POSITIONING A PIXEL IN A COORDINATE SYSTEM

Transcription

1 GEOREFERENCING AND GEOCODING EARTH OBSERVATION IMAGES GABRIEL PARODI STUDY MATERIAL: PRINCIPLES OF REMOTE SENSING AN INTRODUCTORY TEXTBOOK CHAPTER 6 POSITIONING A PIXEL IN A COORDINATE SYSTEM The essential difference is the imposition of a referenced geometry. Left: raw image Right: image where a process was executed to allow to give each pixel a coordinate. After the coordinate system is decided the process of assigning a coordinate to any pixel is called georeferencing. 1

2 GEOMETRIC ASPECTS OF IMAGE DATA 2D approaches: Solves X, Y (medium and coarse satellite imagery) Heights of objects are negligible Location: Georeferencing Reorientation: Geocoding (resampling) 3D approaches: Solves X, Y, Z (Aerial Photos and very high resolution satellite imagery) Heights of objects are essential Deals with relief displacement Monoplotting Orthoimage production Stereoplotting Challenge: Clear concepts of location and orientation? Location (absolute) Orientation (relative to) GEOREFERENCING: 2D APPROACHES Y Column X Map Geographic Coordinate Image Screen Coordinate We find a mathematical relation between. Pixel coordinates (Row, Column) inherent of the image. Map coordinates (a coordinate system for the Earth point where the pixel is x,y) The distortion is NOT TO CORRECTED in the image, but the geographic coordinate of each point is right. 2

3 INTRO TO GEOREFERENCE (2D) Georeferencing solves 2 problems: Assign coordinates to pixels, via a model that solves the coordinate distortion. Corrects for distortions produced by several causes. After georeferencing is possible: To measure in the image To spatially combine vector and raster data Compare and fuse images (software dependent) To produce images in a certain map projection you need GEOCODING!!! (1 step more) CAUSES OF GEOMETRIC DISTORTION The perspective of the sensor optics (oblique viewing) The curvature and rotation of the earth. The terrain relief: Relief Displacement Others The motion of the scanning system. The motion and instability of the platform. The platform attitude, altitude and velocity. 3

4 DISTORTION DECIDES THE MATHEMATICAL RELATION Image is evenly distorted a linear transformation (conformal, affine) is applied (small FOV images. i.e. Landsat) Image is unevenly distorted higher order transformations (large FOV images. i.e. NOAA AVHRR, MSG) Conformal Projective Affine GEOREFERENCE MODELS Conformal (4 Parameters) Affine (6 Parameters) Perspective (8 Parameters) n -Polynomial > 12 Parameters) 4

5 2D GEOREFERENCE: LEAST SQUARES ADJUSTMENT In general x = a + b(i) + c(j) y = d + e(i) + f(j) 2D APPROACHES: GEOREFERENCING IMAGE SYSTEM AND MAP PROJECTION SYSTEM (1) Measured Modeled Difference m 1 n 2 x dx i n i 1 m n y dy i mtotal( RMSE) mx my n i 1 Errors are measured at the ground control points!! The accuracy of the georeference can be characterized based on this error, but it applies only to the GCP and it cannot be ensured that the same error applies for all points in the map!! 5

6 PROCEDURE Select appropriate transformation Determine required accuracy Determine transformation parameters Select ground control points Sufficient to solve the transformation equations and derive an error estimate Accurate and reliable Distributed Compute transformation Assess residual errors and RMSE If RMSE does not match requirements: Review all GCP s Review selected transformation GCP distribution & error 1 st order Transformation More than sufficient GCP s Slave Reference 6

7 GCP DISTRIBUTION & ERROR 1 st order Transformation Sufficient distribution Slave Reference GCP distribution & error Slave Reference 1 st order Transformation Insufficient # of GCP s to determine RMSE Poor distribution (on a line) 7

8 GCP distribution & error Slave Reference Reference 1 st order Transformation Insufficient # of GCP s to determine RMSE Geocoding Process: what it is? Original image Georeferenced image N Geocoded image Map N 8

9 GEOCODING PROCESS Geocoding 1. Georeference 2. Resampling + Select output coordinate/projection Select resampling method Define cell size GEOCODING AN IMAGE Georeferenced image Grid overlay Matching our projection Is the Frame of our geocoded image Resampling Corrected image 9

10 WHAT IS RESAMPLING? Center pixels for the georeferenced image Center pixels for the geocoded image. Resampling Method: chosen to assign new values to the geocoded pixels NEAREST NEIGHBOUR RESAMPLING Geocoded pixel (black) adopts the value of the closest georeferenced pixel (red) Preserve radiometrics (DN) 10

11 BI-LINEAR RESAMPLING Geocoded pixel value is weighted from 4 closest georeferenced. Weight ~ 1/d Distorted radiometry but smooth changes. Not advisable for DEM Why? BI-CUBIC RESAMPLING Takes 16 closest pixels. Creates 4 cubic polynomials (black curves) Create 1 perpendicular cubic polynomial passing over the interpolation point (red line) Interpolated value is obtained 11

12 RESAMPLING METHODS Nearest neighbor Maintains original DN values Good for Quantitiave RS (e.g Image Classification) and thematic images Results in jagged edges Bilinear interpolation Smoothed look Bicubic Edges look enhanced, might be shifted Bil and BIC good for scanned maps VERY HIGH RESOLUTION: 3-D APPROACHES Necessary when: We want 3D data (x, y, z) We want 2D data but the relief causes errors beyond requirements Requires transformation of image coordinates to (X,Y,Z) and vice versa 12

13 DSM AND DTM (DEM) DSM: Digital surface model DTM Digital Terrain relief model DEM: Digital Model for raster representations DSM ACQUISITION Radar Interferometry (INSAR) Stereo models Laser Scanning (airborne) Digitising/vectorising 13

14 INTERIOR ORIENTATION Eustasius June 1982 Message PadWatch Altimeter Principle point Fiducial marks 2205 Interior orientation: position of the projection center with respect to the image: Image Coordinate System. Camera calibration report states the location of the principal point and the principal distance Fiducial marks EXTERIOR ORIENTATION Single image Determines the position and orientation of the projection center with respect to the terrain (location (x,y,z) and orientation (ω, ψ, κ) Exterior orientation solved by: RPC (polynomials) Indirect camera orientation (GCP s) Direct camera orientation (GPS and IMU) Integrated camera orientation (combination of the two) 14

15 RELATIVE ORIENTATION (STEREO PAIR) Find conjugate points in overlap Relationship between the two Image Coordinate Systems ABSOLUTE ORIENTATION Follows relative orientation and defines the relationship between the stereo model and the terrain 15

16 CORRECTION OF RELIEF DISPLACEMENT If relief prevents to derive accurate planimetric coordinates for a photo, then relief needs to be considered and corrected a DTM is required to correct for relief displacement on a single photograph digital monoplotting measured image coordinates are transformed to terrain coordinates production of orthophotos or orthoimages the photograph is scanned to provide a digital image the pixels are transformed and resampled EFFECTS OF TERRAIN RELIEF relief displacement is given by : r = r h/h N r c r H N r h R R 16

17 SCHEMATIC RELIEF DISTORTIONS Vertical AP, Frame camera Central projection Line camera, scanner DIGITAL MONOPLOTTING Monoplotting is a procedure of single image photogrammetry for obtaining realtime 3D coordinates from the measurements in image space. The required datasets are: a DTM and an aerial image with its orientation parameters or a georeferenced orthoimage respectively. No resampling is done 17

18 ORTHOPHOTO/ORTHOIMAGE Orthoimage delivers only (X,Y) coordinates! On the original image the map grid is distorted Geometrically correct orthoimage STEREO RESTITUTION: PARALLAX DIFFERENCES Projection O' O" centres left photo b' b" a' a" right photo B H h A Air base AB P a xa' xa'' P b xb' xb' ' H a H AB P a f 18

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