CN110838137A - Three-dimensional point cloud rigid body registration method and system based on pseudo Huber loss function - Google Patents
Three-dimensional point cloud rigid body registration method and system based on pseudo Huber loss function Download PDFInfo
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Abstract
The invention relates to a three-dimensional point cloud rigid body registration method and a system based on a pseudo Huber loss function, wherein the registration method comprises the following steps: s1, obtaining a model point cloud P and a data point cloud Q; s2, establishing a three-dimensional point cloud rigid body registration model based on a pseudo Huber loss function according to the model point cloud P and the data point cloud Q; and S3, optimizing the three-dimensional point cloud rigid registration model to obtain a first rigid transformation value between the model point cloud P and the data point cloud Q. According to the method, the three-dimensional point cloud rigid registration model based on the pseudo Huber loss function is established, the pseudo Huber loss function is continuous and conductive, and is insensitive to abnormal points, so that the influence of external points on the registration process can be effectively reduced, and the registration efficiency and precision are improved.
Description
Technical Field
The invention belongs to the field of three-dimensional point cloud data processing, and particularly relates to a three-dimensional point cloud rigid body registration method and system based on a pseudo Huber loss function.
Background
Rigid registration of point cloud is one of the key technologies for three-dimensional point cloud processing, and is a key problem in the research fields of computer vision, image analysis and the like. Most of the existing point cloud registration algorithms assume that two point cloud data are completely the same, and a one-to-one correspondence relationship exists between the two point cloud data, so that the existing point cloud registration algorithm can only solve the rigid body registration problem of completely corresponding point clouds, namely, the point cloud to be registered is a subset or a proper subset of the model point cloud.
However, in the actual point cloud registration problem, the acquired point cloud contains points outside the measurement surface, which are called outer points, due to the influence of physical limitations of the point cloud acquisition sensors, boundaries between three-dimensional features, occlusion, multiple reflections, noise, and the like. Rigid registration of three-dimensional point cloud containing external points is a difficult point and a hot point problem at the present stage. For example, the exact correspondence point cloud registration algorithm proposed by Besl et al based on Iterative Closest Point (ICP); dalley et al uses a threshold metric method to eliminate the interference of outliers in the iterative process, sets the threshold size by calculating the Schultz distance, and eliminates outliers in the point cloud.
Therefore, in the rigid registration process of the three-dimensional point cloud containing the external points, the external points will affect the precision of point cloud registration, thereby resulting in obtaining an erroneous registration result.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a three-dimensional point cloud rigid body registration method and system based on a pseudo Huber loss function. The technical problem to be solved by the invention is realized by the following technical scheme:
the embodiment of the invention provides a three-dimensional point cloud rigid body registration method based on a pseudo Huber loss function, which comprises the following steps:
s1, obtaining a model point cloud P and a data point cloud Q;
s2, establishing a three-dimensional point cloud rigid body registration model based on a pseudo Huber loss function according to the model point cloud P and the data point cloud Q;
and S3, optimizing the three-dimensional point cloud rigid registration model to obtain a first rigid transformation value between the model point cloud P and the data point cloud Q.
In one embodiment of the present invention, the three-dimensional point cloud rigid body registration model is:
s.t.RTR＝I det(R)＝1
wherein b is an abnormal value threshold, R is a rotation matrix, t is a translation vector, c is a spatial correspondence relationship between the model point cloud P and the data point cloud Q, and P is the model point cloud
Point of (1), NpE N, q as a data point cloud
Point of (1), Nq∈N。
In one embodiment of the present invention, step S3 includes:
s31, calculating the spatial corresponding relation between the model point cloud P and the data point cloud Q in the k-th optimization process according to the second rigid body transformation value;
s32, calculating a first rigid body transformation value of the model point cloud P and the data point cloud Q in the k-th optimization process according to the space corresponding relation;
s33, judging whether the optimization meets a preset condition; if not, returning to the step S31; if yes, terminating the optimization;
and S34, outputting the first rigid body transformation value.
In one embodiment of the present invention, the step S32 includes:
s321, updating the model point cloud P and the data point cloud Q according to the spatial correspondence;
s322, calculating a third rigid body transformation value between the updated model point cloud P and the updated data point cloud Q by utilizing a Levenberg-Marquardt algorithm;
and S323, calculating the first rigid body transformation value according to the third rigid body transformation value.
In an embodiment of the present invention, determining whether the optimization satisfies a preset condition includes:
updating the model point cloud P and the data point cloud Q according to the first rigid body transformation value;
determining a first mean square error ε between the updated model point cloud P and the data point cloud QkWhether or not to satisfy epsilonk≤εminWherein, epsilonminIs the second mean square error between the model point cloud P and the data point cloud Q.
In an embodiment of the present invention, determining whether the optimization satisfies a preset condition includes:
judging whether the optimization times k meet the condition that k is more than or equal to kmaxWherein k ismaxFor a preset number of optimizations.
Another embodiment of the present invention provides a three-dimensional point cloud rigid body registration system based on a pseudo Huber loss function, including:
the point cloud acquisition module is used for acquiring a model point cloud P and a data point cloud Q;
the model establishing module is used for establishing a three-dimensional point cloud rigid body registration model based on a pseudo Huber loss function according to the model point cloud P and the data point cloud Q;
and the model optimization module is used for optimizing the three-dimensional point cloud rigid body registration model by using a preset method to obtain a first rigid body transformation value between the model point cloud P and the data point cloud Q.
In one embodiment of the invention, the model optimization module comprises:
the spatial corresponding relation obtaining module is used for calculating the spatial corresponding relation between the model point cloud P and the data point cloud Q in the k-th optimization process according to the second rigid body transformation value;
a rigid body transformation value acquisition module used for calculating a first rigid body transformation value of the model point cloud P and the data point cloud Q in the k-th optimization process according to the space corresponding relation;
the judgment module is used for judging whether the optimization meets a preset condition or not and carrying out continuous optimization or termination optimization on the space corresponding relation and the first rigid body transformation value according to a judgment result;
and the output module is used for outputting the first rigid body transformation value.
In one embodiment of the present invention, the rigid body transformation value obtaining module includes:
the point cloud updating module is used for updating the model point cloud P and the data point cloud Q according to the spatial correspondence;
the first rigid body transformation value acquisition submodule is used for calculating a third rigid body transformation value between the updated model point cloud P and the updated data point cloud Q;
and the second rigid body transformation value acquisition submodule is used for calculating the first rigid body transformation value according to the third rigid body transformation value.
Compared with the prior art, the invention has the beneficial effects that:
according to the invention, by establishing the three-dimensional point cloud rigid registration model based on the pseudo Huber loss function, the pseudo Huber loss function has continuous conductibility and is insensitive to abnormal points, and the influence of external points on the registration process can be effectively reduced, so that the registration efficiency and precision are improved.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Drawings
Fig. 1 is a schematic flow chart of a three-dimensional point cloud rigid body registration method based on a pseudo Huber loss function according to an embodiment of the present invention;
fig. 2 is a schematic flow chart of another three-dimensional point cloud rigid body registration method based on a pseudo Huber loss function according to an embodiment of the present invention;
fig. 3 is a schematic structural diagram of a three-dimensional point cloud rigid body registration system based on a pseudo Huber loss function according to an embodiment of the present invention;
fig. 4 is a schematic structural diagram of another three-dimensional point cloud rigid body registration system based on a pseudo Huber loss function according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to specific examples, but the embodiments of the present invention are not limited thereto.
Example one
The purpose of the rigid registration of the three-dimensional point clouds is to establish a spatial correspondence between the two point clouds and to find an optimal rigid transformation relationship between the two point clouds. Typically, rigid registration of three-dimensional point clouds involves solving two things: (1) establishing a corresponding relation between two point clouds; (2) and solving a rigid body transformation relation between the two point clouds. The rigid body registration process is to solve the two contents simultaneously by using the minimization of a certain measurement function so as to obtain the optimal rigid body transformation relation between two point clouds.
Given two point clouds
And point cloud
Assuming that there is some kind of mapping C from point cloud P to point cloud Q, P → Q, and a rigid transformation T from point cloud P to point cloud Q, the following similarity measure function can be defined:
J(T(P),C(P)) (1)
the point cloud rigid registration process can be regarded as the following optimization problem:
wherein, R is a rotation matrix, and t is a translation vector.
However, in the conventional rigid body registration process, due to the rapid increase of the quadratic curve, the influence of the outer point on the rigid body transformation solving is large, and the registration result error is large. In order to effectively avoid the problem, a pseudo Huber loss function insensitive to the external point is adopted to establish a three-dimensional point cloud rigid body registration model robust to the external point.
Referring to fig. 1, fig. 1 is a schematic flow chart of a three-dimensional point cloud rigid body registration method based on a pseudo Huber loss function according to an embodiment of the present invention. The rigid registration method of the three-dimensional point cloud comprises the following steps:
and S1, acquiring the model point cloud P and the data point cloud Q.
Specifically, the obtained model point cloud P is
Data point cloud Q of
And S2, establishing a three-dimensional point cloud rigid body registration model based on the pseudo Huber loss function according to the model point cloud P and the data point cloud Q.
The pseudo Huber loss function is a smooth version of the Huber function, which has continuous conductibility and can effectively suppress the influence of outliers, and is defined as:
where b is the outlier threshold and a is the residual error. For smaller values of a, the loss function approximates to a/2 values, while for larger values of a, the loss function can approximate to a straight line with a slope of b, and thus is insensitive to outliers.
For the rigid registration problem of the three-dimensional point cloud corresponding to the part containing the external point, the external point can be regarded as an abnormal value, and therefore, a target function of rigid registration can be established by using a pseudo Huber loss function.
For a given two point clouds containing outliers: model point cloud
And data point clouds
The following similarity metric function based on the pseudo Huber loss function and its minimization constraint can be establishedConditions are as follows:
wherein b is an abnormal value threshold, R is a rotation matrix, t is a translation vector, c is a spatial correspondence relationship between the model point cloud P and the data point cloud Q, and P is the model point cloud
Point of (1), NpE N, q as a data point cloud
Point of (1), Nq∈N。
The nonlinear target function (4) is a three-dimensional point cloud rigid body registration model based on a pseudo Huber loss function. Therefore, the rigid body registration problem of the three-dimensional point cloud is converted into the minimum optimization problem of the nonlinear objective function (4).
And S3, optimizing the three-dimensional point cloud rigid registration model to obtain a first rigid transformation value between the model point cloud P and the data point cloud Q. In this embodiment, the rigid body transformation value obtained in each step includes the rotation matrix R and the translational vector t corresponding to the step, and the first rigid body transformation refers to the optimal rigid body transformation. When the three-dimensional point cloud rigid registration model (4) is solved, the corresponding relation and the rigid transformation relation of the point cloud need to be solved at the same time.
Specifically, the first rigid body transformation is solved by an iteration method, so that before iteration is performed, an initialization parameter, that is, a preset iteration number k, is setmax(i.e., maximum number of iterations), second mean square error ε between model point cloud P and data point cloud Qmin(mean square error minimum) and initial value R of rotation matrix0And the initial value t of the translation vector0Let the current iteration number k be 1.
Referring to fig. 2, fig. 2 is a schematic flowchart of another pseudo Huber loss function-based three-dimensional point cloud rigid body registration method according to an embodiment of the present invention. In fig. 2, an iterative method is used to optimize the three-dimensional point cloud rigid registration model, and each iterative process includes two basic steps:
and S31, calculating the spatial corresponding relation between the model point cloud P and the data point cloud Q in the k-th optimization process according to the second rigid body transformation value.
Specifically, the second rigid body transformation value is a rigid body transformation value obtained by the k-1 step of the iterative process: rotation matrix Rk-1And a translation vector tk-1. For the 1 st iteration process, the transformation value of the second rigid body is the initial value R of the rotation matrix0And the initial value t of the translation vector0(ii) a And for the 2 nd step iteration process, the transformation value of the second rigid body is the rotation matrix R obtained by the 1 st step iteration1And a translation vector t1(ii) a And so on.
Further, the spatial correspondence between the model point cloud P and the data point cloud Q in the k-th iteration process
The formula (5) is satisfied:
wherein, i is 1,2, …, Np。
For the solution of the point cloud corresponding relationship in the formula (5), the embodiment adopts a closest point search algorithm based on Delaunay triangulation to implement: firstly, randomly distributed scattered points in a three-dimensional space are connected by straight line segments to form a closely adjacent tetrahedron set which is not overlapped and has no gap in space, and the vertex of each tetrahedron is an original scattered point; then, performing Delaunay triangulation on the model point cloud P, wherein the Delaunay triangulation must meet two basic criteria, namely a hollow circle characteristic and a maximized minimum angle characteristic; on the basis, a triangulation search strategy is adopted to find the corresponding point of the data point cloud Q in the model point cloud P.
And S32, calculating a first rigid body transformation value of the model point cloud P and the data point cloud Q in the k-th optimization process according to the space corresponding relation.
Specifically, the first rigid body transformation value may be calculated using any one of a gaussian-newton iterative algorithm, a particle swarm optimization algorithm, and a Levenberg-Marquardt algorithm. The first rigid body transformation value is preferably calculated using the Levenberg-Marquardt algorithm. The method for calculating the first rigid body transformation value by adopting the Levenberg-Marquardt algorithm specifically comprises the following steps:
s321, obtaining a spatial corresponding relation between the data point cloud Q and the model point cloud P according to the k step iteration
Updating the model point cloud P and the data point cloud Q, wherein the updated model point cloud P isThe updated data point cloud Q is
And S322, calculating a third rigid body transformation value between the updated model point cloud P and the data point cloud Q by utilizing a Levenberg-Marquardt algorithm.
Specifically, a third rigid body transformation value R between the model point cloud P and the data point cloud Q*And t*The following equation is satisfied:
wherein R is*For a rotation matrix between the updated model point cloud P and the data point cloud Q, t*For the translation vector between the updated model point cloud P and the data point cloud Q, R and t satisfy RTR ═ I and det (R) ═ 1.
Specifically, the formula (6) is optimized and solved by adopting a Levenberg-Marquardt algorithm, wherein initial values of R and t in the optimization process of the Levenberg-Marquardt algorithm are respectively set as 3-order unit matrix I3And a 3-dimensional zero-column vector. The third rigid body transformation value R obtained by solving through a Levenberg-Marquardt algorithm*And t*Is the optimal rigid body transformation value.
The Levenberg-Marquardt algorithm is a nonlinear optimization algorithm, and is applied to a three-dimensional point cloud rigid body registration model based on a pseudo Huber loss function, so that the model optimization has higher convergence speed, and the accuracy of an optimization result is higher.
S323, calculating a first rigid body transformation value between the model point cloud P and the data point cloud Q in the k-th iteration process according to the third rigid body transformation value: rotation matrix RkAnd a translation vector matrix tkThe calculation formula is as follows:
Rk＝R*Rk-1，tk＝R*tk-1+t*(7)
wherein R iskRotation matrix for the k-th iteration, tkFor the translation vector of the k-th iteration, Rk-1Rotation matrix for step k-1 iteration, tk-1Is the translation vector of the step (k-1).
S33, judging whether the optimization meets the preset conditions: if yes, terminating the optimization; if not, returning to the step S31, increasing the iteration number k by 1, performing the (k + 1) th iteration, and continuing to optimize the spatial correspondence between the two point clouds and the first rigid body transformation value.
Specifically, as long as the convergence condition satisfies either of the following two conditions, the iteration is terminated, and the rotation matrix R of the k-th iteration is outputkAnd a translation vector matrix tk。
① judging the mean square error epsilon between the model point cloud P and the data point cloud Q after the k step iterationkMinimum mean square error epsilon between model point cloud P and data point cloud Q after rigid body transformationminThe relationship between them.
Specifically, the matrix R is rotated according to the first rigid body transformation valuekAnd a translation vector matrix tkUpdating the model point cloud P and the data point cloud Q, and calculating the mean square error between the updated model point cloud P and the data point cloud Q after the kth iteration
If epsilonk≤εminAnd ending the iteration and finishing the optimization.
② determining the number of iterations k and the maximum number of iterations kmaxThe relationship between them.
If k is not less than kmaxAnd ending the iteration and finishing the optimization.
And S34, outputting the first rigid body transformation value.
Specifically, after the optimization is terminated, outputting a first rigid body transformation value of the kth iteration: rotation matrix RkAnd a translation vector matrix tk，RkAnd tkNamely the optimal rigid body transformation of the model point cloud P and the data point cloud Q.
In the embodiment, the three-dimensional point cloud rigid body registration model based on the pseudo Huber loss function is established, the pseudo Huber loss function has continuous conductivity and is insensitive to abnormal points, and the influence of external points on the registration process can be effectively reduced, so that the registration efficiency and precision are improved. In the process of carrying out optimal registration on the three-dimensional point cloud rigid body registration model based on the pseudo Huber loss function, a Levenberg-Marquardt algorithm is adopted to quickly optimize a target function and improve the registration efficiency.
Example two
Referring to fig. 3, fig. 3 is a schematic structural diagram of a three-dimensional point cloud rigid body registration system based on a pseudo Huber loss function according to an embodiment of the present invention.
The three-dimensional point cloud rigid body registration system comprises:
a point cloud obtaining module for obtaining model point cloudAnd data point clouds
The model establishing module is used for establishing a three-dimensional point cloud rigid body registration model based on a pseudo Huber loss function according to the model point cloud P and the data point cloud Q:
s.t.RTR＝I det(R)＝1
wherein b is an abnormal value threshold value,r is a rotation matrix, t is a translation vector, c is a spatial correspondence of a model point cloud P and a data point cloud Q, and P is the model point cloud
Point of (1), NpE N, q as a data point cloud
Point of (1), Nq∈N。
And the model optimization module is used for optimizing the three-dimensional point cloud rigid registration model to obtain a first rigid transformation value between the model point cloud P and the data point cloud Q.
Further, please refer to fig. 4, fig. 4 is a schematic structural diagram of another three-dimensional point cloud rigid body registration system based on a pseudo Huber loss function according to an embodiment of the present invention. In fig. 4, the model optimization module includes:
the spatial corresponding relation obtaining module is used for calculating the spatial corresponding relation between the model point cloud P and the data point cloud Q in the k-th optimization process according to the second rigid body transformation value;
a rigid body transformation value acquisition module used for calculating a first rigid body transformation value of the model point cloud P and the data point cloud Q in the k-th optimization process according to the space corresponding relation;
the judging module is used for judging whether the optimization meets the preset condition or not and carrying out continuous optimization or termination optimization on the space corresponding relation and the first rigid body transformation value according to the judgment result;
and the output module is used for outputting the first rigid body transformation value after the optimization is terminated.
Further, the rigid body transformation value module comprises:
the point cloud updating module is used for updating the model point cloud P and the data point cloud Q according to the spatial corresponding relation;
the first rigid body transformation value acquisition submodule is used for calculating a third rigid body transformation value between the updated model point cloud P and the data point cloud Q; preferably, a third rigid body transformation value is calculated by using a Levenberg-Marquardt algorithm;
and the second rigid body transformation value acquisition submodule is used for calculating the first rigid body transformation value according to the third rigid body transformation value.
For the registration process of each module to the model point cloud P and the data point cloud Q in the three-dimensional point cloud rigid body registration system based on the pseudo Huber loss function, please refer to embodiment one, which is not described in detail in this embodiment.
The three-dimensional point cloud registration system can effectively reduce the influence of the external points on the registration process, and quickly optimize the objective function, so that the registration precision and efficiency are improved simultaneously.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.
Claims (9)
1. A three-dimensional point cloud rigid body registration method based on a pseudo Huber loss function is characterized by comprising the following steps:
s1, obtaining a model point cloud P and a data point cloud Q;
s2, establishing a three-dimensional point cloud rigid body registration model based on a pseudo Huber loss function according to the model point cloud P and the data point cloud Q;
and S3, optimizing the three-dimensional point cloud rigid registration model to obtain a first rigid transformation value between the model point cloud P and the data point cloud Q.
2. The pseudo Huber loss function based three-dimensional point cloud rigid body registration method of claim 1, wherein the three-dimensional point cloud rigid body registration model is:
s.t.RTR＝I det(R)＝1
wherein b is an abnormal valueA threshold value, R is a rotation matrix, t is a translation vector, c is a spatial correspondence relation between the model point cloud P and the data point cloud Q, and P is the model point cloud
Point of (1), NpE N, q as a data point cloud
Point of (1), Nq∈N。
3. The pseudo Huber loss function based three-dimensional point cloud rigid body registration method of claim 1, wherein step S3 comprises:
s31, calculating the spatial corresponding relation between the model point cloud P and the data point cloud Q in the k-th optimization process according to the second rigid body transformation value;
s32, calculating a first rigid body transformation value of the model point cloud P and the data point cloud Q in the k-th optimization process according to the space corresponding relation;
s33, judging whether the optimization meets a preset condition; if not, returning to the step S31; if yes, terminating the optimization;
and S34, outputting the first rigid body transformation value.
4. The pseudo Huber loss function based three-dimensional point cloud rigid body registration method of claim 3, wherein the step S32 comprises:
s321, updating the model point cloud P and the data point cloud Q according to the spatial correspondence;
s322, calculating a third rigid body transformation value between the updated model point cloud P and the updated data point cloud Q by utilizing a Levenberg-Marquardt algorithm;
and S323, calculating the first rigid body transformation value according to the third rigid body transformation value.
5. The pseudo Huber loss function based three-dimensional point cloud rigid body registration method of claim 3, wherein judging whether optimization meets a preset condition comprises:
updating the model point cloud P and the data point cloud Q according to the first rigid body transformation value;
determining a first mean square error ε between the updated model point cloud P and the data point cloud QkWhether or not to satisfy epsilonk≤εminWherein, epsilonminIs the second mean square error between the model point cloud P and the data point cloud Q.
6. The pseudo Huber loss function based three-dimensional point cloud rigid body registration method of claim 5, wherein judging whether optimization meets a preset condition comprises:
judging whether the optimization times k meet the condition that k is more than or equal to kmaxWherein k ismaxFor a preset number of optimizations.
7. A three-dimensional point cloud rigid body registration system based on a pseudo Huber loss function is characterized by comprising the following components:
the point cloud acquisition module is used for acquiring a model point cloud P and a data point cloud Q;
the model establishing module is used for establishing a three-dimensional point cloud rigid body registration model based on a pseudo Huber loss function according to the model point cloud P and the data point cloud Q;
and the model optimization module is used for optimizing the three-dimensional point cloud rigid body registration model to obtain a first rigid body transformation value between the model point cloud P and the data point cloud Q.
8. The pseudo Huber loss function based three-dimensional point cloud rigid body registration system of claim 7, wherein the model optimization module comprises:
the spatial corresponding relation obtaining module is used for calculating the spatial corresponding relation between the model point cloud P and the data point cloud Q in the k-th optimization process according to the second rigid body transformation value;
a rigid body transformation value acquisition module used for calculating a first rigid body transformation value of the model point cloud P and the data point cloud Q in the k-th optimization process according to the space corresponding relation;
the judgment module is used for judging whether the optimization meets a preset condition or not and carrying out continuous optimization or termination optimization on the space corresponding relation and the first rigid body transformation value according to a judgment result;
and the output module is used for outputting the first rigid body transformation value.
9. The pseudo Huber loss function based three-dimensional point cloud rigid body registration system of claim 8, wherein the rigid body transformation value obtaining module comprises:
the point cloud updating module is used for updating the model point cloud P and the data point cloud Q according to the spatial correspondence;
the first rigid body transformation value acquisition submodule is used for calculating a third rigid body transformation value between the updated model point cloud P and the updated data point cloud Q;
and the second rigid body transformation value acquisition submodule is used for calculating the first rigid body transformation value according to the third rigid body transformation value.
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| CN111951307A (en) * | 2020-07-23 | 2020-11-17 | 西北大学 | Three-dimensional point cloud affine registration method and system based on pseudo Huber loss function |
| CN111951307B (en) * | 2020-07-23 | 2023-09-19 | 西北大学 | Three-dimensional point cloud affine registration method and system based on pseudo Huber loss function |
| CN113192111A (en) * | 2021-03-24 | 2021-07-30 | 西北大学 | Three-dimensional point cloud similarity registration method |
| CN113192111B (en) * | 2021-03-24 | 2024-02-02 | 西北大学 | Three-dimensional point cloud similarity registration method |
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