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A fast-paced tutorial on satellite image geometry. Mono & stereo collection geometry. Effects of collection geometry on image quality, perspective and accuracy. RPC & Physical Camera Models Geometry of scan-oriented, map-oriented, orthorectified, and stereo image products This tutorial for producers and users of satellite imagery provides a common vocabulary and understanding of collection and product geometry and effects.
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1
Satellite Image Geometry
Gene DialGIS in the Rockies
2012-09-21
Topics
› Background› Satellite Orbits› Satellite Image Geometry› Stereo Image Geometry› Satellite Image Products
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Niagara Falls
Background
Remote Sensing—Then & Now!
Mys Shmidta Air Field, Soviet Union
Collected August 18th, 1960GeoEye-1 Half Meter Imagery
Kutztown University – Collected Oct. 6, 2008
GeoEye-2 Technical Specs at a GlanceSystem Specification PerformanceSatellite Bus Size
Weight2.3 m x 5.3 m2100 kg dry, 2500 kg wet
Payload ApertureFocal LengthDynamic RangeGSDSwath
1.1 meter aperture16 meter focal length11 bit dynamic range with TDI34 cm Pan, 1.32m MSI14.5 km
Attitude Control System
Actuators
Sensors
Minimum Agility
Honeywell M-95 CMGs
Goodrich GR-1004 Star TrackersSIRU Inertial Reference UnitsMonarch GPS Receiver
Acceleration - 1.0 degree/sec2 Max Slew Rate – 2.7 degree/sec
Data Handling &Communications
Data Recorder
Wideband DLTlmy DLCommand UL
3.2 Terabit High Speed Storage Unit
800 Mbps Dual Pole, X band128 Kbps, X band64 Kbps, S band
X-band High
Gain AntennaTwo Axis Gimbal
Solar Array (5)Power
Control Unit
Battery (2)
Control Moment Gyros (4)
Data Storage Unit (2)Flight
Processor
CMG Electronics (4)
Focal Plane
Radiator
GPS Antenna (2)
Narrowband Antenna (2)
Sun Sensor (2)
Payload Electronics (2)
PL Electronics
Radiator (2)
Star Tracker (2)
See http://www.youtube.com/watch?v=lnv6cDiBF9o 5
Satellite Imagery
Satellite Orbits
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GeoEye-1 IKONOSGeoEye-2
GeoEye ConstellationGeoEye Constellation
Ground SwathsGE1 = Green GE1 = Green IK = Yellow IK = Yellow GE2 = BlueGE2 = Blue
Ground SwathsGE1 = Green GE1 = Green IK = Yellow IK = Yellow GE2 = BlueGE2 = Blue
› Frequent Access‒ Mean Time to Access < 1 day
› Long Duration Accesses‒ Average Access Time ~ 1 min/day
› High Resolution Access‒ GeoEye-1: 41 cm Nadir GSD‒ GeoEye-2: 34 cm Nadir GSD‒ True 50 cm products
› Huge Collection Capacity‒ IKONOS: 240,000 sqkm/day‒ GeoEye-1: 350,000 sqkm/day‒ GeoEye-2: 600,000 sqkm/day
GeoEye ConstellationHigh Resolution ImagesMove Beyond Mapping
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Satellite Image Geometry
Ground Sample Distance (GSD)
› Source image pixels are rectangular, W x H in size› GSD = sqrt(W x H)› A square pixel of GSD x GSD size has the same area as W x H› Product images may be resampled to a different GSD
W
H
GSD
GSD
Field of View
› Field of View (FOV) is angle from one edge of an image to the other.
› All rays of a high-resolution satellite image are at about the same angle.
Aerial camera
Satellite imaging at nadir
Satellite imaging off nadir
SatelliteField of View
Aerial CameraField of View
Camera FOV
Aerial 90°
IKONOS 0.95°
GeoEye-1 1.28°
GeoEye-2 1.22°
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Scan Azimuth› Scan Azimuth
‒ Describes scan direction or motion of aim point on ground
‒ North-to-South Scan Azimuth = 180°
‒ South-to-North Scan Azimuth = 0°
0° = North
90° = East
180° = South
270° = West
So
uth
to
No
rth
Sca
n A
zim
uth
0°
West to EastScan azimuth 90°
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East to WestScan azimuth 270°
Line of Sight (LOS)
› The Line of Sight (LOS) is the direction that the camera is imaging.
› A Line of Sight direction can be described by azimuth and elevation angles.
Lin
e of S
igh
t (LO
S)
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Satellite Collection GeometrySatellite Collection Geometry
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Azimuth
› Azimuth angle‒ Measured in the horizontal plane
at the target‒ Angle from north proceeding
clockwise to the projection of the line of sight into the horizontal plane.
‒ Example: 90° azimuth means the satellite is East of the target when the image is taken.
0° = North
90° = East
180° = South
270° = West
Collection Azimuth› North Up View
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Collection Azimuth› View from sensor perspective
GE1 Image acquired at 53.5° collection azimuth rotated180° - 53.5° CW on right to view from sensor perspective.20
Elevation
› Elevation angle‒ Measured at target‒ Angle from horizontal plane up to
line of sight.
› Alternatives‒ Incidence or Zenith angle‒ Off-Nadir or Obliquity angle
Elevation angle
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Computing height from shadows & layover
SensorElevation
Angle
Sensor
Layover
DV = DH * tan(EL)
DH
DV DV
DH
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Example: Republic Plaza (Singapore)Image collected at 67°
elevation angle Layover measured at 116
mHeight calculationH = 116 m * tan(67°) = 273 mActual height
280 m
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Elevation angle and terrain displacement
› EL = elevation angle› DV = vertical distance› DH = horizontal distance
EL
DH
DV
Zenith Sensor
Earth
DEM
DH = DV / tan(EL)
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Incidence, Elevation, & Off-Nadir Angles
› EL = Elevation = angle at target from horizontal to sensor.› IN = Incidence = angle at target from zenith to sensor.› OB = Obliquity = angle at sensor from nadir to target (off-nadir angle)› IN + EL = 90°› Obliquity is related to elevation by trig formula:
‒ Re = radius of earth ~ 6371 km
‒ Ho = orbit height ~ 681 km
)(
)(
eo
e
RH
ELCosRArcSinOB
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Incidence, Elevation, & Off-Nadir Angles
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Stereo Geometry Orbit Track
Ground Track
AOI
EL1EL2
Convergence Angle
About one minute of orbit timebetween left and right image ofa stereo pair.
About two seconds of orbit timeto scan a 15 km by 15 km stereo scene. Longer scans are possible. A 100 km long stereo pair takes about 20 seconds to scan.
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Field of Regard (FOR)
› Field of Regard: Angle Range that Camera can Image by rotating› Satellite Field of Regard > 90°.› Field of View can be anywhere within the Field of Regard
90° FOR±45° FOR
0.95° FOV within Field of Regard
Field of Regard vs. Elevation Angle
› Wider Field of Regard at lower elevation angle› Wider Field of Regard from higher orbits
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0 100 200 300 400 500 600 700 800 900 10000.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cross-Track Distance, km
GS
D,
m
GSD vs. Cross-Track Distance
IKONOS
GE1GE2
RunSatComparison
Field of Regard
60° Elevation Angle
60° Elevation Angle
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Revist Time (time between satellite accesses)
› Shorter revisit time at lower elevation angle & higher latitude
3-day revisit at 40° N at 60° elevation angle
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Revisit Time
› More frequent revisits at high latitudes because the orbits converge near the poles.
› Ground stations are located at high latitudes can contact the satellite nerly every orbital revolution.
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4
3
13
14
15910
11
12
13
7
5
15
6
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Pan-MSI Alignment› Each MSI pixel covers 4x4 Pan pixels› 4 multispectral (MSI) bands› 1 panchromatic (PAN) band› Simultaneous PAN/MSI collection› 11-bit resolution
MSIGSD
Pan GSD
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CIR RGB
4-meter RGB Multispectral
4-meter CIR Multispectral 1-meter CIR Pan-Sharpened
1-meter RGB Pan-Sharpened
1-meter Panchromatic
Color enhances
interpretation for human
visual perception
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Camera Models
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Rational Polynomial Coefficient (RPC) Camera Models› RPC Camera Models
‒ Generic mathematical model mapping ground to image coordinates.
‒ Sensor software fits coefficients to physical camera model of image.
• Sensors‒ GeoEye, Ikonos, QB, WV, Cartosat …• Application Software‒ ERDAS, BAE, PCI, ZI, …
› Applications‒ Block adjust images with ground control
to improve accuracy.‒ Orthorectification‒ Stereo extraction‒ PhotogrammetryThe mathematics of satellite imagery is
complicated, but RPC models are simpleThe mathematics of satellite imagery is complicated, but RPC models are simple
Satellite Image Product Geometry
Product Geometry
Product Rectification Projection Image Model
Basic Synthetic Array Satellite Scan PathPhysical (attitude,
ephemeris & camera calibrations)
Geo Constant height Map RPC
Ortho DEM Map Ortho
Stereo Constant height Path, Map, or Epi-polar RPC or Physical
Elevationangle
Convergenceangle
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BASIC› Photogrammetric
Applications › Satellite Projected› Physical Camera Model
‒ High Accuracy
› RPC Camera Model‒ Rapid Positioning
IKONOS image of the moon (BASIC product)
GEO› Visual Interpretation
‒ Situational awareness‒ Intelligence‒ Media
› Photogrammetry‒ Block adjust with other imagery
or GCP to improve accuracy.‒ Orthorectify with DEM to
correct for terrain displacement
› Map Projected› RPC Camera Model
‒ High Accuracy
Tsangpo River Basin, Tibet
BASIC and GEO Products
Geo
East to West ScanNorth up Map Projected
N
E
S
W
N
E
S
W
BASIC GEO
RPC Model Physical Model
ProjectionSatellite Map
BASIC
East to West Scan Satellite Projected
Ortho› Applications
‒ Feature Extraction‒ GIS Map Base
› Terrain Corrected› Map Projected› Mosaics Available
Frankfurt Airport, Germany
Georectified or Orthorectified?› Georectified
‒ Terrain displace-ment errors
‒ Quick, Low cost
› Orthorectified‒ DEM corrects for
terrain displacement
‒ Accuracy for mapping
TopographicSurface
Constant Height Line of Sight
Topo-graphicSurface
Ortho-rectifiedImage
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March, 2009
Geospatial eXploitation Products™
What is an Orthophoto?
• An orthophoto is an image that has had all distortion due to camera obliquity, terrain relief, and features removed.
• The SOCET GXP Ortho Manager converts one or more original images into an orthophoto by transforming the pixels to their proper position according to the given sensor, terrain, and feature information.
• In the final product all points in the image appear as if the observer were looking down from nadir position.
DTM
Camera
Orthophoto
Original Image
Orthorectified
Georectified
Stereo› Attributes
‒ High resolution‒ Color‒ 3-dimensional
› Applications‒ DEM extraction‒ 3D feature extraction‒ Geomorphic
visualization
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Stereo
Projection
RPC
Model
Physical
Model
Satellite
Map Epi-Polar
Stereo Image Of Downtown Denver, Colorado
Big Bear Glacier, Alaska
Thank You!