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 ID: 542158
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Slide1
Geometric PreprocessingSlide2
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 pixelMost rigorous, but most difficult Applies only to known sources of errorscan skewcross-track distortionmirror velocity variationsplatform velocity variationsEarth rotationEarth 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.Slide3
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 distortionsTwo steps are involved in non-parametric corrections 1. Rectification 2. ResamplingSlide4
Step 1. Rectification
Calculate new output pixel locations (X, Y)
Relate image location to map location using a “mapping polynomial” functionX’ = a0 + a1X + a2Y + a3XY + a4X
2 + a
5Y2Y’ = b0 + b1X + b2Y + b3XY + b4X2 + b5Y2Using these mapping functions calculate correct map locations (X’, Y’) for input pixel locations (X, Y)Slide5
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 definedspatially small well distributed over entire imageWhat are good GCP’s?Slide6
Illustration of well distributed GCP’sSlide7
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
Input image
distorted
Output image
geometrically correctSlide8
Step 2. Resampling
Fill in the geometrically correct cells with DN values -- i.e., calculate new DN values
Resampling methodsnearest neighbor --assign each corrected output pixel the value of the nearest input pixelbilinear interpolation -- calculate the new output pixel value using interpolations from the four closest input pixelscubic convolution -- interpolate a new pixel value from a larger neighborhood of 9, 16, 25 or 36 surrounding input pixelsSlide9
Distorted
input image
Cubic Convolution
+
&
Bilinear Interpolation
+
Resampling Methods
Pixels used in resampling the outlined pixel
Nearest Neighbor
after MicroImages, Inc. and Aronoff (2005)
Rectified imageSlide10
Image Registration
Registration applies the same techniques as rectification for image to image and image to map overlays
A
B
CSlide11
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 imageRectification -- geometric correction; transformation of a geometrically distorted image so that it can be registered to a mapmoving pixels to correct map locationsResampling -- determination of DN values to fill in the output matrix of the rectified or registered image