CN113048985A - Camera relative motion estimation method under known relative rotation angle condition - Google Patents
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Abstract
Description
技术领域technical field
本申请涉及定位技术领域,特别是涉及一种已知相对旋转角度条件下的像机相对运动估计方法。The present application relates to the field of positioning technology, and in particular, to a method for estimating relative motion of a camera under the condition of a known relative rotation angle.
背景技术Background technique
单像机或多像机的相对运动估计是三维视觉中的一个基本问题,例如机器人定位和地图绘制,增强现实和自动驾驶。单像机系统采用中心透视投影模型建模,单像机的相对运动估计通常利用5个同名点对的本质矩阵算法,或者利用4个同名点对的单应性矩阵算法。多像机系统由固定在单一刚体上的多个单像机组成。它采用通用像机模型建模,且没有单一的投影中心。多像机的相对运动估计通常利用6个同名点对的最小配置解,或者17个同名点对的线性求解方法。Relative motion estimation of single or multi-cameras is a fundamental problem in 3D vision, such as robot localization and mapping, augmented reality and autonomous driving. The single camera system is modeled by the central perspective projection model, and the relative motion estimation of the single camera usually uses the essential matrix algorithm of 5 point pairs with the same name, or the homography matrix algorithm of 4 point pairs with the same name. A multi-camera system consists of multiple single cameras fixed on a single rigid body. It is modeled with a generic camera model and does not have a single center of projection. The relative motion estimation of the multi-camera usually utilizes the minimum configuration solution of 6 identical point pairs, or the linear solution method of 17 identical dot pairs.
当前,手机、无人机等电子设备中通常都有惯性测量单元和像机等传感器,而且惯性测量单元和像机固联安装,因此可以利用惯性测量单元为像机相对运动估计提供旋转角度信息,主要可分为以下两种情况:(1)若惯性测量单元与像机之间的安装关系事先精确标定已知,根据惯性测量单元输出的旋转角度能够直接为像机提供姿态角,从而减少像机相对运动估计中待求解的位姿参数。例如,在惯性测量单元为像机提供统一重力方向的条件下,利用3个同名点对能够估计单像机系统的相对运动,4个同名点对能够估计多像机系统的相对运动。(2)若惯性测量单元与像机之间的安装关系未知,可根据两者固联安装条件下,惯性测量单元和像机在运动过程中各自的相对旋转角相同这一性质,惯性测量单元输出的相对旋转角可以直接用作像机的相对旋转角,同样能减少像机相对运动估计中待求解的位姿参数。利用4个同名点对和5个同名点对分别能估计单像机系统和多像机系统的相对运动。由于不需要对惯性测量单元与像机进行标定,使得惯性测量单元和像机的融合更加灵活方便,在三维重建、视觉里程计等领域具有广泛的应用场景。At present, there are usually sensors such as inertial measurement units and cameras in electronic devices such as mobile phones and drones, and the inertial measurement unit and the camera are fixedly installed. Therefore, the inertial measurement unit can be used to provide rotation angle information for the relative motion estimation of the camera. , which can be mainly divided into the following two cases: (1) If the installation relationship between the inertial measurement unit and the camera is accurately calibrated and known in advance, the rotation angle output by the inertial measurement unit can directly provide the camera with the attitude angle, thereby reducing the The pose parameters to be solved in the camera relative motion estimation. For example, under the condition that the inertial measurement unit provides the camera with a uniform gravity direction, the relative motion of the single-camera system can be estimated by using 3 point pairs with the same name, and the relative motion of the multi-camera system can be estimated with 4 point pairs with the same name. (2) If the installation relationship between the inertial measurement unit and the camera is unknown, according to the property that the inertial measurement unit and the camera have the same relative rotation angle during the movement process under the fixed installation condition of the two, the inertial measurement unit The output relative rotation angle can be directly used as the relative rotation angle of the camera, which can also reduce the pose parameters to be solved in the relative motion estimation of the camera. The relative motion of the single-camera system and the multi-camera system can be estimated by using 4 identical point pairs and 5 identical name point pairs, respectively. Since there is no need to calibrate the inertial measurement unit and the camera, the integration of the inertial measurement unit and the camera is more flexible and convenient, and it has a wide range of application scenarios in the fields of 3D reconstruction and visual odometry.
传统的相对运动估计算法通常采用SIFT和SURF等特征算法获得同名点对。目前多视图几何估计中,通过ASIFT和MODS等特征算法提取的仿射匹配对点,因为包含更多的图像点对信息而受到了越来越多的关注。仿射匹配对点不仅包括同名点对的图像坐标,而且包括同名点对之间领域信息的局部仿射矩阵。每个仿射匹配点对在对极几何关系上给出三个约束方程,能够有效减少相对运动估计方法所需点对的数量。Traditional relative motion estimation algorithms usually use feature algorithms such as SIFT and SURF to obtain point pairs with the same name. In the current multi-view geometric estimation, the affine matching points extracted by feature algorithms such as ASIFT and MODS have received more and more attention because they contain more image point pair information. Affine matching pairs of points include not only the image coordinates of the same-named point pairs, but also the local affine matrix of domain information between the same-named point-pairs. Each affine matching point pair gives three constraint equations on the epipolar geometric relationship, which can effectively reduce the number of point pairs required by the relative motion estimation method.
发明内容SUMMARY OF THE INVENTION
基于此,有必要针对上述技术问题,提供一种能够利用仿射匹配点对解决已知相对旋转角度条件下的像机相对运动估计方法。Based on this, it is necessary to provide a method for estimating the relative motion of a camera under the condition of known relative rotation angles by using affine matching point pairs to solve the above technical problems.
一种已知相对旋转角度条件下的像机相对运动估计方法,所述方法包括:A method for estimating relative motion of a camera under the condition of a known relative rotation angle, the method comprising:
获取像机拍摄的第一视图和第二视图中至少两个仿射匹配点对,选择第j个所述仿射匹配点对建立世界参考系;所述世界参考系的原点为第j个所述仿射匹配点对在三维空间中的位置,所述世界参考系的坐标轴方向与所述第一视图方向一致;Obtain at least two affine matching point pairs in the first view and the second view captured by the camera, and select the jth affine matching point pair to establish a world reference system; the origin of the world reference system is the jth affine matching point pair. the position of the affine matching point pair in the three-dimensional space, and the coordinate axis direction of the world reference system is consistent with the first view direction;
获取所述第一视图和所述第二视图之间的第一位姿关系,获取所述第一视图和所述世界参考系的第二位姿关系,以及获取第二视图和所述世界参考系的第三位姿关系;所述第一位姿关系、所述第二位姿关系以及所述第三位姿关系中均包括旋转矩阵和平移向量;obtaining a first pose relationship between the first view and the second view, obtaining a second pose relationship between the first view and the world reference frame, and obtaining a second view and the world reference The third pose relationship of the system; the first pose relationship, the second pose relationship and the third pose relationship all include a rotation matrix and a translation vector;
对所述旋转矩阵和所述平移向量进行参数化,以及根据所述第一视图和所述第二视图之间的相对旋转角度,确定所述旋转矩阵对应未知数的旋转参数约束;Parameterizing the rotation matrix and the translation vector, and determining the rotation parameter constraint of the unknown corresponding to the rotation matrix according to the relative rotation angle between the first view and the second view;
采用参数化后的所述旋转矩阵和所述平移向量表示所述第一位姿关系以及获取对应的本质矩阵;Using the parameterized rotation matrix and the translation vector to represent the first attitude relationship and obtain the corresponding essential matrix;
获取由第j个所述仿射匹配点确定的所述本质矩阵与所述仿射匹配点中仿射匹配矩阵对应的两个仿射变换约束,获取其他所述仿射匹配点确定的所述第一视图和所述第二视图的一个对极几何约束以及所述本质矩阵与所述仿射匹配点中仿射匹配矩阵对应的两个仿射变换约束;Obtain the essential matrix determined by the jth affine matching point and two affine transformation constraints corresponding to the affine matching matrix in the affine matching point, and obtain the One epipolar geometric constraint of the first view and the second view and two affine transformation constraints corresponding to the essential matrix and the affine matching matrix in the affine matching point;
根据第j个所述仿射匹配点对应的两个仿射变换约束,以及其他所述仿射匹配点确定的一个对极几何约束和两个仿射变换约束,求解得到所述旋转矩阵和所述平移向量,根据所述旋转矩阵和所述平移向量确定像机相对运动关系。According to the two affine transformation constraints corresponding to the jth affine matching point, as well as one epipolar geometric constraint and two affine transformation constraints determined by the other affine matching points, the rotation matrix and all the The translation vector is used to determine the relative motion relationship of the camera according to the rotation matrix and the translation vector.
上述已知相对旋转角度条件下的像机相对运动估计方法,利用惯性测量单元提供的相对旋转角度,并根据仿射匹配对点和像机运动模型之间的约束。提出了基于两个仿射匹配点对的相对运动估计最小解,分别估计单个像机和多像机系统的运动,从而极大减少求解单像机和多像机系统相对运动估计问题所需要的点对数量,明显提高了算法的精度及鲁棒性,并且适用于惯性测量单元与像机之间安装关系未知或存在变化的情况。The above method for estimating the relative motion of the camera under the condition of the known relative rotation angle uses the relative rotation angle provided by the inertial measurement unit, and matches the constraints between the point and the camera motion model according to affine matching. A minimum solution for relative motion estimation based on two affine matched point pairs is proposed, which estimates the motion of a single camera and a multi-camera system respectively, thereby greatly reducing the relative motion estimation problem of single-camera and multi-camera systems. The number of point pairs significantly improves the accuracy and robustness of the algorithm, and is suitable for situations where the installation relationship between the inertial measurement unit and the camera is unknown or changes.
附图说明Description of drawings
图1为一个实施例中已知相对旋转角度条件下的像机相对运动估计方法;1 is a method for estimating relative motion of a camera under the condition of a known relative rotation angle in one embodiment;
图2为一个实施例中单像机参数分布示意图;Fig. 2 is a schematic diagram of parameter distribution of a single camera in one embodiment;
图3为一个实施例中多像机参数分布示意图。FIG. 3 is a schematic diagram of parameter distribution of a multi-camera in an embodiment.
具体实施方式Detailed ways
为了使本申请的目的、技术方案及优点更加清楚明白,以下结合附图及实施例,对本申请进行进一步详细说明。应当理解,此处描述的具体实施例仅仅用以解释本申请,并不用于限定本申请。In order to make the purpose, technical solutions and advantages of the present application more clearly understood, the present application will be described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, but not to limit the present application.
在一个实施例中,如图1所示,提供了一种已知相对旋转角度条件下的像机相对运动估计方法,包括以下步骤:In one embodiment, as shown in FIG. 1 , a method for estimating the relative motion of a camera under the condition of a known relative rotation angle is provided, including the following steps:
步骤102,获取像机拍摄的第一视图和第二视图中至少两个仿射匹配点对,选择第j个仿射匹配点对建立世界参考系。Step 102: Acquire at least two affine matching point pairs in the first view and the second view captured by the camera, and select the jth affine matching point pair to establish a world reference system.
世界参考系的原点为第j个仿射匹配点对在三维空间中的位置,世界参考系的坐标轴方向与第一视图方向一致。The origin of the world reference system is the position of the jth affine matching point pair in the three-dimensional space, and the coordinate axis direction of the world reference system is consistent with the direction of the first view.
步骤104,获取第一视图和第二视图之间的第一位姿关系,获取第一视图和世界参考系的第二位姿关系,以及获取第二视图和世界参考系的第三位姿关系。Step 104: Obtain the first pose relationship between the first view and the second view, obtain the second pose relationship between the first view and the world reference system, and obtain the third pose relationship between the second view and the world reference system .
第一位姿关系、第二位姿关系以及第三位姿关系中均包括旋转矩阵和平移向量。The first pose relationship, the second pose relationship, and the third pose relationship all include a rotation matrix and a translation vector.
步骤106,对旋转矩阵和平移向量进行参数化,以及根据第一视图和第二视图之间的相对旋转角度,确定旋转矩阵对应未知数的旋转参数约束,采用参数化后的旋转矩阵和平移向量表示第一位姿关系以及获取对应的本质矩阵。Step 106: Parameterize the rotation matrix and the translation vector, and determine the rotation parameter constraint of the unknown number corresponding to the rotation matrix according to the relative rotation angle between the first view and the second view, and use the parameterized rotation matrix and translation vector to represent The first pose relationship and the corresponding essential matrix are obtained.
步骤108,获取由第j个仿射匹配点确定的本质矩阵与仿射匹配点中仿射匹配矩阵对应的两个仿射变换约束,获取其他仿射匹配点确定的第一视图和第二视图的一个对极几何约束以及本质矩阵与仿射匹配点中仿射匹配矩阵对应的两个仿射变换约束。Step 108: Obtain the essential matrix determined by the jth affine matching point and two affine transformation constraints corresponding to the affine matching matrix in the affine matching point, and obtain the first view and the second view determined by other affine matching points. An epipolar geometric constraint of , and two affine transformation constraints corresponding to the essential matrix and the affine matching matrix in the affine matching point.
步骤110,根据第j个仿射匹配点对应的两个仿射变换约束,以及其他仿射匹配点确定的一个对极几何约束和两个仿射变换约束,得到旋转矩阵和平移向量,根据旋转矩阵和平移向量确定像机相对运动关系。Step 110: Obtain a rotation matrix and a translation vector according to the two affine transformation constraints corresponding to the jth affine matching point, as well as one epipolar geometric constraint and two affine transformation constraints determined by other affine matching points, and according to the rotation The matrix and translation vector determine the relative motion relationship of the camera.
上述已知相对旋转角度条件下的像机相对运动估计方法,利用惯性测量单元提供的相对旋转角度,并根据仿射匹配对点和像机运动模型之间的约束。提出了基于两个仿射匹配点对的相对运动估计最小解,分别估计单个像机和多像机系统的运动,从而极大减少求解单像机和多像机系统相对运动估计问题所需要的点对数量,明显提高了算法的精度及鲁棒性,并且适用于惯性测量单元与像机之间安装关系未知或存在变化的情况。The above method for estimating the relative motion of the camera under the condition of the known relative rotation angle uses the relative rotation angle provided by the inertial measurement unit, and matches the constraints between the point and the camera motion model according to affine matching. A minimum solution for relative motion estimation based on two affine matched point pairs is proposed, which estimates the motion of a single camera and a multi-camera system respectively, thereby greatly reducing the relative motion estimation problem of single-camera and multi-camera systems. The number of point pairs significantly improves the accuracy and robustness of the algorithm, and is suitable for situations where the installation relationship between the inertial measurement unit and the camera is unknown or changes.
对于单像机相对运动估计,假定第j个仿射匹配点对表示为,其中和分别是第一视图和第二视图中同名点对的归一化齐次图像坐标,是2×2的局部仿射变换矩阵,表征着和周围无穷小邻域内的仿射变换关系。同名点对相应的单位方向向量可以通过如下等式计算:,。本发明实施例输入条件是两个仿射匹配点对(最少一个仿射匹配点对和一个同名点对)和惯性测量单元提供的单像机相对旋转角度。For single-camera relative motion estimation, it is assumed that the j-th affine matching point pair is expressed as ,in and are the normalized homogeneous image coordinates of point pairs with the same name in the first and second views, respectively, is a 2×2 local affine transformation matrix, signifies and Affine transformation relation in the surrounding infinitesimal neighborhood. The corresponding unit direction vector of the point pair with the same name can be calculated by the following equation: , . The input conditions of the embodiment of the present invention are two affine matching point pairs (at least one affine matching point pair and one point pair with the same name) and the relative rotation angle of the single camera provided by the inertial measurement unit.
在其中一个实施例中,获取对旋转矩阵进行参数化得到的旋转矩阵为:In one of the embodiments, the rotation matrix obtained by parameterizing the rotation matrix is obtained as:
其中,是四元数齐次向量,R表示第一位姿关系对应的旋转矩阵;in, is a quaternion homogeneous vector, and R represents the rotation matrix corresponding to the first pose relationship;
根据第一视图和第二视图之间的相对旋转角度,确定旋转矩阵对应未知数的旋转参数约束为:According to the relative rotation angle between the first view and the second view, the rotation parameter constraint of the unknown corresponding to the rotation matrix is determined as:
其中,表示相对旋转角度。in, Indicates the relative rotation angle.
在其中一个实施例中,获取对平移向量进行参数化得到的第二位姿关系中平移向量和第三位姿关系中平移向量分别为:In one of the embodiments, obtaining the translation vector in the second pose relationship and the translation vector in the third pose relationship obtained by parameterizing the translation vector are:
其中,表示所述第二位姿关系中平移向量,表示所述第二位姿关系中平移向量参数化的未知深度参数,表示第一视图中归一化齐次图像坐标的单位向量,表示第三位姿关系中平移向量,表示第三位姿关系中平移向量的未知深度参数,表示第二视图中归一化齐次图像坐标的单位向量;in, represents the translation vector in the second pose relationship, represents the unknown depth parameter parameterized by the translation vector in the second pose relationship, a unit vector representing the normalized homogeneous image coordinates in the first view, represents the translation vector in the third pose relation, represents the unknown depth parameter of the translation vector in the third pose relation, a unit vector representing the normalized homogeneous image coordinates in the second view;
采用参数化后的旋转矩阵和平移向量表示第一位姿关系为:Using the parameterized rotation matrix and translation vector to represent the first pose relationship is:
其中,表示第一位姿关系中的平移向量,I表示单位矩阵;in, represents the translation vector in the first pose relation, and I represents the identity matrix;
以及获取对应的本质矩阵为:And get the corresponding essential matrix as:
其中,E表示本质矩阵,表示反对称矩阵。where E represents the essential matrix, represents an antisymmetric matrix.
在其中一个实施例中,对极几何约束为:In one embodiment, the epipolar geometric constraints are:
其中,为第一视图和第二视图中同名点对的归一化齐次图像坐标;in, is the normalized homogeneous image coordinates of the point pairs with the same name in the first view and the second view;
仿射变换约束为:The affine transformation constraints are:
其中,下标(1:2)表示前两个方程式。where the subscript (1:2) represents the first two equations.
在其中一个实施例中,根据旋转参数约束,确定单像机的相对运动参数为四个自由度;选择所述第j个仿射匹配点对应的两个仿射变换约束,以及其他仿射匹配点确定的一个对极几何约束,构建第一求解模型为:In one embodiment, according to the rotation parameter constraints, the relative motion parameters of the single camera are determined to be four degrees of freedom; two affine transformation constraints corresponding to the jth affine matching point, and other affine matching points are selected. An epipolar geometric constraint determined by the point, the first solution model is constructed as:
; ;
其中,中的元素项为未知数,和的二次项,表示矩阵大小为三行二列;in, The element term in is unknown , and the quadratic term of , express The size of the matrix is three rows and two columns;
选择其他仿射匹配点建立世界参考系,得到第二求解模型为:Select other affine matching points to establish the world reference system, and obtain the second solution model as:
其中,中的元素项为未知数,和的二次项;in, The element term in is unknown , and the quadratic term;
根据第一求解模型和第二求解模型,得到关于未知数的六个方程为:According to the first solution model and the second solution model, it is obtained about the unknown The six equations are:
通过Gröbner基求解法获得六个方程的代数解,根据代数解确定第一位姿关系的旋转矩阵R,根据中零空间确定,根据计算得到第二位姿关系中平移向量和第三位姿关系中平移向量,表示矩阵前二行前二列的子矩阵,表示矩阵前二行前二列的子矩阵,表示矩阵的行列式,表示由未知数组成的二行二列子矩阵。The algebraic solutions of the six equations are obtained by the Gröbner basis solution method, and the rotation matrix R of the first attitude relationship is determined according to the algebraic solutions. Medium null space determination ,according to Calculate the translation vector in the second pose relationship and the translation vector in the third pose relationship, representation matrix The submatrix of the first two rows and the first two columns, representation matrix The submatrix of the first two rows and the first two columns, represents the determinant of the matrix, represented by the unknown A two-row two-column submatrix.
在其中一个实施例中,当像机为多像机系统时,获取多像机系统中像机的外参数;其中,多像机系统包括:拍摄第一视图或第二视图的像机,以及透视像机;In one embodiment, when the camera is a multi-camera system, the camera in the multi-camera system is acquired extrinsic parameters ; wherein, the multi-camera system includes: a camera for capturing a first view or a second view , and a perspective camera;
采用Plücker向量对所述多像机系统中平移向量进行参数化,得到平移向量为:Using the Plücker vector to parameterize the translation vector in the multi-camera system, the translation vector obtained is:
其中,是像机的序列号,是仿射匹配点对的序列号,是视图的序列号。单位方向向量可以通过计算得出,,是像机中对应的归一化齐次图像坐标;in, is the serial number of the camera, is the sequence number of the affine matching point pair, is the serial number of the view. unit direction vector able to pass Calculated, , camera middle the corresponding normalized homogeneous image coordinates;
根据参数化后的旋转矩阵和平移向量,得到第一视图和第二视图对应的两个透视相机之间的第四位姿关系为:According to the parameterized rotation matrix and translation vector, the fourth pose relationship between the two perspective cameras corresponding to the first view and the second view is obtained as:
计算第四位姿关系对应的本质矩阵为:The essential matrix corresponding to the calculation of the fourth pose relationship is:
。 .
在其中一个实施例中,根据所述旋转参数约束,确定多像机系统的相对运动参数为五个自由度;In one of the embodiments, according to the rotation parameter constraint, the relative motion parameter of the multi-camera system is determined to be five degrees of freedom;
选择所述第j个所述仿射匹配点对应的两个仿射变换约束,以及其他所述仿射匹配点确定的一个对极几何约束和一个仿射变换约束,构建第三求解模型为:Select two affine transformation constraints corresponding to the jth affine matching point, as well as an epipolar geometric constraint and an affine transformation constraint determined by the other affine matching points, and construct a third solution model as follows:
选择其他所述仿射匹配点建立世界参考系,得到第四求解模型为:Select other affine matching points to establish the world reference system, and obtain the fourth solution model as:
根据所述第三求解模型和所述第四求解模型,得到关于未知数的八个方程为:According to the third solution model and the fourth solution model, it is obtained about the unknown The eight equations are:
通过Gröbner基求解法获得八个方程的代数解,根据所述代数解确定多像机系统第一位姿关系的旋转矩阵R,根据中零空间确定,根据计算得到第二位姿关系中平移向量和第三位姿关系中平移向量。The algebraic solutions of the eight equations are obtained by the Gröbner basis solution method, and the rotation matrix R of the first attitude relationship of the multi-camera system is determined according to the algebraic solutions, according to Medium null space determination ,according to The translation vector in the second pose relationship and the translation vector in the third pose relationship are obtained by calculation.
以下分别以单像机和多相机两种情况进行进一步说明。The following are further descriptions in the case of a single camera and a multi-camera.
单像机Mono camera
选择任意一个仿射匹配点对来定义世界参考系W,如图2所示。假设当前选择了第j个仿射匹配点对,选取第j个仿射匹配点对在三维空间中的位置作为W的原点,且W的坐标轴方向与视图1(图2中View1)一致。将视图1和视图2(图2中View2)之间的位姿关系表示为,将视图1和参考系W之间的位姿关系表示为,视图2和参考系W之间的位姿关系表示为。特别地,,。使用Cayley参数化来表示旋转矩阵,可以表示为:Choose any affine matching point pair to define the world reference frame W, as shown in Figure 2. Assuming that the jth affine matching point pair is currently selected, the position of the jth affine matching point pair in the three-dimensional space is selected as the origin of W, and the coordinate axis direction of W is consistent with view 1 (View1 in Figure 2). The pose relationship between
其中是四元数齐次向量。假设视图1和视图2之间的相对旋转角度是已知的。值得注意的是,相对旋转角度即使在惯性测量单元与像机之间的安装关系未知或存在变化的情况下,它也可以直接由惯性测量单元提供。三个未知数满足以下约束:in is a quaternion homogeneous vector. It is assumed that the relative rotation angle between
其中是两个视图之间的相对旋转角度。in is the relative rotation angle between the two views.
接下来,将和参数化为两个未知深度参数的线性函数:Next, will and parameterized as two unknown depth parameters The linear function of :
两个视图之间的相对运动由两个变换的组合确定:(i)从视图1到W,(ii)从W到视图2。未知数,和被参数化为。形式上,相对运动表示为:The relative motion between the two views is determined by the combination of two transformations: (i) from
本质矩阵可以表示为:The essential matrix can be expressed as:
通过将式带入式可知,本质矩阵中的每项元素都与线性相关。through the formula Bring in It can be seen that each element in the essential matrix is related to Linear correlation.
一个仿射匹配点对能够为几何模型估计提取三个独立的约束,包括一个从同名点对关系导出的对极几何约束和两个从局部仿射变换矩阵导出的仿射变换约束。在像机内参已知的情况下,视图1和视图2之间的对极几何约束如下所示:An affine matched point pair can extract three independent constraints for geometric model estimation, including an epipolar geometric constraint derived from the homonymous point pair relationship and two from the local affine transformation matrix Exported affine transformation constraints. With the camera intrinsics known, the epipolar geometric constraints between
描述本质矩阵与局部仿射变换矩阵的关系的仿射变换约束可以表示如下:Description Essential Matrix with local affine transformation matrix The affine transformation constraints of the relation can be expressed as follows:
其中下标(1:2)表示前两个方程式。where the subscript (1:2) represents the first two equations.
由于已经选择一个仿射匹配点对作为世界参考系的原点来对平移向量进行特殊参数化,发现所选仿射匹配点对中的同名点对应关系不能贡献一个新的约束,因为所得方程的系数都为零。因此,当第j个仿射匹配点对被用于建立世界参考系W时,两个仿射匹配点对能够提供五个方程。具体而言,第j个仿射匹配点对基于式提供两个方程。另一个仿射匹配点对提供了基于式和式的三个方程。通过将式带入到式和式中并使用隐变量方法,可以将两个仿射匹配点对提供的五个方程写为:Since an affine matched point pair has been chosen as the origin of the world reference frame to specifically parameterize the translation vector, it is found that the homonymic point correspondence in the chosen affine matched point pair cannot contribute a new constraint because the coefficients of the resulting equation are all zero. Therefore, when the jth affine matched point pair is used to establish the world reference frame W, two affine matched point pairs can provide five equations. Specifically, the jth affine matching point pair is based on the formula Two equations are provided. Another affine matching point pair provides a Japanese the three equations. through the formula bring-in Japanese and using the latent variable approach, the five equations provided by the two affine matched point pairs can be written as:
其中,中的元素项为未知数,和的二次项。in, The element term in is unknown , and the quadratic term.
在通过惯性测量单元获得两个像机之间的相对旋转角度后,单像机的相对运动估计问题为四个自由度。但是,两个仿射匹配点对可以提供六个独立的约束。这意味着约束的数量大于未知数的数量,并且存在冗余的约束。因此,最少一个仿射匹配点对和一个同名点对就足以估计已知相对旋转角度条件下的单像机相对运动。可以从式中任选三个方程来探索最小解的情况。更具体地说,将第j个仿射匹配点对的两个仿射变换约束和另一个仿射匹配点对的一个对极几何约束进行联立组合,得到具有5个未知数的3个方程,即式的前三个方程:After the relative rotation angle between the two cameras is obtained by the inertial measurement unit, the relative motion estimation problem of a single camera is four degrees of freedom. However, two affine matched point pairs can provide six independent constraints. This means that the number of constraints is greater than the number of unknowns, and there are redundant constraints. Therefore, at least one affine matching point pair and one point pair with the same name is sufficient to estimate the relative motion of the single camera under the condition of known relative rotation angle. can be from the formula Choose three of the equations to explore the case of the minimum solution. More specifically, the simultaneous combination of two affine transformation constraints for the jth affine matching point pair and one epipolar geometric constraint for the other affine matching point pair yields 3 equations with 5 unknowns, Instant The first three equations of :
由于式具有非零解,因此的秩满足。因此,的所有2×2子行列式必须为零。这给出了关于三个未知数的三个方程。due to the formula has a nonzero solution, so rank satisfaction . therefore, All 2x2 sub-determinants of must be zero. This gives about three unknowns the three equations.
总而言之,假设选择第j个仿射匹配点对来建立世界基准系W。由于在最小解情况下需要有两个仿射匹配点对,所以也可以选择另外一个仿射匹配点对来建立世界参考系W。假设选择了第j'个AC,就可以得到一个类似于式的方程组:To summarize, suppose that the jth affine matching point pair is chosen to establish the world reference frame W. Since two affine matching point pairs are required in the case of the minimum solution, another affine matching point pair can also be selected to establish the world reference frame W. Assuming that the j'th AC is selected, an equation similar to system of equations:
将式和式进行联立,就可以得到关于三个未知数的六个方程;general Japanese Simultaneously, we can get about the three unknowns the six equations;
上式为关于的四次方程组。The above formula is about of the quadratic equations.
对于式和组成的多项式方程组,可通过Gröbner基方法获得代数解。为了保持数值稳定性并避免在Gröbner基的计算过程中进行大量运算,在有限场中构造了多项式方程组的随机实例。然后,使用计算机代数系统Macaulay 2来计算Gröbner基。最后,使用自动Gröbner基求解算法找到相应的解。For the formula and consists of a system of polynomial equations, which can be solved algebraically by the Gröbner basis method. In order to maintain numerical stability and avoid extensive computations during the computation of Gröbner basis, the finite field A random instance of a system of polynomial equations is constructed in . The Gröbner basis is then calculated using the computer
上述求解方法最多有20个复数解和尺寸为36×56的消除模板。一旦获得了旋转参数,则立即使用式获得。然后,利用式,通过找到的零空间来确定。接下来,可以通过式计算 和。最后,根据式计算单像机的相对运动。The above solution method has up to 20 complex solutions and elimination templates of size 36×56. Once the rotation parameters are obtained , the immediate use get . Then, using the formula , by finding the null space to determine . Next, it is possible to pass the formula calculate and . Finally, according to the formula Calculate the relative motion of the single camera.
多像机multi camera
选择第j个仿射匹配点对来定义世界参考系W,如图3所示。选取第j个仿射匹配点对在三维空间中的位置作为W的原点,且W的坐标轴方向与视图1(图3中View1)一致。在多像机系统的参考中将的外参数表示为。将视图1和参考系W之间的转换表示为,将视图2(图3中View1)和参考系W之间的转换表示为。注意,,。接下来,对和进行参数化。可以将由Plücker向量描述的线上的所有点参数化为:The jth affine matching point pair is selected to define the world reference frame W, as shown in Figure 3. The position of the jth affine matching point pair in three-dimensional space is selected as the origin of W, and the coordinate axis direction of W is consistent with view 1 (View1 in Figure 3). In the reference to the multi-camera system will be The external parameters are expressed as . Denote the transformation between
其中是单位方向矢量,是矩矢量,是未知深度参数。in is the unit direction vector, is the moment vector, is the unknown depth parameter.
假设选择第j个仿射匹配点对对应的三维空间位置来定义世界参考W的原点。将连接和摄像机的光心的Plücker线表示为。则在视图k中,点满足:Assume that the 3D space position corresponding to the jth affine matching point pair is selected to define the origin of the world reference W. will connect and camera The Plücker line of the optical center is expressed as . Then in view k, point Satisfy:
等效地,也可以表述为:Equivalently, it can also be expressed as:
其中,是像机的序列号,是仿射匹配点对的序列号,是视图的序列号。单位方向向量可以通过计算得出,其中是像机中对应的归一化齐次图像坐标。在这里,将和参数化为两个未知深度参数的线性函数。in, is the serial number of the camera, is the sequence number of the affine matching point pair, is the serial number of the view. unit direction vector able to pass calculated, where camera middle The corresponding normalized homogeneous image coordinates. Here, will and parameterized as two unknown depth parameters the linear function of .
每个仿射匹配点对关联着视图1和视图2中两个透视像机。两个像机之间的相对运动由四个变换的组合确定:(i)从一个透视像机到视图1,(ii)从视图1 到W,(iii)从W到视图2,(iv)从视图2到另一台透视像机。在这四个转换中,(i)和(iv)部分由已知的外参确定。在(ii)和(iii)部分中,存在未知数,和,它们被参数化为。相对运动可以表示为:Each affine matching point pair is associated with two perspective cameras in
每个仿射匹配点对中两个透视像机之间相对运动被表示出来后,本质矩阵可以表示为:The relative motion between the two perspective cameras in each affine matched point pair After being represented, the essential matrix It can be expressed as:
通过将式代入式,本质矩阵中的元素项都与呈线性关系。然后,将式带入到式和式,可以从两个仿射匹配点对中获得五个方程,这些方程来自第j个仿射匹配点对的两个仿射变换约束和另一个仿射匹配点对的三个方程组成。这些方程可以表示为:through the formula Substitute , the element entries in the essential matrix are all the same as a linear relationship. Then, the formula bring-in Japanese , five equations can be obtained from the two affine matched point pairs consisting of two affine transformation constraints for the jth affine matched point pair and three equations for the other affine matched point pair. These equations can be expressed as:
中的元素项均为未知数,,和的二次项。 The elements in are all unknowns , ,and the quadratic term.
在通过惯性测量单元获得两个多像机系统之间的相对旋转角度后,多像机的相对运动估计问题为五个自由度。考虑到两个仿射匹配点对提供六个独立的约束,约束的数量大于未知数,并且存在冗余约束。因此,从式中随机选择四个方程来探索最小解的情况。例如,第j个仿射匹配点对的两个仿射变换约束以及另一个仿射匹配点对的一个对极几何约束和第一个仿射变换约束联立成含有五个未知数中的四个方程,即式的前四个方程:After the relative rotation angle between the two multi-camera systems is obtained by the inertial measurement unit, the relative motion estimation problem of the multi-camera is five degrees of freedom. Considering that two affine matched point pairs provide six independent constraints, the number of constraints is greater than the unknown, and there are redundant constraints. Therefore, from the formula In the case where four equations are randomly selected to explore the minimum solution. For example, two affine transformation constraints for the jth affine matching point pair and an epipolar geometric constraint and the first affine transformation constraint for another affine matching point pair are simultaneously combined into four equations with five unknowns , i.e. The first four equations of :
由于式具有非零解,因此的秩满足。因此,的所有3×3子行列式必须为零。这给出了关于三个未知数的四个方程。due to the formula has a nonzero solution, so rank satisfaction . therefore, All 3x3 sub-determinants of must be zero. This gives about three unknowns of the four equations.
同样,可以选择另一个仿射匹配点对来建立世界参考系W。假设选择了第个仿射匹配点对,可以建立一个类似于式的方程组:Likewise, another affine matching point pair can be chosen to establish the world reference frame W. Suppose you choose the affine matching point pairs, it is possible to establish a formula similar to system of equations:
将式和式进行联立,可以得到关于三个未知数的八个方程;general Japanese Simultaneously, we can get about the three unknowns the eight equations;
这些方程的次数为6。此外,在刚刚的问题中发现了一个额外的约束,即的秩为1。The degree of these equations is 6. Furthermore, an additional constraint was found in the question just now, namely rank is 1.
仿射变换约束为上述问题提供了额外的方程。只有当使用第j个仿射匹配点对来建立世界参考系W时,第j个仿射匹配点对的两个仿射变换约束才用于构造额外方程。因此,对于多像机的相对运动估计问题,存在三个额外的方程:Affine transformation constraints provide additional equations for the above problem. The two affine transformation constraints of the jth affine matching point pair are used to construct additional equations only when the jth affine matching point pair is used to establish the world reference frame W. Therefore, there are three additional equations for the relative motion estimation problem of multi-cameras:
上式为关于的四次方程组。The above formula is about of the quadratic equations.
使用Gröbner基方法进行求解。将式和式中的这些多项式方程分别表示为约束和约束。单独使用约束可用于非交叉或交叉仿射匹配点对条件下的相对运动估计。但是,同时使用和可以减少可能的解的数量。Solve using the Gröbner basis method. general Japanese These polynomial equations in are represented as constraints and constraints . Use constraints alone Can be used for relative motion estimation under the condition of non-cross or cross-affine matched point pairs. However, using both and The number of possible solutions can be reduced.
一旦获得了旋转参数,就可以立即计算得。然后利用式,通过找到的零空间来确定。接下来,可以通过式计算 和。最后,通过组合变换和来计算多像机的相对运动。Once the rotation parameters are obtained , it can be calculated immediately . Then use the formula , by finding the null space to determine . Next, it is possible to pass the formula calculate and . Finally, by combining transformations and to calculate the relative motion of the multi-camera.
本发明可以达到以下的技术效果:The present invention can achieve the following technical effects:
1)本发明针对惯性测量单元直接提供相对旋转角度的条件下,充分利用视图之间的仿射匹配点对信息,极大减少求解单像机和多像机系统相对运动估计问题所需要的点对数量,明显提高了算法的精度及鲁棒性。1) Under the condition that the inertial measurement unit directly provides the relative rotation angle, the present invention makes full use of the affine matching point pair information between the views, and greatly reduces the points required to solve the relative motion estimation problem of the single-camera and multi-camera systems For the number of pairs, the accuracy and robustness of the algorithm are significantly improved.
2)本发明利用惯性测量单元与像机固联安装条件下,惯性测量单元和像机在运动过程中各自的相对旋转角相同这一性质,惯性测量单元输出的相对旋转角可以直接用作像机或多像机的相对旋转角,可应用于惯性测量单元与像机之间的安装关系未知或存在变化等更广泛的场景。2) The present invention utilizes the property that the inertial measurement unit and the camera have the same relative rotation angle during the motion process under the fixed installation condition of the inertial measurement unit and the camera, and the relative rotation angle output by the inertial measurement unit can be directly used as the image. The relative rotation angle of the camera or multi-camera can be applied to a wider range of scenarios where the installation relationship between the inertial measurement unit and the camera is unknown or there are changes.
3)针对惯性测量单元直接提供单像机相对旋转角度的条件下,单像机相对运动具有4个自由度。提出了一种新的单像机相对运动估计最小配置解求解方法,该求解方法通过2个仿射匹配点对可以准确估计出单像机的相对运动。3) Under the condition that the inertial measurement unit directly provides the relative rotation angle of the single camera, the relative motion of the single camera has 4 degrees of freedom. A new method for solving the minimum configuration solution for relative motion estimation of a single camera is proposed, which can accurately estimate the relative motion of a single camera through two affine matching point pairs.
4)针对惯性测量单元直接提供多像机相对旋转角度的条件下,多像机相对运动具有5个自由度。提出了一种新的多像机相对运动估计最小配置解求解方法,该求解方法通过2个交叉或非交叉仿射匹配点对可以准确估计多像机系统的相对运动。4) Under the condition that the inertial measurement unit directly provides the relative rotation angle of the multi-camera, the relative motion of the multi-camera has 5 degrees of freedom. A new method for solving the minimum configuration solution for multi-camera relative motion estimation is proposed, which can accurately estimate the relative motion of the multi-camera system through two cross or non-cross affine matching point pairs.
5)本发明的方法不需要对惯性测量单元与像机进行标定,使得惯性测量单元和像机的融合更加灵活方便,而且提出的方法具有更高的精度和效率,适用于计算能力有限的设备,例如无人机自主导航、自动驾驶汽车和增强现实设备等。5) The method of the present invention does not need to calibrate the inertial measurement unit and the camera, which makes the integration of the inertial measurement unit and the camera more flexible and convenient, and the proposed method has higher precision and efficiency, and is suitable for equipment with limited computing capabilities. , such as autonomous drone navigation, self-driving cars, and augmented reality devices.
本发明对于固联安装惯性测量单元和像机的手机、无人机等电子设备,利用惯性测量单元为像机提供相对旋转角度信息,利用二个仿射匹配点对估计单像机和多像机系统的相对运动过程如下:The invention uses the inertial measurement unit to provide relative rotation angle information for the camera, and uses two affine matching point pairs to estimate the single-camera and multi-image The relative motion process of the machine system is as follows:
1)通过ASIFT和MODS等算法提取像机相对运动中两视图之间的仿射匹配点对,包括同名点对图像坐标和相应领域信息之间的局部仿射矩阵;1) Extract the affine matching point pair between the two views in the relative motion of the camera through algorithms such as ASIFT and MODS, including the local affine matrix between the image coordinates of the point pair with the same name and the corresponding field information;
2)利用与像机固联安装的惯性测量单元直接输出的相对旋转角度信息;2) Use the relative rotation angle information directly output by the inertial measurement unit fixedly installed with the camera;
3)根据两视图之间提取的仿射匹配点对,惯性测量单元输出的相对旋转角度和本发明提出相对运动估计算法,求解单像机和多像机系统之间的相对运动。同时结合RANSAC框架剔除仿射匹配点对中的误匹配点对,并恢复像机的相对运动结果。3) According to the affine matching point pair extracted between the two views, the relative rotation angle output by the inertial measurement unit and the relative motion estimation algorithm proposed by the present invention, the relative motion between the single-camera and multi-camera systems is solved. At the same time, the RANSAC framework is combined to eliminate the incorrect matching point pairs in the affine matching point pairs, and restore the relative motion results of the camera.
以上实施例的各技术特征可以进行任意的组合,为使描述简洁,未对上述实施例中的各个技术特征所有可能的组合都进行描述,然而,只要这些技术特征的组合不存在矛盾,都应当认为是本说明书记载的范围。The technical features of the above embodiments can be combined arbitrarily. In order to make the description simple, all possible combinations of the technical features in the above embodiments are not described. However, as long as there is no contradiction in the combination of these technical features It is considered to be the range described in this specification.
以上所述实施例仅表达了本申请的几种实施方式,其描述较为具体和详细,但并不能因此而理解为对发明专利范围的限制。应当指出的是,对于本领域的普通技术人员来说,在不脱离本申请构思的前提下,还可以做出若干变形和改进,这些都属于本申请的保护范围。因此,本申请专利的保护范围应以所附权利要求为准。The above-mentioned embodiments only represent several embodiments of the present application, and the descriptions thereof are specific and detailed, but should not be construed as a limitation on the scope of the invention patent. It should be pointed out that for those skilled in the art, without departing from the concept of the present application, several modifications and improvements can be made, which all belong to the protection scope of the present application. Therefore, the scope of protection of the patent of the present application shall be subject to the appended claims.
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