1. Geometric Preprocessing
22. Geometric and Radiometric Preprocessing
March 8, 2000
Geometric Preprocessing
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2. Methods for Geometric Correction
22. Geometric and Radiometric Preprocessing
March 8, 2000
Methods for Geometric Correction
Parametric (analytical)
Mathematically models effects of sensor geometry and motion to derive accurate correction equations for correcting the coordinates of each pixel
Most rigorous, but most difficult
Applies only to known sources of error
scan skew
cross-track distortion
mirror velocity variations
platform velocity variations
Earth rotation
Earth curvature
Data such as Landsat, IKONOS or QuickBird have been largely corrected for these errors.
However, non-systematic errors remain and pixels are not in their correct planimetric map locations.
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3. Methods for Geometric Correction
22. Geometric and Radiometric Preprocessing
March 8, 2000
Methods for Geometric Correction
Non-parametric
Establishes mathematical relationships (mapping polynomials) between the coordinates of pixels in an image and the corresponding coordinates of those points on the ground (via a map)
Can be used irrespective of the analyst’s knowledge of sources and types of distortions
Two steps are involved in non-parametric corrections
1. Rectification
2. Resampling
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4. 22. Geometric and Radiometric Preprocessing
March 8, 2000
Step 1. Rectification
Calculate new output pixel locations (X, Y)
Relate image location to map location using a “mapping polynomial” function
X’ = a0 + a1X + a2Y + a3XY + a4X2 + a5Y2
Y’ = b0 + b1X + b2Y + b3XY + b4X2 + b5Y2
Using these mapping functions calculate correct map locations (X’, Y’) for input pixel locations (X, Y)
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5. 22. Geometric and Radiometric Preprocessing
March 8, 2000
Ground Control Points
The unknowns in these equations (a and b) are solved by determining the coordinates for a set of known locations called ground control points (GCP’s)
GCP’s are features that can be located on both the map and the image; they should be:
well defined
spatially small
well distributed over entire image
What are good GCP’s?
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6. Illustration of well distributed GCP’s
22. Geometric and Radiometric Preprocessing
March 8, 2000
Illustration of well distributed GCP’s
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7. 22. Geometric and Radiometric Preprocessing
March 8, 2000
The end result of selecting GCP’s, solving the mapping functions, and calculating new pixel locations is a new grid or matrix of pixel locations
Output image geometrically correct
Input image distorted
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8. 22. Geometric and Radiometric Preprocessing
March 8, 2000
Step 2. Resampling
Fill in the geometrically correct cells with DN values -- i.e., calculate new DN values
Resampling methods
nearest neighbor --assign each corrected output pixel the value of the nearest input pixel
bilinear interpolation -- calculate the new output pixel value using interpolations from the four closest input pixels
cubic convolution -- interpolate a new pixel value from a larger neighborhood of 9, 16, 25 or 36 surrounding input pixels
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9. 22. Geometric and Radiometric Preprocessing
March 8, 2000
Resampling Methods
Rectified image
Distorted input image
Cubic Convolution +
&
Pixels used in resampling the outlined pixel
Nearest Neighbor
Bilinear Interpolation +
after MicroImages, Inc. and Aronoff (2005)
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10. 22. Geometric and Radiometric Preprocessing
March 8, 2000
Image Registration A B C
Registration applies the same techniques as rectification for image to image and image to map overlays
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11. Summary: 4 R’s of Geometric Preprocessing
22. Geometric and Radiometric Preprocessing
March 8, 2000
Summary: 4 R’s of Geometric Preprocessing
Registration -- overlaying two or more images so that they are in geometric coincidence (but not necessarily geometrically correct)
Reference: Applying a projection/coordinate system to an image
Rectification -- geometric correction; transformation of a geometrically distorted image so that it can be registered to a map
moving pixels to correct map locations
Resampling -- determination of DN values to fill in the output matrix of the rectified or registered image
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