Application provides four registration methods: linear registration, quadratic polynomial registration, rectangular registration and offset registration.
Linear registration
Linear registration, also known as affine transformation, assumes that the actual scale of the map caused by deformation is different in the X and Y directions, so it has the function of correcting the map deformation. Assuming that X and Y are the original coordinates of the input image and X and Y are the corrected output coordinates, the coordinate transformation formula is as follows:
 |
There are 6 parameters in the above formula: A, B, C, D, E and F, which can be determined by selecting the control points of Registration Layer and Reference Layer with the same name. In theory, the above six undetermined parameters need to know at least three pairs of control point coordinates which are not on the same straight line to realize linear transformation. If the constant term parameters C and F are taken as 0, at least four points are needed, so in practical applications, four or more control points are usually used for linear registration. The undetermined coefficients are solved by the principle of least square method.
Linear transformation is one of the most commonly used registration methods. Because the deformation in X and Y directions is considered at the same time, the length ratio of the corrected coordinates in different directions will be different, which shows that the original coordinates will change such as scaling, rotation, translation and so on to obtain the output coordinates.
Quadratic polynomial registration
Quadratic polynomial registration is a commonly used registration method with high accuracy. Polynomial rectification regards the deformation of Original Image as some kind of curved surface, and the output image is a regular plane. In theory, any surface can be fitted by a polynomial of a suitably high degree. Generally, the quadratic binomial can be used to correct the image with serious deformation and obtain higher accuracy. The correction formula for the quadratic binomial is as follows:
 |
There are 12 parameters in the above formula. Theoretically, 6 pairs of control points are required to realize the conversion. However, in order to obtain a relatively high accuracy, it is generally required that the number of control points corrected by the quadratic polynomial is at least 7 pairs. The accuracy of Image Registration can be significantly improved by properly increasing the number of control points. The polynomial coefficients are obtained by the least squares method using the selected control point coordinates. By comparing the polynomial correction formula with the linear correction formula, it can be seen that the linear registration is actually a first-order polynomial registration, and the quadratic polynomial correction requires more control point pairs than linear registration, and also corrects more deformations.
Rectangular registration
Rectangular registration is essentially a special linear registration with limited conditions. If the original image is a regular rectangle and the corrected image coordinates are still a regular rectangle, the coordinates of the four corner points of the rectangle can be determined by selecting two opposite corner points, and the constant term in the correction formula of linear registration is taken as 0, so that the correction formula can be obtained by solving the coordinates of the two opposite corner points, and the geometric correction is realized. This method is not only convenient and time-saving, but also avoids the error accumulation caused by the selection of multiple control points. Rectangular registration is a simple and convenient registration correction method, but because Output Result can not Calculate Error, its registration accuracy is unknown, and it is a rough correction method with low accuracy.
Offset registration
The migration registration only needs a group of control points and reference points, and the difference values of the X coordinate and the Y coordinate are calculated respectively, and then all the groups of coordinate points of the original Dataset are migrated by using the difference values.
Caution: The offset registration method does not need to calculate the error, in fact, the registration is realized by calculating the difference of the X coordinate value and the difference of the y coordinate value between the origin and the target point to offset the X axis and the y axis respectively.
Related topics