
the pixel of the ortho-image is getting the gray value of the input image corresponding to the position in X, Y, Z
Input: X, Y of ortho-image (chosen), Z interpolated with X, Y from given DEM, transformation of X,Y,Z into image – use of the gray value of this image position for the ortho-image
DEM (given)
Image (use of gray values)
Ortho-image = output (Geometry of map)
Projection center
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Geometric principle of ortho-image
Orthophoto
Inhalt des Bildes,Geometrie der Karte
OberflächeKarte
Projektionszentrum
Bild
Gelände
Karte Entzerrung
Projection pixel by pixel from image to DEM in chosen map projection
DLDZ
ν
DL = DZ ∗ tan ν
Surface
mapMap = ortho-image rectification
terrain
Projection centre
image
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Interpolation of grey values
input output
1 23 4
position of output pixel transformed toinput image not exactly in the centre ofof a pixel of the input image1.) nearest neighbour 2.) bilinear interpolation3.) cubic convolution
- change of position - smoothening
- smootheningcubic convolution
Nearest neighbourhood
Input image output (ortho-image)
Position of output pixel will not correspond exactly to the centre of an input pixel – problem of interpolation
1. Nearest neighbourhood: unchanged grey value but not accurate location
2. Bilinear Interpolation: correct location, smoothing
3. Cubic convolution: correct location, stronger change of grey values
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Gray value interpolation
bilinear Nearest neighbourhood
SPOT
10m
GSD
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Effect of Resampling and Contrast on Corner Position
convolution resampling moves apparent corner position Change from nearest neighbor to cubic by 0.25 pixels from Gene Dial
Nearest neighbor cubic convolution
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Error in position
∆h∆R
Fehler durch zu großen Abstand der Höhenrasterpunkte
∆ ∆R = h • r'c
∆L = ∆Z * tan ν
Height error of DEM ∆h is causing position error ∆R
DEM – Z given with spacing in X and Y
real surface
∆L
ν
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Error in position
wall in image
roof in image
not visible
wall in orthoimage (area instead of line)
roof in orthoimage(shifted)
Orthoimage
DEMShift of the roof
Perspective imageRichtige Lage nur im Niveau des DHM
R = h •∆ ∆ r'f
Correct position only in level of DEM
c
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Shift of roof position in orthoimage based on height of ground
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Location of building / roof top
Overlay of orthoimage with correct ground
position
Roof top shifted against ground
correct ground = red line
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Shift of roof tops
red = roof
black = building at height level of terrain
IKONOS ortho-image
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Error in positionProjektions-zentrum
Bridge over valley – DEM presents valley
River with correct position
Bridge shifted corresponding to height of bridge over valley
Projection centre
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Error in position – orthoimage of Bosporus-bridge
IKONOS ortho-image
Gray value coded DEM
Ortho-image
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True orthoimageTrue orthoimage requires height of any individual objectUncorrected bridge
corrected bridges
Information from neighboured image
Uncorrected bridges
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3.1 IKONOS Geo – not an ortho-image
OEEPE test Switzerland
Carterra Geo (= IKONOS Geo)
altitude: 415m – 2197m nominal collection elevation = 67.7° = nadir angle 22.3°
vector
200m
projected image center
RMSX: 124.4m
RMSY: 40.2m
max DX=421m DY=77m
difference IKONOS Geo against check points – points on mountains shifted to left, points in valley shifted to right
relief displacement
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3.1 Discrepancies of IKONOS-Geo
vector
200m
projected image center
128 control points ~ +/-2m
RMSX=+/- 124m, RMSY=+/- 40m
influence of the ground height to location
+ error of IKONOS-direct sensor orientationmountain
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3.1 height correction of Geo-data
height correction depending upon „nominal collection azimuth“ and „nominal collection elevation“ + height of plane for rectification
IKONOS 2: flying height perigee 678km -apogee 682km (681km)
nominal collection azimuth and nominal collection elevation also can be computed based on control points located in different height levels
h N
image
mean sea level
plane for rectification
nadir
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3.1 Geo-data after height correction
vector
30m
discrepancies after height correction
RMSX= +/-7.5m RMSY= +/-18.5m (in range specified for CARTERRA Reference +/-25m)
systematic error dominating –
after correction by X: -6.8m, Y: 18.3m RMSE relative +/-3.5m +/-2.3m
influence of limited accuracy of IKONOS orientation by GPS + IMU + star sensors
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3.1 Geo-data after terrain correction + 2D-affine transformation
After height correction + affinetransformation (shift in X, Y, scale in X, scale in Y, rotation, angular affinity):
from:
RMSX=+/-2.57m, RMSEY=+/-1.89m
To
RMSX=+/-2.56m, RMSEY=+/-1.65m
only negligible error caused by in this case by chosen height level
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3.2 Methods of scene orientation
1. Geometric reconstruction of imaging geometry
2. Sensor oriented rational polynomial coefficients (RPCs) with bias correction – based on direct sensor orientation
3. 3D affine transformation
4. Direct Linear Transformation (DLT)
5. Terrain dependent RPCs – based on control points
> = 0
> = 0
> = 4
> = 6
> = 6
required control points
jZYXPijZYXPixij),,(2),,(1
=jZYXPijZYXPiyij),,(4),,(3
=
Pn(X,Y,Z)j = a1 + a2*Y + a3*X +a4*Z + a5*Y*X + a6*Y*Z + a7*X*Z + a8*Y² + a9*X² + a10*Z²+ a11*Y*X*Z + a12*Y³ +a13*Y*X² + a14*Y*Z² + a15*Y²*X + a16*X3 + a17*X*Z² + a18*Y²*Z+ a19*X²*Z+ a20*Z³
Image coordinates xij, yij as function of object coordinates X, Y, Z
rational polynomial coefficients
Use of direct sensor
orientation
No use of sensor
orientation
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Image geometry
geometric difference of original satellite line scanner image against perspective image
main difference caused by earth rotation
second order differences by map projection
scale in orbit direction defined by Dt of sampling
scale across orbit direction by focal length, flying height, size if pixel in image
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3.2 Geometric reconstruction of projected image
Hannover program CORIKON:
Given: from scene centre or first line direction to orbit + Keppler elements of orbit + slow down factor
-Shift of orbit to intersection with ray from scene centre to orbit
-Based on image coordinate in orbit direction ∗ slow down factor, computation of actual projection centre in orbit – individually for every line, respecting earth rotation
- from actual projection centre to geo-referenced image = individual view direction
Can be handled also without control points if given sensor orientation is accurate enough ( ~ 10m)
earth rotation
orbit
blue projection line =IKONOS
green e.g. QuickBird
IKONOS may be taken also with „forward mode“ =
against the motion in the orbit
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3.2 3D affine transformationxij = a1 + a2 *X + a3 *Y + a4 * Z yij = a5 + a6 *X + a7 *Y + a8 * Z 3D affine transformation
mathematic model = parallel projection
xij = a1 + a2 *X + a3 *Y + a4 * Z + a9 * X*Z + a10*Y*Z yij = a5 + a6 *X + a7 *Y + a8 * Z + a11*X*Z + a12*Y*Z extended 3D affine transformation – respects perspective geometry + slow down mode
xij=a1 +a2*X +a3*Y +a4*Z +a9 *X*Z +a10*Y*Z + a13*X*Xyij =a5+a6*X +a7*Y +a8*Z +a11*X*Z + a12*Y*Z + a14*X*Y
3D affine transformation for original images – respects also not parallel boundaries of scene
area covered by OrbView-3 Basic Images
No use of given approximate sensor
orientation
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3.2 Direct Linear Transformation
1111094321
+•+•+•+•+•+•
=ZLYLXLLZLYLXLx
1111098765
+•+•+•+•+•+•
=ZLYLXLLZLYLXLy
Mathematical model = perspective geometry
no use of existing orientation information
at least 6 control points well distributed in 3D required
problems with numerical stability – especially in flat areas
correlation of unknowns in this case with good Z-distribution up to r = 0.99 – has to be avoided
at least 8 control points for sufficient accuracy
IKONOS, ZonguldakMethod not recommended
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3.2 Terrain dependent RPCsComputation of selected polynomial coefficients based on control points – no use of available orientation information
IKONOS, Zonguldak
very sensitive for 3D point distribution
method should never be used= control points
discrepancies at check points – no optimal distribution of control points – listing accurate results (discrepancies at control points < 1m) and no warning for strong correlation by used commercial program
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3.2 Sensor oriented RPCs + geometric reconstruction
First step = terrain relief correction
-Correction of image positions by dL in geo-referenced image (view direction given precise enough)
followed by bias correction (correction with control points)
Bias correction by 2D shift or 2D affinetransformation
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3.2 Terrain relief correction + affine or shift (bias correction)
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1 2 3 4 5 6 70
0,2
0,4
0,6
0,8
1
1,2
1,4
1 2 3 4 5 6 7
RMSE at check
points [m]
RMSE at check points
[m]
3 4 5 6 8 15 32number of control points
3 4 5 6 8 15 32number of control points
geometric reconstruction rational polynomial coefficients
only shiftonly shift
affine transformationaffine transformation
IKONOS Zonguldak
after terrain correction just shift to control points, no advantage of 2D-affine transformation for IKONOS scenes - confirmed by other scenes
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3.2 QuickBird OR Standard
0.590.44affine + view direction
0.630.680.510.38affine
0.881.880.571.63shift
RMSYRMSXRMSYRMSX
after terrain relief correction
RPCs geometric reconstruction
QuickBird Zonguldakafter terrain relief correction
2D-affine transformation required
Scene orientation by RPCs or geometric reconstruction: first step = terrain relief correction(shift of position depending upon ∆h against reference plane), second step = horizontal transformation to control points
QuickBird Zonguldak
With exception of IKONOS after terrain relief correction 2D-affine transformation required
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3.2 Adjustment of original images (level 1A)
mathematical model of BLASPO for original satellite line scanner images
projection center = function of scene coordinate, colinearity equation in sensor line across orbit, in orbit direction depending upon position in orbit (function of image coordinate in orbit direction)
Unknowns: 4 orientation unknowns + at least 2 affinity parameters
by theory 3 control points required
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3.2 data handling – control point measurement
Measurement of control points
Image positions e.g. with DPCOR
overview
1 : 1
zoom
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3.2 data handling – control point measurement
Exact definition of points measured on ground in zoom-window important
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3.2 data handling – computation of orientationAvailable information for IKONOS:
1. Metadata file
scene location, reference height, nominal collection azimuth, nominal collection elevation (view direction from the scene center to the satellite), sun elevation . . .
2. RPC-file
rational polynomial coefficients – relation of ground coordinates (φ, λ, Z) to scene coordinates (based on direct sensor orientation – GPS, gyros, star sensors in satellite)
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3.2 geometric relation of stereo model Rio 1
Nominal Collection Azimuth: 39.2258°Nominal Collection Elevation: 67.1910°
Scene 2
Nominal Collection Azimuth : 146.18870°Nominal Collection Elevation : 75.63181°
BX: 82818.7 BY: 364479.8 Base: 373.787km, height: 681kmDirection of base in UTM: 85.7760°HEIGHT / BASE: 1.8109Speed of satellite: 7.712 km/secFootprint speed: 6.787 km/secBase = 373.8km corresponding to 48 sec
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3.2 orientation based on geometric reconstruction (CORIKON)SELECTED SENSOR: IKONOS GEO INCLINATION 98.2000 DEGREESHEIGHT ABOVE SEA LEVEL 681.0 KM
INFORMATION FROM METADATA-FILEpo_219791_metadata.txt------------------------------SCENE CORNER 1 672825.8 7466561.1SCENE CORNER 1 672711.5 7456595.1SCENE CORNER 1 656821.3 7456769.3SCENE CORNER 1 656925.1 7466734.7
UTM ZONE: 23 WGS84, EQUATOR: 10000.
4 Source Images IN METADATA-FILEUSE OF SOURCE IMAGE 1
SCAN AZIMUTH 180.02 degrees= WITH SATELLITE MOVEMENT
SCAN DIRECTION 180. degreesNominal Collection Azimuth: 39.2258 degrees
= KAPPA : -143.58420 GRADSNominal Collection Elevation: 67.1910 degrees
= NADIR ANGLE : 25.34339 GRADSSun Angle Azimuth: 90.2283 degrees Sun Angle Elevation: 63.04599 degrees Acquisition Date/Time: 2007-01-19 13:09 GMT UL Map X: 656821.33UL Map Y: 7466734.70PIXEL SIZE X: 1.000 Y: 1.000
Columns: 16008 pixels Rows: 10144 pixels Reference Height: 191.06 meters
SCENE CENTRE LONGITUDE: -43.373486 LATITUDE: -22.945011
Information from metadata file
tfw – information for approximate geo-reference
Pixel size x
y
tfw – information
(TIFF world file)
X,Y upper left corner
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3.2 orientation based on geometric reconstruction (CORIKON)ELLIPSOID:WGS 84 WORLD GEODETIC SYSTEM 1984 6378137.000 6356752.314 298.2572221009
APPROXIMATE PROJECTION CENTRE: -179586. -219992. 675282.ABSOLUTE POSITION: 489131. 7241631. 675282.
NOMINAL COLLECTION AZIMUTH : 39.22580 DEGREES= KAPPA : 256.41578 GRADS
NOMINAL COLLECTION ELEVATION: 67.19095 DEGREES= NADIR ANGLE : 25.34339 GRADS
ELEVATION OF RECTIFICATION : 191.1 MINCLINED DISTANCE FROM SAT. : 732560.5 M
CONTROL POINTS FROM rio_gps.dat MEAN HEIGHT 6.068
37 CONTROL POINTS
SCENE COORDINATES FROM po_219791_pan_0000000.pix 34 10228.67 6866.00 667050.00 7459868.705 10520.67 6916.33 667342.00 7459818.378 10673.00 7162.00 667494.33 7459572.702 10481.00 7051.33 667302.33 7459683.374 10460.67 6891.00 667282.00 7459843.70
Information from metadata file
+ image and ground coordinates of control points
Pixel location geo-reference (UTM) – based on tfw-information
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3.2 orientation based on geometric reconstruction (CORIKON)Terrain relief correction – shift of position depending upon the actual point height in relation to reference height
Followed by 2-dimensional transformation to control points – for IKONOS shift sufficient
SHIFT IN X: -50.28SHIFT IN Y: -60.22
CORRESPONDING UPPER LEFT CORNER: 660711.202 7466703.867POINT X Y Z DX DY
1 671110.54 7459645.12 8.03 -.86 -.302 671142.82 7459593.40 7.82 -.58 -.154 671123.76 7459755.26 12.64 -.81 -.505 671182.92 7459728.92 9.47 .22 -.35. . .
SQUARE MEAN OF DIFFERENCESSX = +/- .65 SY = +/- .64 MEAN SX/SY = +/- .65NX = 31 NY = 31
= accuracy of relation ground coordinates to image coordinates
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3.2 orientation based on geometric reconstruction (RAPORI)Scene orientation based on the rational polynomial functions (RPCs)
RPC FROM po_219791_pan_0000000_rpc.txt
LINE_OFF: 5052.00 pixelsSAMP_OFF: 6058.00 pixelsLAT_OFF: -22.94500000 degreesLONG_OFF: -43.37350000 degreesLINE_SCALE: +005052.00 pixels LINE_SCALE: 5052.00 pixelsSAMP_SCALE: 6058.00 pixelsLAT_SCALE: .04630000 degreesLONG_SCALE: .05970000 degreesHEIGHT_SCALE: 522.000 meters
-.60182697E-03 .13414378E-01 -.10148187E+01 .33623271E-01-.12956355E-02 -.59764000E-04 .22205936E-02 .26652111E-03-.18441909E-01 -.54303498E-04 .71094857E-05 .10584617E-05-.67021745E-04 .47601907E-07 -.46274839E-04 .21589959E-03
. . . 80 coefficients
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3.2 orientation based on geometric reconstruction (RAPORI)Based on RPC computation of image coordinates from ground coordinates
Terrain relief correction + 2-dimensional transformation to control points – shift for IKONOS sufficientPOINT X Y Z DX DY
1 671109.68 7459644.82 8.03 -.82 -.312 671142.25 7459593.25 7.82 -.50 -.134 671122.95 7459754.76 12.64 -.80 -.535 671183.14 7459728.57 9.47 .27 -.36
. . .
SQUARE MEAN OF DIFFERENCESSX = +/- .65 SY = +/- .63 MEAN SX/SY = +/- .64NX = 31 NY = 31
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3.2 orientation based on geometric reconstruction (CORIKON)
1m
Discrepancies at control points
In this case no good distribution of control points in scene – control points just in area 500m x 500m
-scene size 10km x 12km
-- no problem in case of IKONOS
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3.3 calibration of IRS-1C pan
Filter
Filter
CCD 2
CCD 1 + 3
CCD 1 CCD 3CCD 2 8.6 km
image separation to3 CCD-lines
IRS-1C combination of 3 CCD-linesoriginal sub-images available
test area Hannover
December, 24, 1996 21.3°
December, 25, 1996 0.0°
December, 26, 1996 -23.5°
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Institut für Photogrammetrie und GeoInformation
3.3 calibration of IRS-1C pan
20 pixel 20 pixel20 pixel
control + tie pointsorbit 1
orbit 2
orbit 3
350km
830k
m 21°
24°
Institut für Photogrammetrie und GeoInformation
3.3 calibration of IRS-1C pan
vector 9m
adjustment with special IRS-parameters
SX=7m SY=5m SZ=9m
5.8m GSD
~ 1 pixel = usual accuracy which can be reached with space images
33
Institut für Photogrammetrie und GeoInformation
3.3 3D affine transformation - Z-distribution of control points
x = a1 + a2 ∗ X + a3 ∗ Y + a4 ∗ Z y = a5 + a6 ∗ X + a7 ∗ Y + a8 ∗ Z8 unknowns, simple method, no use of existing orientation information- at least 4 control points required, well distributed in X, Y and Z
Black Sea
Mathematical model = parallel projection
Orientation with 3D affine transformationIKONOS, Zonguldak, GPS control points
4 control points, well distributed in X, Y, but not in Z (control points in tilted plane),no discrepancies at control points
SX=1.91m SY=18.53m at check points
correlation coefficients of unknowns exceeding 0.999 = warning by Hannover program TRAN3D – such warnings missing in commercial software
no correlation between X and Y
control point
Institut für Photogrammetrie und GeoInformation
3.3 IKONOS Geo Zonguldak: 3D affine transformation
[m]No real improvement by extended 3D affinetransformation
respecting perspective geometry
1.0 GSD
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Institut für Photogrammetrie und GeoInformation
3.3 comparison of orientation methods - IKONOS
IKONOS, Zonguldak
Hannover programs
1. TRAN3D DLT
2. TRAN3D3D-affine transformation
3. CORIKONgeometric reconstruction
4. RAPORIRPCs
with limited over-determination results strongly depending upon individual control points
0
0,5
1
1,5
2
2,5
3
1 2 3 4 5 6 7 8 91 2 3 4 5 6 8 15 32
number of control points
3D affine transformation
RMSE at check
points [m]
geometric reconstruction
bias corrected rational polynomial coefficients
SY
SX
SY
SXSYSX
DLT
Institut für Photogrammetrie und GeoInformation
3.3 QuickBird OR Standard, Zonguldak
3D-affine + DLT limited in accuracy because of slow down factor 1.6 + field of view
sensor oriented
6 other control points 3.62 4.03
35
Institut für Photogrammetrie und GeoInformation
3.3 Geometric reconstruction – QuickBird OR Standard
10 unknowns: SX=0.48 SY=0.47m 2 unknowns: SX=1.84 SY=0.89m
Hannover program CORIKON
Institut für Photogrammetrie und GeoInformation
3.3 comparison of orientation methods – QuickBird OR Standard
Average SX/SY [m]Root mean square discrepancies an independent check points
( 40 = control points)
Test area Zonguldak
3D affine transformation + DLT not so accurate, extended 3D affinetransformation required (not parallel view direction)
for RPC and geometric reconstruction 2D affine transformation after terrain relief correction
1.0 GSD (62cm)
Control points
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Institut für Photogrammetrie und GeoInformation
3.3 Orientation of QuickBird Basic Imagery
1.181.2755124511.851.190.170.349124500.941.280.510.6413124500.951.200.480.601512450
0.831.0048124501.251.2320712450
RMSY
[m]
RMSX
[m]
RMSY
[m]
RMSX
[m]No.Scene
Check pointsGround Control Points
corner points
Results of bundle orientation QuickBird area Arizona, reference = digital orthophotos from USGS (DOQQs) –limited accuracy
1.380.780.960.5419.015Autom.
1.390.690.560.5313.420Autom.
0.720.690.740.4914.125Autom.
0.640.5511.4398Autom.
0.640.8514.6174Manual
YXYX
Check Points
RMS [m]
GCPsRMS [m]
σo[µm]
measurement
Results Atlantic City , reference = orthophotos by aerial photographs
accuracy ~ 1 pixel operationalGeometric reconstruction
Institut für Photogrammetrie und GeoInformation
3.3 Analysis of systematic errors
Systematic discrepancies at control / check points
- root mean square error does not describe type of systematic errors
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Institut für Photogrammetrie und GeoInformation
3.3 Analysis of systematic errors by program BLAN
-1
-0,8
-0,6
-0,4
-0,2
0
0,2
0,4
0,6
0,8
1 2 3 4 5 6 7 8 9 10 11 12 13
12 km
6km
covariance
distance
Covariance function (correlation as function of point distance)
Σ( DXi • Dxj )CX =
nh • SX • SX
This covariance function indicates systematic errors
0
0,5
1
1,5
2
2,5
3
3,5
4
4,5
5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Relative standard deviation12 km
6km
distance
RSX =√ Σ(Dxi - Dxj)2 / (2•nx)
relative neighboured points indicates accuracy without influence of systematic errors
not only the size of RMS is important, also structure of discrepancies
Institut für Photogrammetrie und GeoInformation
3.3 OrbView-3 Basic, test area ZonguldakStereo configuration h/b = 1.4
Scenes scanned across orbit
Covered area, correct scale, lines not parallel
Image type: original images, only radiometric correction + geometric correction by inner orientation
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Institut für Photogrammetrie und GeoInformation
3.3 Orientation of original image - OrbView-3 Basic ExpressRMS average of RMSX and RMSYat independent check points
for RPC and geometric reconstruction 2D affine transformation after terrain relief correction required
Orientation of original images not with 3D affine or DLT, only 3D affine for original images (14 unknowns) not too far away from RPC and geometric reconstruction, but high number of well distributed control points required
Institut für Photogrammetrie und GeoInformation
3.3 OrbView-3 Basic Express
OrbView-3: 1m GSD, 2m projected pixel size 50% over-sampling
not same image quality like IKONOS
With 4 – 12 control points only ~ 1.6m accuracy by RPC-solution,
RMSX / RMSY = 1.3m for 29 control points
- no GSD accuracy reached like with IKONOS and QuickBird with same control points in Zonguldak area
staggered CCD-lines
Pointing accuracy can be estimated with relative accuracy (one point in relation to neighboured point)
IKONOS: relative accuracy 0.75m for distances up to 1km
OrbView-3: relative accuracy 1.0 m for distances up to 1km
With OrbView-3 Basic Enhanced same accuracy, only improvement of direct sensor orientation
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Institut für Photogrammetrie und GeoInformation
3.3 OrbView-3 bias corrected RPCNo sub-pixel accuracy has been reached – same control points used for orientation of IKONOS and QuickBird – with QuickBird RMSX, RMSY ~ 0.5m
with IKONOS (also 1m GSD like OrbView-3) RMSX, RMSY ~ 0.9m
Reason 1: because of over-sampled pixels image quality a little below IKONOS
Reason 2: image geometry
Relative standard deviation of closely neighbored points ~ 1m indicates pointing accuracy
Loss of accuracy over larger distance = caused by image geometry
Relative standard deviation
distance between points
[m]
Institut für Photogrammetrie und GeoInformation
3.3 OrbView-3 Basic, 3D-affine transformation
x = a1 + a2 ∗ X + a3 ∗ Y + a4 ∗ Z y = a5 + a6 ∗ X + a7 ∗ Y + a8 ∗ Z
8 unknowns, simple method, no use of existing orientation information
-at least 4 control points required, well distributed in X, Y and Z
Mathematical model = parallel projection = only approximation
Discrepancies scene 443940
RMSX=8.1m RMSY=21.1m
Scene 471890
RMSX=6.7m RMSY=12.0m
Not sufficient for GSD=1m
40
Institut für Photogrammetrie und GeoInformation
3.3 OrbView-3 Basic, extended 3D-affine transformationxij = a1 + a2 *X + a3 *Y + a4 *Z + a9*X*Z + a10*Y*Zyij = a5 + a6 *X + a7 *Y + a8 * Z+ a11*X*Z + a12*Y*Z
3D-affine transformation improved for changing view direction
For 12 unknowns 6 three dimensional well distributed control points required
Discrepancies scene 443940
RMSX=3.1m RMSY=2.9m
Scene 471890
RMSX=3.3m RMSY=1.9m
Quite better like simple 3D-transformation, but still not good + too many control points required
Institut für Photogrammetrie und GeoInformation
3.3 OrbView-3 Basic, 3D-affine transformation for original imagesxij=a1 +a2*X +a3*Y +a4*Z +a9 *X*Z +a10*Y*Z +a13*X*Xyij =a5+a6*X +a7*Y +a8*Z +a11*X*Z + a12*Y*Z+a14*X*Y 3D affine transformation extended for original images – respects also not parallel boundaries of scenefor 14 unknowns 7 three dimensional well distributed control points required
Discrepancies scene 443940
With all control points:
RMSX=1.7m RMSY=2.2m
Scene 471890
RMSX=2.5m RMSY=1.9m
better like extended 3D-transformation, but still not good + too many control points required
(30% higher RMSE like bias corrected RPC)
41
Institut für Photogrammetrie und GeoInformation
3.3 OrbView-3 Basic Express, bias corrected RPCScene 443940
Shift to control: RMSX=2.21m RMSY=2.09m
Affine transformation to control
RMSX=1.68m RMSY=1.89M
Scene 471890
Shift to control: RMSX=1.55m RMSY=1.57m
Affine transformation to control
RMSX=1.54m RMSY=1.26m
Better results with affine transformation after terrain relief correction
Institut für Photogrammetrie und GeoInformation
3.3 QuickBird Basic Atlantic City, 380 control points
[m]
RMSYRMSX
BLASPO
14 ad
d. pa
r.
BLASPO
6 unk
nowns
RPC
3D af
fine
3D af
fine
exten
ded
3D af
fine for
origin
al im
ages
DLT
0.66
0.654.97
2.630.63
0.95
9.6
16.1
6.0
7.1 2.9
4.8
9.1
9.9
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Institut für Photogrammetrie und GeoInformation
3.3 Comparison SPOT 5, level 1A with level 1BLevel 1A = original image (just improved by inner orientation by satellite vendor)Level 1B = projection to plane with constant height
SPOT 5: GSD = 5m
Level 1B: SX=4.87m SY=3.51m (4.24m) Level 1A: SX=4.02m SY=4.15m (4.09m)42 control points
-Same original scene, only different processing, in images separate control point measurements, control points determined by GPS
similar average accuracy for both products
Institut für Photogrammetrie und GeoInformation
3.3 Original images images projected to surfacelevel 1A-type – level 1B-type
QuickBird OR Standard – projected to surface with constant height
QuickBird Standard – projected to GTOPO30 DEM (spacing 30 arcsec =920m)
GTOPO30 too large spacing for orthoimage – improvement like with OR Standard
no difference in accuracy – only additional handling step for QuickBird Standard
IKONOS only available as level 1B-type
Orientation with sensor oriented RPCs or geometric reconstruction same accuracy with original images like with images projected to surface
small advances in handling projected images
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Institut für Photogrammetrie und GeoInformation
3.3 SPOT 5 HRS, original images, geometric reconstruction
Orientation by bundle adjustment with BLASPO using general orbit information + control points
Control points = trigonometric points of survey administration, definition in images not very precise
distribution of control not optimal
3.5m5.0m7.7mmodel 23.9m5.8m6.0mmodel 1SZSYSX
0.7pixels 1.1pixels 0.6pixels
Institut für Photogrammetrie und GeoInformation
3.3 Cartosat-1Scientific Assessment Programme (C-SAP)
Warsaw, Poland
(Feb. 25, 2006)GSD: 2.5m x 2.5m
2.3m x 2.5msun elevation: 30.4°
Mausanne, France January 2006
(Jan. 31, 2006)GSD: 2.8m x 2.5m
2.4m x 2.5msun elevation: 28.9°
Mausanne, France February 2006(Feb. 6, 2006)
GSD: 2.5m x 2.5m2.3m x 2.5m
sun elevation: 31.1°
Cartosat-1 2 optics 26° ahead, 5° behind
∆t for nadir 58 secdistance to base
relation 1.44
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Institut für Photogrammetrie und GeoInformation
3.3 Orientation Cartosat-1Orientation by bias corrected rational polynomial coefficients (RPCs) with Hannover program RAPORIO
First step: transformation of image position to ground coordinate system based on given heightSecond step: 2D-transformation to control points – affine transformation required
in January Mausanne scene up to 6km shift (other below 360m), by this reason additional correction of view direction in RAPORIO tested – not significant, no improvement of results, so finally only 2D-affine transformation (at least 3 control points required)
Mausanne, February –limited control point identification
Warsaw:SX, SY ~ 0.6 GSDSpx = 0.5 GSD
Mausanne, January:SX, SY ~ 0.8 GSDSpx = 0.7 GSD
Institut für Photogrammetrie und GeoInformation
3.3 CORONA – panoramic film camera
panoramic image
flight direction
scan direction
US: CORONA (stereo, height to base ratio = 1.8, KH-4B ~ 2m GSD)
1. transformation of image points to tangential plane (sub-scene ~ 15km x 55km, maximal vector = 185µm)
2. Orientation by bundle block adjustment (Hannover program BLUH) determination of effect of movement during imaging by self calibration, horizontal accuracy up to 2m, relative vertical accuracy 3m)
systematic image errors – typical S-shape
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Institut für Photogrammetrie und GeoInformation
3.3 Orientation of different space images
With accurate control points and correct mathematical model GSD-accuracy usually possible
1.62.87EROS A1 (from JRC)0.70.7IKONOS, Zonguldak
0.51.24IRS Cartosat-1, Warsaw1.61.61OrbView-3, Zonguldak0.80.47QuickBird OR Standard, “
1.60.8
9.15.1
IRS-1C, 1B, ZonguldakIRS ResourceSat, Hannover
0.95.1IRS-1C, 1A, Hannover0.7 / 1.16.1SPOT HRS, Bavaria
0.84.1SPOT5 1A/1B, Zonguldak0.54.6SPOT level 12A, Hannover1.38.5Kompsat-1, Zonguldak0.710.8ASTER, Zonguldak
RMSX/Y [GSD]RMSX/Y [m]
control points not accurate
control points not accurate
Image geometry
1m GSD, 2m pixel size
Institut für Photogrammetrie und GeoInformation
3.3 conclusion – image orientation
available information about the scene orientation should be used, leading to best solution with smallest number of control points
bias corrected RPCs or geometric reconstruction of image geometry
Same accuracy with original images (level 1A-type like QuickBird Basic, OrbView-3 Basic, SPOT level 1A) and projected images to a specified plane (level 1B-type like IKONOS Geo, QuickBird ORStandard or Standard, SPOT level 1B) accuracy only depending upon GSD or projected pixel size
Terrain dependent RPCs should not be used – very sensitive for extrapolation
DLT not useful
3D-affine transformation limited to IKONOS, requires more control points like RPCs or geometric reconstruction + well distributed control points in 3D – statistical test of unknowns necessaryExtended 3D-affine transformation can be used, but too many control points requiredApproximate orientation solutions should be avoided
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