Selecting the type of transformation

1. Transforming your scanned nomenclature sheets of topographic maps by sheet frame.

The sheet frame has from 4 to 10 points. By measuring only the frame, it is impossible to estimate the distortion inside the frame. Therefore for transformation it is possible to choose or linear methods of transformation («Offset, rotate, scale» or «Affine Transform») or a polynomial up to 2 degrees (6 coefficients).

If the number of measured points is equal to the number of coefficients of the polynomial, then all points absolutely exactly will be adjusted with the frame of sheet at transforming. However, when the number of coefficients is more than 4, it is necessary to analyze the matrixes of distortion.

If inside of a frame there are the distortions exceeding the tolerance, it is necessary to reduce the number of polynomial coefficients.

Using a rubber sheet to transform the map only by frame is impractical because of the insufficient number of points to construct a uniform triangulation.

2. Transform your scanned nomenclature sheets of topographic maps by the crossings points of kilometer grid.

To select the method of transforming the scanned sheets of topographic maps it is necessary to estimate the errors of scan. The most complete distribution of errors on the field of scan can be estimated by the residual differences on the measured points of the sheet frame and the lines crossings of kilometer grid. To do this you must load the points from the frame of sheet and the kilometer grid and measure its in remeasurement mode with the transition to the next point. When measuring points is recommended to establish the method of transformation «Offset, rotate, scale».

After measuring all the points it is necessary to estimate the mean-square error (MSE) and the residual divergences. Sorting the points in the table in descending order of absolute values of the residual differences in X and Y is performed by pressing the left mouse button on the title of the appropriate column.

If the residual divergences on certain points in several times greater than the value of MSE, you must verify the accuracy of measurements. To do this, you must switch to the remeasurement with the transition to the next point and select the first point with maximum residual discrepancy. If the point is measured incorrectly - remeasure it, if it is right to move to the next point by pressing the «N».

After remeasurement of points the decision about choosing the method of transformation is made.

If the standard deviation and maximum residual divergency does not exceed the tolerance (usually the standard deviation - 0.1 mm. in the map scale, the maximum divergency - 0.2 mm.), then eliminate nonlinear distortion is not necessary.

In this case the transformation can be done in the method «Offset, rotate, scale», or «Affine transformation».

If the residual divergences exceed the tolerance on the accuracy of transformation, we can reduce the divergency by choosing a polynomial in the «polynomial (manual setting), changing the number of polynomial coefficients. The greater the number of coefficients, the less residual divergences and, hence, standard deviation. However, increasing the degree of the polynomial leads to a significant deformation of the surface of distortions outside the area of location of the control points. Therefore, we must necessarily build a matrix of distortions for analysis of nonlinear corrections beyond the area of location of the control points. If in the area of transformation in matrixes of distortions there are values in excess of the tolerance for the accuracy of transformation, we must either reduce the number of coefficients, or choose the type of transformation «Linear - nonlinear rubber sheet».

To obtain an absolutely accurate transformed images in the locations of control points you must use types of transformation «Linear - nonlinear rubber sheet». These types of transformation use Delaunay triangulation to calculate the parameters of the transformation of each triangle. Since the parameters of transformation in different triangles are different, it is possible distortion of the surface of the amendments on the edges of the triangles. This will lead to a fracture of the straight lines on the transformed image at the edges of the triangles.

For the analysis of the surface distortion is necessary to construct matrixes of distortions and see if there was sharp jumps at the boundaries of the triangles. If the distortions are present, then you need to either measure additional points in these areas, or re-check the accuracy of the measurement of points of these triangles.

In general, the surface of the corrections of nonlinear rubber sheet is smoother than linear. However, the final decision on a choice of type of transformation is made after comparing the matrixes of distortions.

One should also note that because of the impossibility of constructing a Delaunay triangulation outside the location region of the control points to enable mode «Remove distortion by adding virtual points on the boundary of transformation». To transform the nomenclature sheet is recommended to use 40 virtual points.

3. Transformation of images.

If ortho-transformation was not done, the images areas have significant distortions in the relief and the parameters of the camera projection. If the terrain is flat, you may transform images without taking into account a relief by method of linear - nonlinear rubber sheet. However, in this case it is necessary to measure a lot of evenly spaced points. Number of points is determined depending on the terrain and the required accuracy of transformation.

For measuring points in the output coordinate system is necessary to use large-scale vector or raster map. After measuring points must necessarily examine the matrixes of distortions

4. Elimination of non-local deformations of a raster map.

If an existing raster map has minor divergences with respect to more accurate vector or raster map, then to remove local distortions  it is possible having performed transformation of map using transformation «rubber sheet». The input and output coordinate systems are virtually identical, so to measure points more conveniently in one window.

Measurement of points is best to do in two stages. First, to measure the points at which the displacement exceeds the tolerance, then to measure in addition points in locations where there is a bit of measured points. As a result, the measured points should be approximately evenly spaced on a raster.