Geometric Preprocessing 22. Geometric and Radiometric Preprocessing March 8, 2000 Geometric Preprocessing FR 4262

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. FR 4262

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 FR 4262

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) FR 4262

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? FR 4262

Illustration of well distributed GCP’s 22. Geometric and Radiometric Preprocessing March 8, 2000 Illustration of well distributed GCP’s FR 4262

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 FR 4262

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 FR 4262

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) FR 4262

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 FR 4262

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 FR 4262