GEOG 4110/5100 Advanced Remote Sensing Lecture 4

Transcription

1 GEOG 4110/5100 Advanced Remote Sensing Lecture 4 Geometric Distortion Relevant Reading: Richards, Sections

2 Review What factors influence radiometric distortion? What is striping in an image? How do we fix it? What factors influence temperature as observed from space What methods are there for filtering clouds

3 Various techniques for retrieving temperature Split window: uses 2 channels (windows) that overlap in spectral sensitivity Dual window: uses 2 channels that do not overlap Triple window: Uses 3 channels All rely on the principle that atmospheric constituents affect different wavelengths in different ways.

4 Multi-Channel Sea Surface Temperature (MCSST) Algorithms AVHRR Split Window Algorithm T s = a 0 + a 1 *band4 + a 2 (band4 - band5) + a 3 (band4 - band5)(sec(φ) -1) a 0, a 1, a 2, and a 3 are constants that are theoretically and empirically derived Differ for night and day Differ from AVHRR instrument to AVHRR instrument f is the satellite zenith angle Dual Window Algorithm T s = a 0 + a 1 *band4 + a 2 (band3 - band4) + a 3 (sec(φ) -1) Triple Window Algorithm various combinations of bands 3, 4, and 5 for different instruments Band 3: 3.55μm 3.93μm; Band 4: 10.3μm 11.3μm; Band μm 12.5μm 4

5 MCSST Day Coefficients Split Window Satellite a0 a1 a2 a3 NOAA NOAA NOAA NOAA NOAA NOAA NOAA MetOp-A Coefficients derived from radiative transfer models and buoy observations 5

6 Filter Response Function Mapping Polynomials for Image Projection Assumes geometrically correct map of image region is available Need to map known locations (map) to corresponding locations in image u = f(x,y) v = g(x,y) 6

7 Geometric Distortion Geometric Distortion: Errors in image geometry, (location, dimensions, etc.) Sources Earth rotation during image acquisition Sensor scan characteristics Wide field of view of some sensors Curvature of the Earth Sensor realities (not perfect) Variations in platform altitude, attitude and velocity Panoramic effects related to image geometry

8 Desired Grid on Which to Map Image

9 Earth Rotation Effect t s = L/w 0 r e Acquisition time L = swath width w 0 = scan angle velocity r e = ~ km Radius of the Earth For Landsat 7: L = 185 km w 0 = mrad/s t s = s v e = w e r e cosl Earth s surface velocity w e = µrad/s Earth s Angular Velocity l= Latitude At 40 Latitude v e = 355 m/s

10 Earth Rotation Effect at 40 Latitude In the ~27.4 s it takes to acquire a Landsat scene, a point on the Earth s surface moves (Dx e ) 9.73 km, or 5.4% of the scene width Dx e = v e DT = 355 m/s 27.4 s = 9727 m Accounting for ~13 angle N/S offset at 40 latitude associated with inclination: D x = Dx e cos13 = 9.48 km (5.3% of scene width)

11 Distortion From Scan Geometry Pixels elongated significantly in the cross-track direction due to angular projection Pixels elongated slightly in the along-track direction due to increased distance from surface to sensor θ Along Track

12 Image Edge Compression (S-Bend Distortion) θ θ β/2 For constant angle increments (β), pixels are offset more near the edge of a scan than near nadir (S-bend distortion) Pixel spacing = P/cos 2 θ (P/2) θ P/2 Resulting effect when pixels are placed on a uniform grid is cross-track compression

13 Image Edge Compression (S-Bend Distortion) Cross-track distortion is SN/TN = q/tanq For edge of Landsat swath: (q/tanq) max = At scan edge (92.5 km from nadir point) pixel will be 314 m out of position, compared with pixel at scan point.

14 Earth s Curvature

15 Variations in Platform Attitude, Velocity, and Altitude Altitude Flight Direction Pitch Velocity Roll Pitch: Rotation of platform about horizontal axis perpendicular to flight direction Roll: Rotation of platform about axis of flight Yaw: Rotation of platform about vertical axis Yaw

16 Correction of Geometric Distortion

17 Mathematical Modeling: Example Aspect Ratio Distortion Correction Aspect Ratio: relative vertical and horizontal scales (width/heigh) x ½ x x AR=1 x AR=0.5 Samples are sometimes acquired too quickly across a scan line compared to the instrument IFOV e.g. Landsat MSS acquires pixels at 56 m intervals with an IFOV of 79 m Landsat effective pixel size is 79 m x 56 m (along-track across-track) Image displayed on a square grid will be too wide for its height Have to compress in width by a factor of 79/56 or Another example is aircraft moving too slow or too fast compared to cross-track scan 17

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19 Correction of Geometric Distortion Mapping Polynomials for Image Projection Assumes geometrically correct map of image region is available Need to map known locations (map) to corresponding locations in image u = f(x,y) v = g(x,y) 19

20 Explicit Mapping Functions Ideally, we would like to know the function that allows us to map from known locations to image locations (x,y to u,v) y x v u Usually we don t, so we have to determine them by matching distinct features in image, to known location on map, e.g. Road intersections, bends in rivers, coastline features, etc. ground-control points (GCPs) Generally chosen as simple polynomials of the first, second, or third degree Requires 3, 6, and 10 GCPs respectively u = a 0 + a 1 x + a 2 y + a 3 xy + a 4 x 2 + a 5 y 2 v = b 0 + b 1 x + b 2 y + b 3 xy + b 4 x 2 + b 5 y 2 20