During the registration process, Application calculates the residual error, RMSE, and root mean square total error for all control points.
Residual error
The residual is the difference between the actual observation and the regression estimate. In the registration process, the observation points are the control points on the Reference Layer, which can be the points obtained by puncturing the Reference Layer, or the control points obtained by inputting the X and Y coordinates. The calculated points are the control points obtained from the puncturing points on the Registration Layer, and the fitting points calculated according to a certain registration algorithm. The residuals are divided into X residuals and Y residuals:
- X residual: X residual is the distance between the observation point and the calculation point in the X coordinate direction.
- Y residual: Y residual is the distance between the observation point and the calculation point in the Y coordinate direction.
RMSE
For linear registration and polynomial registration, after a certain Ground Control Point is selected, the following formula is used to calculate the RMSE (RMSerror) of each Ground Control Point:
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Where, X and y are the coordinates of the Ground Control Point in the Original Image, and X ′ and y ′ are the coordinates of the control point calculated by a polynomial of degree 1 or 2, i.e., the estimated coordinates. The magnitude of the difference between the estimated coordinates and the original coordinates represents the accuracy of the geometric correction of each control point. For both linear and polynomial registration, the system calculates the sum point RMSE in the X, y directions. Generally, a GIS application has an acceptable total RMSE, so when the RMSE of some control points is greater than acceptable total RMSE, the control points can be removed or modified to reduce the overall RMSE and improve the registration accuracy.
Total RMSE
The overall RMSE during registration reflects the accumulation of errors generated during registration of all registration points, which is usually used as the Calibrate Precision value of the matching result. The total RMSE (TotalRMSerror) is calculated using the following formula:
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In the formula, n represents the number of control points selected in the registration, and the value of RMS is the RMSE of the control points. When the RMSE of some control points is greater than acceptable total RMSE, these control points can be removed or adjusted to ensure that the overall RMSE is within the acceptable range.
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