CN108280858B - Linear global camera motion parameter estimation method in multi-view reconstruction - Google Patents
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Abstract
The invention relates to a linear global camera motion parameter estimation method in multi-view reconstruction, belonging to the technical field of multi-view geometry and three-dimensional reconstruction, comprising the following steps: s1: inputting a plurality of images, and matching the plurality of images of the fixed scene pairwise; s2: optimizing all cameras in the same coordinate system by adopting a multi-view geometry-based theory and a global optimization method; s3: calculating absolute rotation of all cameras; s4: and calculating the absolute translation vector of the camera according to the geometric constraint relation of polar lines in the multi-view geometry by using the absolute rotation and point matching of the camera. The method can process the reconstruction application of a large scene, has small noise influence, is simple to calculate, does not need additional other information, and greatly improves the precision of the motion parameters.
Description
Technical Field
The invention belongs to the technical field of multi-view geometry and three-dimensional reconstruction, and relates to a linear global camera motion parameter estimation method in multi-view reconstruction.
Background
In computer vision, three-dimensional reconstruction is a research hotspot problem, a reconstructed three-dimensional model has wide application scenes, and three-dimensional reconstruction technology plays an important role in human life. Particularly, the three-dimensional reconstruction based on the image has very wide application in the fields of three-dimensional game development, reconstruction of ancient cultural relics, design of three-dimensional digital cities, design of industrial machine prototypes and the like, so that the research on the three-dimensional reconstruction technology based on the image is one of important directions in the field of computer vision and graphics research. Through years of research and development of computer technology, some problems, such as calibration of a camera, acquisition of internal parameters and the like, are solved well, and meanwhile, solving of external parameters of the camera, namely estimation of motion parameters, is a good method which cannot be found, especially under the condition of large-scale scenes and noise influence. At present, motion parameter estimation is the focus of research in three-dimensional reconstruction.
With the progress of research, researchers have proposed many motion parameter estimation methods. The motion parameter estimation methods include a linear solution method, an iterative solution method, namely, a method of continuously iterating to approximate a real value, a local optimization method, and a global optimization method, namely, all cameras are put together and unified to a same coordinate system to perform optimization solution, an independent solution method, a structure solution method, and a calculation estimation method with a scene point in a recovery space. The problem is now treated basically as an optimization problem.
Although each of these motion parameter estimation methods has advantages, there are also different disadvantages. Either the computation is too complex to balance between computational complexity and accuracy, or it is difficult to implement, or it is not accurate enough to be computationally simple but not as efficient, or it is sensitive to noise. And the reconstruction application of thousands of image scenes on a large scale cannot be effectively solved.
Disclosure of Invention
In view of the above, the present invention aims to provide a linear global camera motion parameter estimation method in multi-view reconstruction, and in order to overcome the defects of the existing motion parameter estimation method such as sensitivity to noise and low precision, the linear global parameter estimation method provided by the present invention has the characteristics of noise immunity and accuracy, so that the method can calculate paired essential matrices based on a multi-view geometric method, thereby overcoming the influence of errors or errors in initializing paired essential matrices, and the method is linear and has high calculation efficiency.
In order to achieve the purpose, the invention provides the following technical scheme:
a linear global camera motion parameter estimation method in multi-view reconstruction comprises the following steps:
s1: matching a plurality of images of a fixed scene pairwise;
s2: optimizing all cameras in the same coordinate system by adopting a multi-view geometry-based theory and a global optimization method;
s3: calculating absolute rotation of all cameras;
s4: and calculating the absolute translation vector of the camera according to the geometric constraint relation of polar lines in the multi-view geometry by using the absolute rotation and point matching of the camera.
Further, step S1 specifically includes:
s11: matching a plurality of images of a fixed scene pairwise;
s12: and judging the matching points obtained by pairwise matching, if the interior points are judged to be insufficient or not meet the requirements, defining the matching point pairs as missing, and not reserving the matching point pairs or skipping the images corresponding to the matching point pairs.
Further, step S2 is to optimize all cameras in the same coordinate system by using a multi-view geometry-based theory and global optimization method, calculate the absolute rotation matrix of the cameras by using the objective function,
wherein R isiThe rotation matrix is absolute and represents the orientation or direction of the camera i under the global coordinate system;
is a relative rotation matrix representing the rotation of the ith camera relative to the jth camera; rjRepresenting the orientation or heading, R, of camera j in a global coordinate systemnRepresenting the orientation or direction of the camera n under the global coordinate system, n representing the number of images, | · | | survivalFRepresenting the Frobenius norm of a matrix.
Further, the objective function is calculated by:
s21: all relative rotations are collected to construct a 3n multiplied by 3n symmetric matrix G;
s22: counting the number of relative rotation matrices valid for each row block in the matrix G, a 3n × 3n matrix D is constructed.
Further, the symmetric matrix G is a matrix of,
the matrix D is a matrix of a number of,
wherein, I is an identity matrix,
a relative rotation matrix for the cameras representing the rotation of the ith camera relative to the jth camera; dkAnd k is more than or equal to 1 and less than or equal to n, and the number of effective relative rotations obtained in the k-th row block in the matrix G is represented.
Further, step S4 specifically includes:
s41: calculating a translation vector of the camera according to the absolute rotation of the camera and the matching point;
s42: and according to the epipolar geometry constraint relation in the multi-view geometry, combining the matching point pairs to obtain an absolute translation vector.
Further, in step S41, the translation vector of the camera is obtained from the essential matrix, which is,
Eij＝Ri T(Ti-Tj)Rj
wherein, Ti＝[ti]×，
TiRepresents tiInner product of an obliquely symmetric matrix, TjRepresents tjInner product of an oblique symmetric matrix, tiIs the absolute translation vector of the ith camera, representing the position in global coordinates, tjRepresenting an absolute translation vector for the jth camera;
in step S42, the absolute translation vector obtained by combining the matching point pair satisfies:
wherein the content of the first and second substances,
the m characteristic point on the ith image is taken;
is the mth characteristic point on the jth image.
The invention has the beneficial effects that: the linear global camera motion parameter estimation method in multi-view reconstruction provided by the invention adopts a global optimization idea on the basis of multi-view geometry, all cameras are put into the same coordinate system to be considered together, two 3n multiplied by 3n matrixes are calculated, and finally the motion parameters of the cameras under the global coordinate are obtained linearly.
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In order to make the object, technical scheme and beneficial effect of the invention more clear, the invention provides the following drawings for explanation:
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a diagram of an aperture imaging model;
FIG. 3 is a schematic view of epipolar geometry;
fig. 4 is a presentation from image to motion.
Detailed Description
Preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
The invention provides a linear global camera motion parameter estimation method in multi-view reconstruction, based on feature point matching and multi-view geometric theory, firstly matching every two of images of a series of fixed scenes to obtain matching point pairs, calculating paired intrinsic matrices from the matching point pairs, and decomposing the intrinsic matrices to obtain paired relative rotation matrices; then, global optimization is carried out by utilizing the paired relative rotations according to an objective function to obtain an absolute rotation matrix; then, a new expression of the essential matrix is found out by the multi-view geometric theory, a linear equation system is constructed by combining image characteristic point pairs, and an absolute translation vector is solved, as shown in fig. 1, the method specifically comprises the following steps:
step 1: inputting a series of images, and matching the images by a feature matching algorithm.
A series of ordered or unordered images of a fixed scene are matched pairwise by surf feature descriptors to obtain matching points. And judging the obtained matching points, defining the matching points as missing once the internal points are insufficient or not in accordance with the requirements, and not reserving the matching points or skipping the two images.
Step 2: and calculating by using the matching points based on the multi-view theory to obtain an intrinsic matrix, and decomposing singular values of the intrinsic matrix to obtain a pair of relative rotation matrixes.
Step 201: an essence matrix is calculated, which is an important concept in the multi-view geometry theory, relating to the camera extrinsic parameters, relating the physical coordinates of a spatial point P observed by the left camera to the position of the same point observed by the right camera, as shown in fig. 2.
Step 202: decomposed essential matrix EijA pair of relative rotations is obtained. The essential matrix formula is as follows:
wherein, tijRepresenting the position of the ith camera relative to the jth camera as a relative translation vector;
indicates a correspondence to tijAn inner product skew-symmetric matrix; rijIs a relative rotation matrix representing the rotation of the ith camera relative to the jth camera.
The principle of singular value decomposition is used to separate the essential matrix EijIt can be decomposed into a rotation matrix RijAnd a translation vector tij. But obtain more than one rotation, then need to carry out screening, its screening principle is: the spatial point should be in front of the two cameras, as shown in fig. 2, and the spatial point P should be in front of the left and right cameras.
In addition, according to the epipolar geometry principle in multi-view geometry, the spatial point P and its projection points on image i and image j are denoted as P, respectivelyiAnd pjWhich satisfies epipolar geometric constraints as shown in fig. 3. The specific relation equation is as follows:
definition of the present embodiment
Representing the focus of the camera in a global coordinate system, defining RiE SO (3), representing the orientation of the camera in the global coordinate system, the following relation being defined for a pair of images i and j:
Rij＝Ri TRj
at the same time, it is easy to verify:
when all the relative rotation matrices are obtained, step 3 may be entered.
And step 3: and establishing an objective function by utilizing the relative rotation, and solving the objective function according to the characteristic value decomposition to obtain an absolute camera rotation matrix.
After the processing of step 2, the relative rotation between all the two images is obtained, that is, the absolute rotation is solved according to the relative rotation.
First, an objective function is constructed according to formula (3), and the objective function is as follows:
to solve the objective function, a 3n × 3n symmetric matrix G is constructed, containing all pairs of relative rotation matrices, and the formula is as follows:
a3 × 3n matrix R is also defined, such that the matrix R contains all absolute pairs of rotations, which are defined as follows:
R＝[R1 R2 ... Rn]
then, counting the number of effective relative rotation matrixes in each row block in the G matrix to construct a D matrix, wherein the construction formula is as follows:
where I is the identity matrix and dkRepresenting the effective relative rotation in k-line blocks in matrix G
K is more than or equal to 1 and less than or equal to n.
Thus, GR can be verifiedT＝DRTThus matrix D-1G three eigenvectors with eigenvalues of 1 form a matrix RTThe column (c). To extract the absolute rotation matrix, a 3n × 3 matrix M is defined, which contains these eigenvectors, where M is defined as:
M＝[M1；M2；...Mn]
wherein each MiIs an estimate of the absolute rotation of the ith camera.
Finally, each M is decomposed by using singular valuesiEach absolute rotation matrix R is obtainedi。
And 4, step 4: and according to the multi-view geometric theory, constructing a linear equation by using an absolute rotation matrix and the matching point pairs, and solving to obtain an absolute camera translation vector.
Absolute rotation R of each camera obtained by step 3iTurning to solving for the absolute translation vector of the camera, first find an expression of the essential matrix that contains only rotation and translation:
Eij＝Ri T(Ti-Tj)Rj
wherein, Ti＝[ti]×，
Further, according to the epipolar geometry constraint relationship in the multi-view geometry, combining the equations obtained by matching the point pairs:
wherein the content of the first and second substances,
is the m-th feature point on the ith image,
is the m-th feature point on the i-th image.
Finally, according to least square, solving a linear equation system, and obtaining an absolute translation vector t of each camera by finding feature vectors of 4 minimum feature values of a 3n multiplied by 3n matrixi。
Thus, the motion parameter of each camera, namely the absolute rotation matrix R of each camera is estimatediAnd absolute translation vector tiWhich is shown in fig. 4 by image-to-camera motion estimation.
Finally, it is noted that the above-mentioned preferred embodiments illustrate rather than limit the invention, and that, although the invention has been described in detail with reference to the above-mentioned preferred embodiments, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the scope of the invention as defined by the appended claims.
Claims (1)
1. A linear global camera motion parameter estimation method in multi-view reconstruction is characterized in that: comprises the following steps:
s1: inputting a plurality of images, and matching the plurality of images of the fixed scene pairwise;
s2: optimizing all cameras in the same coordinate system by adopting a multi-view geometry-based theory and a global optimization method;
s3: calculating absolute rotation of all cameras;
s4: calculating an absolute translation vector of the camera according to a polar line geometric constraint relation in multi-view geometry by using the absolute rotation and matching point pairs of the camera;
step S1 specifically includes:
s11: matching a plurality of images of a fixed scene pairwise;
s12: judging matching point pairs obtained through pairwise matching, if the matching point pairs are judged to be insufficient or not meet the requirements, defining the matching point pairs as missing, and not reserving the matching point pairs or skipping images corresponding to the matching point pairs;
step S2 is to optimize all cameras in the same coordinate system by using a multi-view geometry-based theory and global optimization method, calculate the absolute rotation matrix of the cameras by an objective function,
wherein R isiThe rotation matrix is absolute and represents the orientation or direction of the camera i under the global coordinate system;
representing the i-th phase relative to each other as a relative rotation matrixRotation at jth camera; rjRepresenting the orientation or heading, R, of camera j in a global coordinate systemnRepresenting the orientation or direction of the camera n under the global coordinate system, n representing the number of images, | · | | survivalFRepresents the Frobenius norm of a matrix;
the objective function is calculated as follows:
s21: all relative rotations are collected to construct a 3n multiplied by 3n symmetric matrix G;
s22: counting the number of effective relative rotation matrixes of each row block in the matrix G, and constructing a matrix D of 3n multiplied by 3 n;
the symmetric matrix G is a matrix of a symmetric matrix G,
the matrix D is a matrix of a number of,
wherein, I is an identity matrix,
a relative rotation matrix for the cameras representing the rotation of the ith camera relative to the jth camera; dkRepresenting the number of effective relative rotations obtained in the k-th row of blocks in the matrix G, wherein k is more than or equal to 1 and less than or equal to n;
step S4 specifically includes:
s41: calculating a translation vector of the camera according to the absolute rotation of the camera and the matching point pair;
s42: according to the epipolar geometry constraint relation in the multi-view geometry, combining the matching point pairs to obtain an absolute translation vector;
in step S41, the translation vector of the camera is obtained from the intrinsic matrix, which is,
Eij＝Ri T(Ti-Tj)Rj
wherein, Ti＝[ti]×，
TiRepresents tiInner product of an obliquely symmetric matrix, TjRepresents tjInner product of an oblique symmetric matrix, tiIs the absolute translation vector of the ith camera, representing the position in global coordinates, tjRepresenting an absolute translation vector for the jth camera;
in step S42, the absolute translation vector obtained by combining the matching point pair satisfies:
wherein the content of the first and second substances,
the m characteristic point on the ith image is taken;
is the mth characteristic point on the jth image.
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| CN109741403B (en) * | 2018-12-29 | 2023-04-07 | 重庆邮电大学 | Camera translation calibration method based on global linearity |
| CN110782524B (en) * | 2019-10-25 | 2023-05-23 | 重庆邮电大学 | Indoor three-dimensional reconstruction method based on panoramic image |
| CN111161355B (en) * | 2019-12-11 | 2023-05-09 | 上海交通大学 | Multi-view camera pose and scene pure pose resolving method and system |
| CN111724466B (en) * | 2020-05-26 | 2023-09-26 | 同济大学 | 3D reconstruction optimization method and device based on rotation matrix |
| CN111986247B (en) * | 2020-08-28 | 2023-10-27 | 中国海洋大学 | Hierarchical camera rotation estimation method |
| CN114170296B (en) * | 2021-11-10 | 2022-10-18 | 埃洛克航空科技（北京）有限公司 | Rotary average estimation method and device based on multi-mode comprehensive decision |
| CN114972536B (en) * | 2022-05-26 | 2023-05-09 | 中国人民解放军战略支援部队信息工程大学 | Positioning and calibrating method for aviation area array swing scanning type camera |
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