v.rectify uses control points to calculate a 2D or 3D transformation matrix based on a first, second, or
third order polynomial and then converts x,y(, z) coordinates to standard map coordinates for each object
in the vector map. The result is a vector map with a transformed coordinate system (i.e., a different
coordinate system than before it was rectified).
The -o flag enforces orthogonal rotation (currently for 3D only) where the axes remain orthogonal to each
other, e.g. a cube with right angles remains a cube with right angles after transformation. This is not
guaranteed even with affine (1st order) 3D transformation.
Great care should be taken with the placement of Ground Control Points. For 2D transformation, the
control points must not lie on a line, instead 3 of the control points must form a triangle. For 3D
transformation, the control points must not lie on a plane, instead 4 of the control points must form a
triangular pyramid. It is recommended to investigate RMS errors and deviations of the Ground Control
Points prior to transformation.
2D Ground Control Points can be identified in g.gui.gcp.
3D Ground Control Points must be provided in a text file with the points option. The 3D format is
equivalent to the format for 2D ground control points with an additional third coordinate:
x y z east north height status
where x,y,z are source coordinates, east,north,height are target coordinates and status (0 or 1)
indicates whether a given point should be used. Numbers must be separated by space and must use a point
(.) as decimal separator.
If no group is given, the rectified vector will be written to the current mapset. If a group is given and
a target has been set for this group with i.target, the rectified vector will be written to the target
project and mapset.
CoordinatetransformationandRMSE
The desired order of transformation (1, 2, or 3) is selected with the order option. v.rectify will
calculate the RMSE if the -r flag is given and print out statistcs in tabular format. The last row gives
a summary with the first column holding the number of active points, followed by average deviations for
each dimension and both forward and backward transformation and finally forward and backward overall
RMSE.
2Dlinearaffinetransformation(1stordertransformation)
x’ = a1 + b1 * x + c1 * y
y’ = a2 + b2 * x + c2 * y
3Dlinearaffinetransformation(1stordertransformation)
x’ = a1 + b1 * x + c1 * y + d1 * z
y’ = a2 + b2 * x + c2 * y + d2 * z
z’ = a3 + b3 * x + c3 * y + d3 * z The a,b,c,d coefficients 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, nor is it ortho-photo rectification using a DEM, not second
order polynomial, etc. It can be used if (1) you have geometrically correct data, and (2) the terrain or
camera distortion effect can be ignored.
PolynomialTransformationMatrix(2nd,3dordertransformation)v.rectify uses a first, second, or third order transformation matrix to calculate the registration
coefficients. The minimum number of control points required for a 2D transformation of the selected order
(represented by n) is
((n + 1) * (n + 2) / 2) or 3, 6, and 10 respectively. For a 3D transformation of first, second, or third
order, the minimum number of required control points is 4, 10, and 20, respectively. It is strongly
recommended that more than the minimum number of 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 polynomial equations are determined using a modified Gaussian elimination method.
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