Dario Papale Contributi: Vern Vanderbilt, TA- Quinn Hart, M. Meroni, CCRS

1. Remote sensing and modeling in forestry Lecture 8 Corrections and calibrations - 2 Dario Papale Contributi: Vern Vanderbilt, TA- Quinn Hart, M. Meroni, CCRS

2. Images corrections Data collected by remote sensing sensors need, before their use in our applications, a number of corrections in order to remove or reduce disturbances and distortions added during the acquisition and transission to the receiving stations. This pre-processing step can be split in three main corrections classes: Radiometric corrections Atmospheric corrections Geometric corrections

3. Shadow in the images There are characteristics that affect the reflectance of a surface (in addition to the surface characteristics and atmosphere condition): • Altitude, that affect the tickness of the atmosphere • Slope and Aspect, that affect the quantity of incoming radiation • The possibility that an area is under shadow due to closeby mountains and for this reason receive only diffuse radiation These problems can be corrected using a digital elevation model and a 3d reconstruction of the area.

4. Shadow in the images A simplified approach that doesn’t need the DEM is based on the use of ratios between spectral bands

5. Geometric corrections Remote sensing data are often used together with others spatial data in GIS systems. For this reason it is important to apply correction algorithms to make the RS images congruent or accordat to a defined reference system. The remote sensing images are in fact affected by different geometric distortion types that are corrected using two different correction techniques: Systematic corrections Georeferencing and Orthorettification

6. Systematic corrections Needed to remove geometric distortions due to the data acquisition procedure (sensor, platform, Earth…) and that are in general stable in time: • Data acqusition method (scanner, CCD etc.) • Platform movement • Earth rotation • Earth shape (curvature) All these corrections are in general applied to the images acquired by satellites directly at the receiving stations. They are based on the sensor knowledge but they are not enough…

7. Georeferencing This technique is based on the assumption that there is a relation (of degree n) between the coordinates of each pixel in the original image x’ and y’ (row and column) and its coordinates in the reference system selected x and y x’ = f (x, y) = a0 + a1x + a2y + a3xy y’ = g (x, y) = b0 + b1x + b2y + b3xy

8. Ground Control Points To parameterize the equations it is needed to identify a number of control points (GCP GroundControlPoints) where we can retrive the image coordinates and the geographic coordinates. For this reason these points must be easy to identify and with known locations. Each GCP will have two coordinates (x’ ; y’ ) and (x ; y) that are used to estimate the coefficients of the equations x’ = f (x, y) = a0 + a1x + a2y + a3xy y’ = g (x, y) = b0 + b1x + b2y + b3xy Coefficients ai and bi are estimated minimizing an error function like the mean squared error using all the N GCP:

9. Functions and GCP The equations can be of different degrees but in general maximum the third order is used. Clearly the higher is the order the higher the number of GCPs needed. • Minimum number of GCP needed is 3 (I) 6 (II) and 9 (III) but it is important to use as many points as possible considering that it is important to: • Select fix elements (rivers are dangerous) • Distribute the GCP uniformly in the image and possibly in flat areas • Evaluate the error of each single GCP

10. Geometric distortions

11. A B’ C B θ H h B A C Projection in map When georeferencing is not enough… Image All these dstortions are function of the view angle θ, view height H and object altitude h H and θ are linked to sensor and platform and for this reason known. To know h a DEM is needed o b’ b O B’

12. Pixel displacement (S) P P’’ P’ s Orthorectification When mountains are present or view height is relatively low the orthorectification is needed. In this case a Digital Elevation Model is needed.

13. Additional distortions in airborne sensors To correct these images DEM and a large number of GCP are needed Also the information about the istantaneous position of the platform can be used (X, Y, Z, Roll, Pitch e Yaw) but this is a field of activities still under development (direct georeferencing).

14. Resampling • Once the equation that links image coordinates with geographic coordinates is parameterized the image can be processed. The procedure follows a number of steps: • A new empty matrix with geographic coordinates is created • The georeferencing function is used to calculate the position of each pixel in the original image • A method is used to decide the DN of the georeferenced image starting from the DNs of the original pixels. Three main methodss are used: Nearest Neighbour Bilinear Bicubic

15. x’ = f (x, y) y’ = g (x, y) Resampling x’i; y’i xi; yi N i i Y Y’ X x = f--1 (x’, y’) y = g-1 (x,’ y’) X’

16. Nearest Neighbour The radiance value DN (x,y) attributed to the output pixel is the DN of the pixel with the closest center to the new re-projected pixel. • ADVANTAGES • DN in the new image are like the original • Fast • DISADVANTAGES • Geometric shift up to ½ pixel

17. Bilinear The radiance value DN (x,y) attributed to the output pixel is the average of the DNs of the four pixels around center to the new re-projected pixel. • ADVANTAGES • Geometrically more accurate • Relatively fast • DISADVANTAGES • Changes the DN values

18. Bicubic The radiance value DN (x,y) attributed to the output pixel is the average of the DNs of the sixteen pixels around center to the new re-projected pixel. • ADVANTAGES • Geometrically more accurate • DISADVANTAGES • Changes the DN values • Relatively slow

19. Final remarks • Where do we take the new coordinates: • Geographic coordinates from maps or GPS • Geographic coordinates from digital maps (raster or vector) • Relative coordinates from another image (that could be already georeferenced) • In orthorectification we need also the DEM • Resampling strategy • Nearest neighbour for qualitative data • Bilinear or bicubic for quantitative data • If you want to keep the original DN and the shift problem is not important, nearest neighbour also for quantitative data