## DESCRIPTION

i.rectify uses the control points included in the source data or identified with the Ground Control Points Manager to calculate a transformation matrix and then converts x,y cell coordinates to standard map coordinates for each pixel in the image. The result is a planimetric image with a transformed coordinate system (i.e., a different coordinate system than before it was rectified). Supported transformation methods are first, second, and third order polynomial and thin plate spline. Thin plate spline is recommended for ungeoreferenced satellite imagery where ground control points (GCPs) are included. Examples are NOAA/AVHRR and ENVISAT imagery which include throusands of GCPs.

If no ground control points are available, the Ground Control Points Manager must be run before i.rectify. An image must be georeferences before it can reside in a standard coordinate LOCATION, and therefore be analyzed with the other map layers in the standard coordinate LOCATION. Upon completion of i.rectify, the rectified image is deposited in the target standard coordinate LOCATION. This LOCATION is selected using i.target.

More than one raster map may be rectified at a time. Each cell file should be given a unique output file name. The rectified image or rectified raster maps will be located in the target LOCATION when the program is completed. The original unrectified files are not modified or removed.

If the -c flag is used, i.rectify will only rectify that portion of the image or raster map that occurs within the chosen window region in the target location, and only that portion of the cell file will be relocated in the target database. It is important therefore, to check the current mapset window in the target LOCATION if the -c flag is used.

If you are rectifying a file with plans to patch it to another file using the GRASS program r.patch, choose option number one, the current window in the target location. This window, however, must be the default window for the target LOCATION. When a file being rectified is smaller than the default window in which it is being rectified, NULLs are added to the rectified file. Patching files of the same size that contain NULL data, eliminates the possibility of a no-data line in the patched result. This is because, when the images are patched, the NULLs in the image are "covered" with non-NULL pixel values. When rectifying files that are going to be patched, rectify all of the files using the same default window.

### Coordinate transformation

The desired order of transformation (1, 2, or 3) is selected with the order option. The program will calculate the RMSE and check the required number of points.

#### Linear affine transformation (1st order transformation)

  x' = ax + by + c
  y' = Ax + By + C

The a,b,c,A,B,C are determined by least squares regression based on the control points entered. This transformation applies scaling, translation and rotation. It is NOT a general purpose rubber-sheeting like TPS, nor is it ortho-photo rectification using a DEM, not second order polynomial, etc. It can be used if (1) you have geometrically correct images, and (2) the terrain or camera distortion effect can be ignored.

#### Polynomial Transformation Matrix (2nd, 3d order transformation)

i.rectify uses a first, second, or third order transformation matrix to calculate the registration coefficients. The number of control points required for a selected order of transformation (represented by n) is

  ((n + 1) * (n + 2) / 2)

or 3, 6, and 10 respectively. It is strongly recommended that one or more additional points be identified to allow for an overly-determined transformation calculation which will generate the Root Mean Square (RMS) error values for each included point. The RMS error values for all the included control points are immediately recalculated when the user selects a different transformation order from the menu bar. The polynomial equations are performed using a modified Gaussian elimination method.

#### Thin plate spline (TPS) transformation

TPS transformation is selected with the -t flag. This method of coordinate transformation is recommended for satellite imagery where hundreds or thousands of GCPs are included, and for historical printed or scanned maps with unknown georeferencing and/or known localized distortions.

TPS combines a linear affine transformation with individual transformation coefficients for each GCP, using the radial basis kernel function with the distance dist between any two points:

  dist2 * log(dist)

As a consequence, localized distortions can be removed with TPS transformation. For example, scan line sensors will have due to the changing viewing angle larger distortions towards the end points of the scan line than at the center of the scan line. Even higher order polynomial transformations are not able to remove these locally different distortions, but TPS transformation can. For best results, TPS requires an even and, for localized distortions, dense spacing of GCPs.

### Resampling method

The rectified data is resampled with one of seven different methods: nearest, bilinear, cubic, lanczos, bilinear_f, cubic_f, or lanczos_f.

The method=nearest method, which performs a nearest neighbor assignment, is the fastest of the resampling methods. It is primarily used for categorical data such as a land use classification, since it will not change the values of the data cells. The method=bilinear method determines the new value of the cell based on a weighted distance average of the 4 surrounding cells in the input map. The method=cubic method determines the new value of the cell based on a weighted distance average of the 16 surrounding cells in the input map. The method=lanczos method determines the new value of the cell based on a weighted distance average of the 25 surrounding cells in the input map.

The bilinear, cubic and lanczos interpolation methods are most appropriate for continuous data and cause some smoothing. These options should not be used with categorical data, since the cell values will be altered.

In the bilinear, cubic and lanczos methods, if any of the surrounding cells used to interpolate the new cell value are NULL, the resulting cell will be NULL, even if the nearest cell is not NULL. This will cause some thinning along NULL borders, such as the coasts of land areas in a DEM. The bilinear_f, cubic_f and lanczos_f interpolation methods can be used if thinning along NULL edges is not desired. These methods "fall back" to simpler interpolation methods along NULL borders. That is, from lanczos to cubic to bilinear to nearest.

If nearest neighbor assignment is used, the output map has the same raster format as the input map. If any of the other interpolations is used, the output map is written as floating point.

## NOTES

If i.rectify starts normally but after some time the following text is seen:
`ERROR: Error writing segment file`
the user may try the -c flag or the module needs more free space on the hard drive.

## SEE ALSO

The GRASS 4 Image Processing manual

m.transform, r.proj, v.proj, i.group, i.target
Ground Control Points Manager

## AUTHORS

William R. Enslin, Michigan State University, Center for Remote Sensing

Modified for GRASS 5.0 by:
Luca Palmeri (palmeri@ux1.unipd.it)
Bill Hughes
Pierre de Mouveaux (pmx@audiovu.com)
CMD mode by Bob Covill