Mapping from Space 3. Sensor orientation

1

Institut für Photogrammetrie und GeoInformation

Mapping from Space3. Sensor orientation

Dr. Karsten JacobsenInstitute of Photogrammetry and GeoInformation

Leibniz University [email protected]


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

2


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)


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

3


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


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

4


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


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

5


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= + •


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°

6


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


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

7


3.1 Well defined control-“points”

Kompsat-1 optimal IKONOS IKONOSpoint not well defined in detail corner point


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

8


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


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

9





Precise definition of control points required for acceptable accuracy, but not simple

Discrepancies of orientation

10


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


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

11


Ortho-image

perspective image map / ortho-image

parallel projection

Ortho-image: geometry of map, contents of image

image

DEM

Ortho-image


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

12


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


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

13


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


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

14


Gray value interpolation

bilinear Nearest neighbourhood

SPOT

10m

GSD


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

15


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


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

16


Shift of roof position in orthoimage based on height of ground


Location of building / roof top

Overlay of orthoimage with correct ground

position

Roof top shifted against ground

correct ground = red line

17


Shift of roof tops

red = roof

black = building at height level of terrain

IKONOS ortho-image


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

18


Error in position – orthoimage of Bosporus-bridge

IKONOS ortho-image

Gray value coded DEM

Ortho-image


True orthoimageTrue orthoimage requires height of any individual objectUncorrected bridge

corrected bridges

Information from neighboured image

Uncorrected bridges

19


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


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

20


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


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

21


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


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

22


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


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


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

24


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


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

25


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


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

26


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


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


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)

28


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


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

29


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


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

30


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


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

31


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


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°

32



20 pixel 20 pixel20 pixel

control + tie pointsorbit 1

orbit 2

orbit 3

350km

830k

m 21°

24°



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


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


3.3 IKONOS Geo Zonguldak: 3D affine transformation

[m]No real improvement by extended 3D affinetransformation

respecting perspective geometry

1.0 GSD

34


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


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


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


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

36


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


3.3 Analysis of systematic errors

Systematic discrepancies at control / check points

- root mean square error does not describe type of systematic errors

37


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


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

38


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


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

39


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]


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


Not sufficient for GSD=1m

40


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


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


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


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


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


Better results with affine transformation after terrain relief correction


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

42


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


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

43


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


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

44


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


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

45


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


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

Mapping from Space 3. Sensor orientation

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