CN114663527A - Camera self-calibration method under general motion - Google Patents

Abstract

The invention discloses a camera self-calibration method under motion, which comprises seven steps. Compared with the prior art, the invention has the advantages that: the geometric relation between the Steiner curve and the absolute quadratic curve of the symmetrical part of the basic matrix under general motion is utilized, the complete calibration of five internal parameters of the camera and the calibration of six external parameters of the camera can be automatically realized, the operation of the calibration process is simple, only at least three pictures of general motion need to be shot in one calibration, the time of the calibration operation of the camera is saved, and the scheme has the advantages of simplicity, convenience in calculation and accurate result.

Description

Camera self-calibration method under general motion

Technical Field

The invention relates to the technical field of three-dimensional vision, in particular to a camera self-calibration method under general motion.

Background

In the field of three-dimensional vision, it is often necessary to accurately calibrate internal and external parameters of a camera so as to accurately perform operations such as subsequent photogrammetry, autonomous navigation based on vision, motion estimation, three-dimensional reconstruction and the like. However, in the method for completing camera self-calibration under general motion in actual calculation, the original technology neglects the inherent constraint of the basic matrix, and only part of camera parameters can be calculated by using the Kruppa equation; for five unknown camera parameters, there are still five possible solutions of the quintic power of two in the five quadratic equations. And the calculation accuracy is not accurate enough. Other methods attempt to simplify the Kruppa equation by eliminating the scale factors through some specific operations, however, there is still some ambiguity in the obtained camera auto-calibration constraints and the results are not accurate enough.

Disclosure of Invention

In order to solve the technical problems, the technical scheme provided by the invention is as follows: a camera self-calibration method under general motion comprises the following steps:

step one, a basic matrix is obtained through feature point correspondence;

step two, decomposing the basic matrix to obtain a conical quadratic curve Steiner curve Fs and a fixed point xa;

step three, obtaining general characteristic vector constraints of the absolute quadratic curve image and the Fs;

step four, obtaining initial estimation of three internal references and absolute secondary curve images of the camera by general feature vector constraint;

acquiring a circular ring point from the intersection point of the absolute quadratic curve image and Fs, and then acquiring initial solutions of two vanishing lines and two circle centers;

step six, establishing an objective function optimization double circle center;

and seventhly, obtaining the internal parameters of the camera by the optimal solution of the double circle centers.

Compared with the prior art, the invention has the advantages that: the geometric relation between the Steiner curve and the absolute quadratic curve of the symmetrical part of the basic matrix under general motion is utilized, the complete calibration of five internal parameters of the camera and the calibration of six external parameters of the camera can be automatically realized, the operation of the calibration process is simple, only at least three pictures of general motion need to be shot in one calibration, the time of the calibration operation of the camera is saved, and the scheme has the advantages of simplicity, convenience in calculation and accurate result.

Drawings

Fig. 1 is a schematic diagram of a second step in a camera self-calibration method under general motion.

Fig. 2 is a schematic diagram of step three in a camera self-calibration method under general motion.

Fig. 3 is a schematic diagram of step five of the camera self-calibration method under general motion.

Fig. 4 is a schematic diagram of step six of the camera self-calibration method under general motion.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings.

In the embodiment shown in fig. 1 to 4, the present invention provides a method for calibrating a camera under general motion, which includes the following steps:

step one, a basic matrix is obtained through feature point correspondence;

step two, decomposing the basic matrix to obtain a conical secondary curve Steiner curve Fs and a fixed point xa;

step three, obtaining general characteristic vector constraints of the absolute quadratic curve images and Fs;

step four, obtaining initial estimation of three internal references and absolute secondary curve images of the camera by general feature vector constraint;

acquiring a circular ring point from the intersection point of the absolute quadratic curve image and Fs, and then acquiring initial solutions of two vanishing lines and two circle centers;

step six, establishing an objective function optimization double circle center;

and seventhly, obtaining the internal parameters of the camera by the optimal solution with double circle centers.

Wherein:

1. at least three images with overlapping regions are taken of the scene to be measured. And selecting two adjacent image pairs, and acquiring high-precision feature points and matching by using a feature extraction and matching method such as SIFT. Based on the matching feature points in the image pair, the exact basis matrix F is estimated using the eight-point method or other methods, as well as the RANSAC method.

2. In the embodiment shown in FIG. 1, the fundamental matrix F can be decomposed into symmetrical parts F_s＝(F+F^T) /2 and asymmetric part F_a＝(F-F^T)/2. Wherein the symmetrical part F_sIs a circleConic Steiner curve, asymmetric part F_aIs an antisymmetric matrix, which can be written as F_a＝[x_a]_×Thus point x_aIs F_aThe zero vector of (2). Meanwhile, the zero vector of the basic matrix F can obtain the polar point pair { e, e' }, which falls on the quadratic curve F_sAbove, their connecting line l_aSatisfy about F_sPole line quadrature constraint of_a＝F_sx_a. To summarize, in the geometric representation of the fundamental matrix F, the symmetrical part F_sIs a conic section with F as asymmetrical part_aZero vector of (2), i.e. point x_a. The pair of poles { e, e' } falls on the quadratic curve F_sAbove, they are the zero vectors of the fundamental matrix F, their connecting lines l_aSatisfy la ═ l_a＝F_sx_a。

3. In the embodiment shown in FIG. 2, let the absolute conic image be ω, then v_⊥＝ω^*l_aIn the middle line l_aAnd point v_⊥Is a pair of epipolar lines and poles with respect to the absolute conic section image omega. Connection point v_⊥And point x_aA fixed shaft l can be obtained_s. ω and the symmetrical part F of the basic matrix_sForm omega^*F_sThe general eigenvector corresponding to the maximum eigenvalue is the point v₁It is located on the line l_aThe other two general feature vectors are points v₂And v₃They are located at_sOn the image of (a), the absolute conic image ω and the symmetric part F of the fundamental matrix_sThe common eigenvector of (A) can form a common extreme triangle Deltav₁v₂v₃. Wherein, with ω and F_sGeneral eigenvector v corresponding to the largest eigenvalue₁On the line l_aThe other two general feature vectors v₂And v₃On the axis l_sAbove, and l_sAnd l_aAbout ω quadrature, i.e. l_s ^Tω^*l_a＝0。

4. Due to omega^*F_sGeneral eigenvector v corresponding to maximum eigenvalue₁On the line l_aIn the above, the following constraints can be obtained,

three independent constraints are included. When the main shaft point (u) is known₀，v₀) Then, three unknown parameters, i.e., f, (v) can be recovered from the equation_1x，v_1y). Where f is the focal length of the natural camera, (v)_1x,v_1y) Is a generic feature vector v₁The coordinates of (a). Using at least three images to obtain three image pairs, using and not limited to the above constraints, for camera parameters with known principal axis points, three camera parameters can be recovered, namely focal length f_x，f_yAnd a skew parameter s, and an initial estimate of the absolute conic image can be obtained

5. In the embodiment shown in FIG. 3, the image is due to an absolute quadratic curve

And a symmetrical part F of a pair of image elementary matrices F_sThere are two pairs of imaginary intersections, which are the circle points i_i，j_iAnd i is 1 and 2. Suppose F_sIs the projection of a circle on a plane in space, and two vanishing lines l are corresponding to the ambiguity of the normal direction of the plane_hiAnd i is 1 and 2. Their intersection v₁On the line l_aUpper, and two pairs of circle points i_i，j_iRespectively located on the two vanishing lines. Due to the vanishing line l_hiAbout F by projection from the centre of a circle_sWith polar line pole constraint, two circular projection can be recovered

And the center of the circle

On the axis l_sUpper, ω and a pair of image momentsSymmetrical part F of matrix F_sThere are two pairs of virtual intersections, which are circular points, located on the two vanishing lines brought by the plane normal ambiguity, respectively.

6. In the embodiment shown in fig. 4, the double center of the Fs is optimized: initial estimation at two centers of a circle respectively

Uniformly selecting a plurality of sampling points in the nearby area

Fixed shaft image can be obtained by connecting a pair of sampling points

From the center of a circle

Epipolar pole constraint computation on Fs corresponds to two horizontal lines

Further in a horizontal line

Two pairs of circular points are obtained from two pairs of imaginary intersections with Fs

They satisfy

This constraint can be the calculation of an absolute quadratic curve image

4 independent constraints are provided. Thus obtaining more circle points using at least three images and absolute conic image constraints

Calculated by the method in step 4

Are points, respectively

And calculating a relative absolute conic section

Pole of (2)

Constructing an objective function, which may include, but is not limited to, the following constraints: 1) x is the number of_a，

On the shaft

The above step (1); 2) dot

On-line l_aC, removing; 3) l_sAnd l_aQuadrature with respect to ω; l_lAnd l_rRegarding ω orthogonality, the objective function brought about by the above constraints is optimized to solve an optimal solution for the center oi (i ═ 1, 2).

7. Calculating a corresponding horizontal line l with respect to the epipolar pole constraint of Fs from the optimal solution of the center oi (i ═ 1,2)_hi(ii) a Further on a horizontal line l_hiTwo pairs of imaginary intersections with Fs obtain a circle point i_i，j_iI is 1, 2; they satisfy

It can provide 4 independent constraints for calculating the absolute quadratic curve image omega. Thus at least 3 images forming 3 image pairs will contain 6 pairs of circle points which provide 12 independent constraints to calculate the absolute quadratic curve image omega. The 5 internal parameters of the camera are obtained by Cholesky decomposition ω. The camera external parameters are thus obtainable from the decomposed essential matrix. Using more images will improve the accuracy of the camera self-calibration algorithm.

While there have been shown and described the fundamental principles and principal features of the invention and advantages thereof, it will be understood by those skilled in the art that the invention is not limited by the embodiments described above, which are given by way of illustration of the principles of the invention, but is susceptible to various changes and modifications without departing from the spirit and scope of the invention as defined by the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (1)

1. A camera self-calibration method under general motion is characterized by comprising the following steps:

step one, a basic matrix is obtained through feature point correspondence;

step two, decomposing the basic matrix to obtain a conical quadratic curve Steiner curve Fs and a fixed point xa;

step three, obtaining general characteristic vector constraints of the absolute quadratic curve images and Fs;

step four, obtaining initial estimation of three internal references and absolute secondary curve images of the camera by general feature vector constraint;

step five, obtaining a circular point by the intersection point of the absolute secondary curve image and Fs, and then obtaining initial solutions of two vanishing lines and two circle centers;

step six, establishing an objective function optimization double circle center;

and seventhly, obtaining the internal parameters of the camera by the optimal solution of the double circle centers.

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