Camera calibration method based on Rodrigues matrix

Abstract

The present invention belongs to the field of photogrammetry, and particularly relates to a camera calibration method based on the Rodrigues matrix. Its characteristics are as follows: 1) obtaining the initial values of the exterior orientation elements for calibration based on the Rodrigues matrix; 2) iteratively adjusting and calculating the camera calibration parameters based on the Rodrigues matrix. The present invention adopts a camera calibration method based on the Rodrigues matrix, which can obtain relatively accurate initial values for calibration, effectively reduce the number of iterations during the adjustment calculation, and avoid the problem of calculating attitude angles using trigonometric functions. The camera calibration parameters calculated by this method are approximately the same as the calibration results obtained by the traditional space resection method, indicating that the present invention has a high calibration accuracy.

Description

Technical Field

[0001] The present invention relates to a camera calibration method based on the Rodrigues matrix and belongs to the field of photogrammetry. Technical Background

[0002] In photogrammetry, high-precision camera parameters are the guarantee of the quality of surveying and mapping results. Therefore, the camera should be calibrated before measurement to obtain high-precision camera parameters. When using the space resection camera calibration method, how to obtain relatively accurate initial values of exterior orientation of images is a key problem in calibration. In addition, in close-range photogrammetry, due to the arbitrary values of attitude angles, it brings certain difficulties to the solution of attitude angles. To solve the above problems, the present invention proposes a camera calibration method based on the Rodrigues matrix, which can simply and effectively solve the problem of obtaining initial values in the space resection camera calibration method and avoid the solution of trigonometric functions of attitude angles in iterative solution. Summary of the Invention

[0003] The object of the present invention is to provide a camera calibration method that is simple, effective and has relatively high precision for the above problems.

[0004] Its technical solution is as follows:

[0005] A camera calibration method based on the Rodrigues matrix, characterized by adopting the following steps:

[0006] 1) Obtaining initial values of calibration elements. Assume that there are m control points with coordinates (X i , Y i , Z i ), i = 1, 2...m. The corresponding image point coordinates on the image are (x i , y i ), then the following 3m equations can be obtained from the collinearity condition equation:

[0007]

[0008] where λ is the scale parameter, R is the rotation matrix, X s , Y s , Z s are the translation parameters. Select two adjacent control points that are approximately in the same plane and assume that their scale parameters are approximately equal. Subtracting the corresponding collinearity equations can eliminate the translation parameters:

[0009]

[0010] Transpose equation (2) and then multiply it by equation (2). Considering that the rotation matrix R is an orthogonal matrix, the initial value of parameter λ can be obtained:

[0011]

[0012] Let the skew-symmetric matrix whose elements a, b, and c are independent, and the rotation matrix R can be expressed as R = (I + S)(I - S) using the Rodrigues matrix -1 .

[0013] Considering the properties of the skew-symmetric matrix S and the rotation matrix:

[0014]

[0015] Equation (2) can be rewritten as:

[0016]

[0017] Expanding gives a linear expression form of the parameters (a, b, c):

[0018]

[0019] where: ΔX i = X i - X i-1 , ΔY i = Y i - Y i-1 , ΔZ i = Z i - Z i-1 , Δx i = x i - x i-1 , Δy i = y i - y i-1 .

[0020] Applying the least squares to solve Equation (6) gives the initial values of the parameters (a, b, c).

[0021] Substituting the parameters (a, b, c) and λ i into Equation (1), the initial values of (X S , Y S , Z S ) can be calculated.

[0022] The initial value of the camera principal distance f can be selected as the camera focal length, and the initial values of all other parameters are 0.

[0023] 2) Iterative adjustment solution of camera parameters.

[0024] The camera calibration method model for space resection based on the Rodrigues matrix is:

[0025] V = AX 外 + BX 内 + CX ad - L (7)

[0026] where X 外 = [ΔX s , ΔY s , ΔZ s , Δa, Δb, Δc], and other symbols are the same as those expressed in the traditional collineation method for camera calibration. Since the matrix

[0027]

[0028] where Δ = 1 + a 2 + b 2 + c 2 .

[0029] Then the coefficient matrix can be deduced as follows:

[0030] The a 14 , a 15 , a 16 , a 24 , a 25 , a 26 in

[0031]

[0032] are as follows:

[0033]

[0034] The expressions of a 11 , a 12 , a 13 , a 21 , a 22 , a 23 in the coefficient matrix A and B, C, L are the same as those in the traditional collineation method for camera calibration.

[0035] Using the initial values given in Application 1), the calibration parameters are iteratively solved using Equation (9) until the parameter change is less than 10 -4 .

[0036] The accuracy comparison between the camera calibration method of the present invention and the camera calibration method based on a three-dimensional control field shown in Figure 2 is shown in Table 1,

[0037]

[0038] Table 1 BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a flowchart of the present invention.

[0040] Figure 2 is a three-dimensional control field for camera calibration. Detailed implementation mode

[0041] Step 1) Control point layout: A certain number of control points are evenly laid out, and the control points are observed to obtain their high-precision coordinates (X i , Y i , Z i ).

[0042] Step 2) Image acquisition and measurement of image point coordinates: Use the camera to be calibrated to acquire multiple images with control points, and measure the image point coordinates (x i , y i ) of the control points on the images.

[0043] Step 3) Calculate the initial values of the calibration parameters: According to

[0044]

[0045] calculate the initial value of λ i , where X i , Y i , Z i and X i-1 , Y i-1 , Z i-1 are adjacent control points on approximately the same plane.

[0046] According to

[0047]

[0048] calculate the initial values of a, b, c, and substitute λ and a, b, c into

[0049]

[0050] calculate the initial values of X S , Y S , Z S .

[0051] The initial value of the camera principal distance f is selected as the camera focal length, and the initial values of the principal point and distortion parameters are 0.

[0052] Step 4) Apply the initial values given in Step 3 to calculate

[0053] V = AX 外 + BX 内 + CX ad - L

[0054] the values of the coefficient matrices A, B, C, L in, and among them: X 外 = [ΔX s , ΔY s , ΔZ s , Δa, Δb, Δc], coefficient matrix a in 14 , a 15 , a 16 , a 24 , a 25 , a 26 is:

[0055]

[0056]

[0057]

[0058]

[0059]

[0060]

[0061] The calculation methods of the other elements in the coefficient matrix A and the values of B, C, and L in are the same as those of the traditional space resection method.

[0062] Step 5) Iteratively solve the calibration parameters until the change in the calibration parameters is less than until the parameter change is less than 10 -4 .

[0063] Experimental data proves that:

[0064] (1) The camera calibration parameters calculated by the present invention are approximately the same as the calibration results obtained by the traditional space resection method, indicating that the present invention has a high calibration accuracy.

[0065] (2) The present invention can obtain a calibration initial value with higher accuracy, effectively reducing the number of iterations and avoiding the problem of calculating attitude angles using trigonometric functions.

[0066] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A camera calibration method based on the Rodrigues matrix, characterized in that: Step 1) Control point layout: Uniformly layout a certain number of control points, and observe the control points to obtain their high-precision coordinates (X i , Y i , Z i ); Step 2) Image acquisition and measurement of image point coordinates: Use the camera to be calibrated to acquire multiple images with control points, and measure the image point coordinates (x i , y i ) of the control points on the images; Step 3) Calculate the initial value of the camera calibration parameter λ i : Calculate the initial value of λ, where X i , Y i , Z i and X i-1 , Y i-1 , Z i-1 are adjacent control points on approximately the same plane; According to calculate the initial values of a, b, and c, and substitute λ and a, b, c into: Calculate X S , Y S , Z S initial values; The initial value of the camera principal distance f is selected as the camera focal length, and the initial values of the principal point and distortion parameters are 0; Step 4) Apply the initial values given in Step 3), based on the Rodrigues matrix, and use the space resection method to iteratively solve the calibration parameters. The error equation is: V = AX 外 + BX 内 + CA ad - L where: X 外 = [ΔX s , ΔY s , ΔZ s , Δa, Δb, Δc]; If the rotation matrix R is expressed using the Rodrigues matrix, then the coefficient matrix A: a 14 , a 15 , a 16 , a 24 , a 25 , a 26 is: In the formula: The calculation methods of the other elements in the coefficient matrix A and the values of B, C, and L are the same as those of the traditional space resection method; Step 5) Iteratively solve the calibration parameters until the change in the calibration parameters between two iterations is less than 10 -4 , and the calibration is completed.

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