CN113192111A - Three-dimensional point cloud similarity registration method - Google Patents
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Abstract
The invention discloses a three-dimensional point cloud similar registration method, which comprises the following steps: obtaining a shape point cloud and a model point cloud, establishing a similar registration optimization model and initializing parameters; obtaining initial values of size factors, initial values of rotation matrixes in rigid body transformation and initial values of translation vectors by using a similar registration optimization model; obtaining a plurality of values by using the size factor, and performing rigid body registration and iteration by using each value to obtain an optimal rotation matrix and a translation vector corresponding to each value; and performing scale factor refinement iteration according to the optimal rotation matrix and translation vector corresponding to each value to obtain the optimal scale factor and the final rotation matrix and translation vector. The three-dimensional point cloud similarity registration method can effectively inhibit the influence of external points and noise and improve the similarity registration accuracy.
Description
Technical Field
The invention belongs to the technical field of three-dimensional point cloud data processing, and particularly relates to a three-dimensional point cloud similar registration method which is particularly suitable for similar registration under the condition that three-dimensional point cloud data contains a large number of noise points and external points.
Background
The three-dimensional image acquisition equipment can only obtain three-dimensional data of one side face of an object at a time, and in order to obtain the whole three-dimensional data of the object, the three-dimensional data needs to be obtained from multiple angles and is registered. For the three-dimensional point cloud registration problem, not only rotation and translation transformation but also scale transformation often exist between point clouds to be registered, which is the similar registration problem. Similar registration is a very important registration problem because the similar registration problem exists in a large amount in data such as medical images, satellite remote sensing images and the like. Most of the existing similar registration methods have the problem of application limitation or poor precision, for example, Ying et al combines a scale factor into an Iterative Closest Point (ICP) algorithm, converts the registration problem into a constraint optimization problem on a 7D nonlinear space, and then adopts a Singular Value Decomposition (SVD) method to iteratively solve the optimization problem. However, the algorithm is difficult to apply to similar registration of actual point cloud data in the presence of a large amount of noise and outliers.
Most of the existing three-dimensional point cloud similar registration algorithms have poor registration accuracy and application limitation, for example, the registration accuracy of the three-dimensional point cloud containing a large amount of noise and external points is poor. Due to the influence of factors such as physical limitation and noise of point cloud data acquisition equipment, a large amount of noise and foreign points exist in the acquired point cloud, so that the similar registration accuracy of the point cloud is influenced, and even an incorrect registration result is obtained.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a three-dimensional point cloud similar registration method. The technical problem to be solved by the invention is realized by the following technical scheme:
the invention provides a three-dimensional point cloud similar registration method, which comprises the following steps:
s1: obtaining a shape point cloud and a model point cloud, establishing a similar registration optimization model and initializing parameters;
s2: obtaining initial values of size factors, initial values of rotation matrixes in rigid body transformation and initial values of translation vectors by using the similar registration optimization model;
s3: obtaining a plurality of values by using the size factor, and performing rigid body registration solving and iteration by using each value to obtain an optimal rotation matrix and a translation vector corresponding to each value;
s4: and performing scale factor refinement iteration according to the optimal rotation matrix and translation vector corresponding to each value to obtain the optimal scale factor and the final rotation matrix and translation vector.
In an embodiment of the present invention, the S1 includes:
s11: obtaining a shape point cloud
And model point clouds
Wherein N ispAs the number of points in the shape point cloud, NqThe point number of the model point cloud is taken as the point number;
s12: establishing a three-dimensional point cloud similar registration optimization model based on a pseudo Huber loss function according to the shape point cloud and the model point cloud:
s.t.RTR＝I3，det(R)＝1
wherein s is the scaleFactor, R is the rotation matrix, t is the translation vector, piIs the three-dimensional coordinate, m, of the ith point in the shape point cloudc(i)Is the ith point p in the shape point cloudiOptimal corresponding point in model point cloud, b is outer point threshold, I3An identity matrix of order 3;
s13: setting maximum iteration number k of rigid body registrationmaxRefining the scale factor by the maximum iteration number nmaxMinimum mean square error epsilon between point clouds after rigid body transformationminAnd the minimum mean square error value of the similarity transformation ε sminAnd making the initial value k of the rigid body registration iteration number equal to 1, and making the initial value n of the scale factor refinement iteration number equal to 1.
In an embodiment of the present invention, the S2 includes:
s21: performing similarity transformation on the model point cloud M to obtain a shape point cloud P after the similarity transformation:
wherein s is a scale factor, R is a rotation matrix, and t is a translation vector;
s22: calculating by using the model point cloud M and the shape point cloud P after similarity transformation to obtain an initial value of the size factor:
wherein p isgAnd mgThe center of gravity, P, of the shape point cloud P and the model point cloud M, respectivelywAnd mwRespectively the centroids of the shape point cloud P and the model point cloud M;
s23: calculating and obtaining an initial value R of the rotation matrix R by utilizing a principal component analysis method0And an initial value t of the translation vector t0。
In an embodiment of the present invention, the S3 includes:
s31: using expressions
Let n equal to 1, according to the initial value s of the size factor0Obtaining a plurality of values
S32: for the plurality of values
Carrying out rigid transformation solving on the shape point cloud P and the model point cloud M to obtain each value
A corresponding optimal rotation matrix and an optimal translation vector.
In an embodiment of the present invention, the S32 includes:
s321: according to the current value
Calculating the space corresponding relation between the shape point cloud P after the similarity transformation of the kth iteration and the model point cloud M
Satisfies the following conditions:
wherein, i is 1,2, …, NpK has an initial value of 1, ck(i) Representing the c-th in the model point cloud in the k-th iterationk(i) Point, mjIs piCorresponding points in the model point cloud M;
s322: according to the spatial corresponding relation obtained after the k-th iteration
Calculating relative rigid body transformation R between two iterations of shape point cloud P and model point cloud M*And t*The calculation formula is as follows:
wherein R is*Representing the relative rotation matrix between two adjacent iterations, t*Representing a relative translation matrix between two adjacent iterations;
s323: using said relative rigid body to transform R*And t*Updating rigid body transformation R of kth iterationkAnd tk：
Rk＝R*Rk-1，tk＝R*tk-1+t*；
S324: computing rigid body transformations R for the kth iterationkAnd tkMean square error of the post-shape point cloud Q and the model point cloud M:
s325: judging epsilonk≤εminOr k is not less than kmaxIf not, making k +1 and returning to step S321 for iteration, if yes, determining the current rigid body transformation matrix RkAnd tkFor optimal rigid transformation of the similarity transformed shape point cloud and model point cloud, where εminIs the minimum mean square error, k, of the shape point cloud and the model point cloud after rigid body transformationmaxRegistering the maximum iteration times for the rigid body;
s326: repeating the steps S321 to S325 to obtain the residual value
A corresponding optimal rotation matrix and an optimal translation vector.
In an embodiment of the present invention, the S4 includes:
s41: the mean square error of each set of similarity transforms is calculated:
wherein the content of the first and second substances,
expressing the square of a two-norm;
s42: in that
Finding out and obtaining mean square error epsilon slMinimum size factor sl minAnd corresponding mean square error slA rotation matrix and a translation vector;
s43: judging ε sl≤εsminOr n is more than or equal to nmaxIf the determination is not true, the process returns to S31 to let n +1, S0Is the mean square error ε S in step S42lMinimum size factor sl minIteration is carried out, if so, the scale factor s solved by the current iteration is outputl minAnd its corresponding rotational matrix and translation vector.
Another aspect of the present invention provides a storage medium, in which a computer program is stored, the computer program being used for executing the steps of the three-dimensional point cloud similar registration method described in any one of the above embodiments.
Yet another aspect of the present invention provides an electronic device, including a memory and a processor, where the memory stores a computer program, and the processor, when calling the computer program in the memory, implements the steps of the three-dimensional point cloud similar registration method as described in any one of the above embodiments.
Compared with the prior art, the invention has the beneficial effects that:
according to the three-dimensional point cloud similar registration method, the pseudo Huber loss function is introduced into the three-dimensional point cloud similar registration optimization model, and the pseudo Huber loss function has an inhibiting effect on both noise and an external point, so that the similar registration accuracy can be effectively improved.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Drawings
Fig. 1 is a flow chart of a three-dimensional point cloud similar registration method according to an embodiment of the present invention;
fig. 2 is a detailed flowchart of a three-dimensional point cloud similarity registration method according to an embodiment of the present invention.
Detailed Description
In order to further explain the technical means and effects of the present invention adopted to achieve the predetermined invention purpose, the following describes in detail a three-dimensional point cloud similarity registration method according to the present invention with reference to the accompanying drawings and the detailed description.
The foregoing and other technical matters, features and effects of the present invention will be apparent from the following detailed description of the embodiments, which is to be read in connection with the accompanying drawings. The technical means and effects of the present invention adopted to achieve the predetermined purpose can be more deeply and specifically understood through the description of the specific embodiments, however, the attached drawings are provided for reference and description only and are not used for limiting the technical scheme of the present invention.
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that an article or device that comprises a list of elements does not include only those elements but may include other elements not expressly listed. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of additional like elements in the article or device comprising the element.
Referring to fig. 1 and fig. 2, fig. 1 is a block flow diagram of a three-dimensional point cloud similarity registration method according to an embodiment of the present invention; fig. 2 is a detailed flowchart of a three-dimensional point cloud similarity registration method according to an embodiment of the present invention. The three-dimensional point cloud similar registration method comprises the following steps:
s1: obtaining a shape point cloud and a model point cloud, establishing a similar registration optimization model and initializing parameters;
step S1 specifically includes:
s11: obtaining a shape point cloud
And model point clouds
Wherein N ispNumber of points, N, of the shape point cloud PmNumber of points of model point cloud M, Np∈N，NmE is N, and N represents a natural number set;
s12: and establishing a three-dimensional point cloud similar registration optimization model based on a pseudo Huber loss function according to the shape point cloud P and the model point cloud M.
The purpose of three-dimensional point cloud similarity registration is to establish a spatial correspondence between two point clouds and to find an optimal similarity transformation between the two point clouds. After the scale factor is found, the similar registration problem is transformed into a rigid body registration problem. The three-dimensional point cloud rigid body registration generally includes two contents: (1) establishing a corresponding relation between two point clouds; (2) and solving rigid body transformation between the two point clouds.
Given shape point cloud
And model point clouds
Assuming that there is some kind of mapping C from the shape point cloud P to the model point cloud M, P → M, and a similarity transformation T from the shape point cloud P to the model point cloud M, a similarity measure function can be defined as follows:
J(T(P),C(P))，
the point cloud similarity registration process can be regarded as an optimization problem as follows:
wherein s is a scale factor, R is a rotation matrix, and t is a translation vector.
In the embodiment, a pseudo Huber loss function which is insensitive to noise and external points is introduced to establish a robust three-dimensional point cloud similar registration optimization model, so that the influence of the noise and the external points on a registration result is suppressed, and the precision of similar registration is improved.
The pseudo Huber loss function is a smooth version of the Huber function, which is continuously conductive and can effectively suppress the effects of noise and outliers, and is defined as:
where b is the outlier threshold and a is the error. For smaller values of a, the loss function approximates to a/2, while for larger values of a, the loss function can approximate to a straight line with slope b, and thus is insensitive to noise and outliers.
For the problem of similar registration of three-dimensional point clouds containing noise and external points, the noise and external points can be regarded as abnormal values, and the influence of the noise and the external points on the registration process can be effectively reduced by establishing a target function of the similar registration by utilizing a pseudo Huber loss function, so that the registration efficiency and precision are improved. Thus, for two point clouds P and M containing noise and outliers, a similar registration optimization model based on a pseudo Huber loss function can be built as follows:
s.t.RTR＝I3，det(R)＝1
where s is a scale factor, R is a rotation matrix, t is a translation vector, piIs the three-dimensional coordinate, m, of the ith point in the shape point cloudc(i)Is the ith point p in the shape point cloudiOptimal corresponding point in model point cloud, b is outer point threshold, I3An identity matrix of order 3 is represented.
Therefore, the three-dimensional point cloud similarity registration problem is converted into a minimization optimization problem of a nonlinear objective function.
S13: setting maximum iteration number k of rigid body registrationmaxRefining the scale factor by the maximum iteration number nmaxMinimum mean square error epsilon between point clouds after rigid body transformationminAnd the minimum mean square error value of the similarity transformation ε sminAnd making the initial value k of the rigid body registration iteration number equal to 1, and making the initial value n of the scale factor refinement iteration number equal to 1.
S2: obtaining initial values of size factors, initial values of rotation matrixes in rigid body transformation and initial values of translation vectors by using the similar registration optimization model;
in this embodiment, step S2 specifically includes:
s21: performing similarity transformation on the model point cloud M to obtain a shape point cloud P after the similarity transformation:
where s is a scale factor, R is a rotation matrix, t is a translation vector, NmThe number of points in the model point cloud M;
s22: and calculating by using the model point cloud M and the shape point cloud P after the similarity transformation to obtain an initial value of the size factor.
In the similarity transformation of the point clouds, the relative distance between the barycenter and the barycenter of the same point cloud is changed in proportion, and under the similarity transformation of different scale factors, the relative distance ratio is the scale factor. Due to the influence of noise and foreign points, the positions of the center of gravity and the center of mass can be changed, and the result is not accurate, so that the initial value of the scale factor is obtained by calculating the distance ratio of the center of gravity and the center of mass of the three-dimensional point cloud, and then the scale factor is solved in a refined manner in an iteration mode.
Giving a model point cloud M, wherein the point cloud after similarity transformation is P, and the centroids of the shape point cloud P and the model point cloud M are respectively assumed to be PgAnd mgThe centroid is respectively pwAnd mwIt is possible to obtain:
wherein the content of the first and second substances,
riis the distance of each point in the three-dimensional point cloud to the centroid.
The initial value of the scale factor s is:
s23: calculating and obtaining an initial value R of the rotation matrix R by utilizing a principal component analysis method0And an initial value t of the translation vector t0。
Specifically, the present embodiment employs Principal Component Analysis (PCA) to solve the initial value of the rigid body transformation. Firstly, calculating a covariance matrix and a mean value of two to-be-registered three-dimensional point clouds, solving a characteristic vector by using the covariance matrix, then establishing a three-dimensional coordinate system of the two to-be-registered point clouds by using the mean value as an origin and the characteristic vector as a coordinate axis, and solving an initial value R of a rotation matrix R in rigid body transformation by aligning the three-dimensional coordinate system0And the initial value t of the translation vector t0。
S3: obtaining a plurality of values by using the size factor, and performing rigid body registration solving and iteration by using each value to obtain an optimal rotation matrix and a translation vector corresponding to each value;
when the three-dimensional point cloud similar registration optimization model is solved, the scale factor s is solved iteratively in a coarse-to-fine mode. Carrying out rigid body transformation solving on each value through a plurality of values corresponding to the given scale factor, and solving through errorsAnd comparing to obtain the optimal similarity transformation. After a scale factor s is given, the similar registration problem is converted into a rigid body registration problem, so that the similar registration optimization model is solved, and the important point is to solve the rigid body transformation. Giving initial values of rigid body transformation R0And t0Thereafter, the present embodiment solves the optimal rigid body transformation by an iterative method.
Step S3 specifically includes:
s31: using expressions
Let n equal to 1, according to the initial value s of the size factor0Obtaining a plurality of values
When the scale factor refinement iteration is started, the initial value s of the scale factor s is used0Obtaining a group of values arranged according to an arithmetic progression, wherein the first value is
The last value is
The difference between adjacent values is
Thereby obtaining m values.
For example, in the first iteration, n is 1, where the first value is 0 and the last value is 2s0The difference between adjacent values is
Thereby obtaining 20 values arranged in an arithmetic progression.
S32: for the plurality of values
Carrying out rigid transformation solving on the shape point cloud Q and the model point cloud M to obtainGet each value
A corresponding optimal rotation matrix and an optimal translation vector.
Specifically, step S32 includes:
s321: according to the current value
Calculating the space corresponding relation between the shape point cloud P after the similarity transformation of the kth iteration and the model point cloud M
Satisfies the following conditions:
wherein, i is 1,2, …, NpK has an initial value of 1, ck(i) Representing the c-th in the model point cloud in the k-th iterationk(i) Point, mjIs piCorresponding points in the model point cloud M;
specifically, for solving the spatial correspondence between the shape point cloud P and the model point cloud M in the above formula, the present embodiment is implemented by using a closest point search algorithm based on Delaunay triangulation. Randomly distributed scattered points in a three-dimensional space are connected by straight line segments to form a close-proximity tetrahedron set which is not overlapped and has no gap in space, and the vertex of each tetrahedron is the original scattered point. The shape point cloud P is subjected to Delaunay triangulation, and 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 model point clouds
Shape point cloud after similarity transformation
The corresponding point in (1).
S322: according to the spatial corresponding relation obtained after the k-th iteration
Calculating relative rigid body transformation R between two iterations of shape point cloud P and model point cloud M*And t*The calculation formula is as follows:
wherein R is*Representing the relative rotation matrix between two adjacent iterations, t*A relative translation matrix between two adjacent iterations is represented.
The LM (Levenberg Marquarelt) algorithm is an algorithm for iteratively solving the extreme value of a function, and the convergence rate of the algorithm is high. In the embodiment, the LM algorithm is adopted to carry out optimization solution on the above formula, and the LM algorithm can be used for solving to obtain the relative rigid body transformation R between the shape point cloud P and the model point cloud M in two iterations*And t*。
S323: using said relative rigid body to transform R*And t*Updating rigid body transformation R of kth iterationkAnd tk：
Rk＝R*Rk-1，tk＝R*tk-1+t*；
S324: computing rigid body transformations R for the kth iterationkAnd tkMean square error of the post-shape point cloud P and the model point cloud M:
s325: judging epsilonk≤εminOr k is not less than kmaxIf not, k is set to k +1 and the process returns to step S321 to iterate, and if so, the current rigid transformation matrix R is determinedkAnd tkFor optimal rigid transformation of the similarity transformed shape point cloud and model point cloud, where εminFor shape points after rigid body transformationMinimum mean square error, k, of cloud and model point cloudmaxRegistering the maximum iteration times for the rigid body;
in particular, the values are found by iteration in the above-mentioned steps
When the corresponding optimal rotation matrix and the optimal translation vector are used, the iteration number is k, the initial value is 1, and after the k iterations, if epsilon isk≤εminOr k is not less than kmaxIf true, determining the current rigid body transformation matrix RkAnd tkTo take a value
A corresponding optimal rotation matrix and an optimal translation vector.
S326: repeating the steps S321 to S325 to obtain the residual value
A corresponding optimal rotation matrix and an optimal translation vector.
In particular, for the remaining values
According to the iterative process from step S321 to step S325, the optimal rotation matrix and the optimal translation vector corresponding to each other can be obtained.
S4: and performing scale factor refinement iteration according to the optimal rotation matrix and translation vector corresponding to each value to obtain the optimal scale factor and the corresponding rotation matrix and translation vector.
In this embodiment, step S4 specifically includes:
s41: the mean square error of each set of similarity transforms is calculated:
wherein the content of the first and second substances,
s42: in that
Finding out and obtaining mean square error epsilon slMinimum value slAnd corresponding mean square error slA rotation matrix and a translation vector;
s43: judging ε sl≤εsminOr n is more than or equal to nmaxIf the determination is not true, the process returns to S31 to let n +1, S0Is the mean square error ε S in step S42lMinimum size factor sl minIteration is carried out, if so, the scale factor s solved by the current iteration is outputl minAnd its corresponding rotational matrix and translation vector.
Specifically, after all values corresponding to the current scale factor are subjected to similarity transformation solving, the mean square error corresponding to each value is obtained, and the obtained mean square error epsilon s is found outlMinimum value sl minAnd corresponding mean square error slRotation matrix and translation vector if ε s is satisfiedl≤εsminOr n is more than or equal to nmaxThen the current value sl minThe corresponding rigid body transformation and translation vector are the final rotation matrix and translation vector of the point cloud matching calculated by the three-dimensional point cloud similar registration method of this embodiment.
If ε s is not satisfiedl≤εsminOr n is more than or equal to nmaxThen, the process returns to S31 to make n equal to n +1, S0Instead, the mean square error ε S in step S42lMinimum size factor sl minAnd performing iteration. For example, when the scale factor refinement is iterated, the process returns to S31, where n is 2 and S is taken0Get sl minAnd performing iterative processing until epsilon s is satisfiedl≤εsminOr n is more than or equal to nmax。
In summary, aiming at the similar registration problem under the condition that the three-dimensional point cloud data contains a large amount of noise and external points, the embodiment of the invention provides a three-dimensional point cloud similar registration method based on a pseudo Huber loss function. In addition, on the basis of establishing a three-dimensional point cloud similar registration optimization model, the embodiment of the invention solves an initial scale factor according to the scale consistency, converts the similar registration problem into a rigid body registration problem, iteratively solves a rigid body transformation matrix and a translation vector according to a scale factor value interval, and finally gives an optimal rigid body transformation and a scale factor. According to the three-dimensional point cloud similar registration method, the pseudo Huber loss function has an inhibiting effect on both noise and an external point, so that the similar registration accuracy can be effectively improved.
Yet another embodiment of the present invention provides a storage medium, in which a computer program is stored, the computer program being used for executing the steps of the three-dimensional point cloud similarity registration method described in the above embodiments. Yet another aspect of the present invention provides an electronic device, including a memory and a processor, where the memory stores a computer program, and the processor implements the steps of the three-dimensional point cloud similar registration method according to the above embodiment when calling the computer program in the memory. Specifically, the integrated module implemented in the form of a software functional module may be stored in a computer readable storage medium. The software functional module is stored in a storage medium and includes several instructions to enable an electronic device (which may be a personal computer, a server, or a network device) or a processor (processor) to execute some steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
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 (8)
1. A three-dimensional point cloud similarity registration method is characterized by comprising the following steps:
s1: obtaining a shape point cloud and a model point cloud, establishing a similar registration optimization model and initializing parameters;
s2: obtaining initial values of size factors, initial values of rotation matrixes in rigid body transformation and initial values of translation vectors by using the similar registration optimization model;
s3: obtaining a plurality of values by using the size factor, and performing rigid body registration solving and iteration by using each value to obtain an optimal rotation matrix and a translation vector corresponding to each value;
s4: and performing scale factor refinement iteration according to the optimal rotation matrix and translation vector corresponding to each value to obtain the optimal scale factor and the final rotation matrix and translation vector.
2. The three-dimensional point cloud similar registration method according to claim 1, wherein the S1 includes:
s11: obtaining a shape point cloud
And model point clouds
Wherein N ispAs the number of points in the shape point cloud, NmThe point number of the model point cloud is taken as the point number;
s12: establishing a three-dimensional point cloud similar registration optimization model based on a pseudo Huber loss function according to the shape point cloud and the model point cloud:
s.t.RTR＝I3，det(R)＝1
where s is a scale factor, R is a rotation matrix, t is a translation vector, piIs the three-dimensional coordinate, m, of the ith point in the shape point cloudc(i)Is the ith point p in the shape point cloudiOptimal corresponding point in model point cloud, b is outer point threshold, I3An identity matrix of order 3;
s13: setting maximum iteration number k of rigid body registrationmaxRefining the scale factor by the maximum iteration number nmaxMinimum mean square error epsilon between point clouds after rigid body transformationminAnd the minimum mean square error value of the similarity transformation ε sminAnd making the initial value k of the rigid body registration iteration number equal to 1, and making the initial value n of the scale factor refinement iteration number equal to 1.
3. The three-dimensional point cloud similar registration method according to claim 2, wherein the S2 includes:
s21: performing similarity transformation on the model point cloud M to obtain a shape point cloud P after the similarity transformation:
wherein s is a scale factor, R is a rotation matrix, and t is a translation vector;
s22: calculating by using the model point cloud M and the shape point cloud P after similarity transformation to obtain an initial value of the size factor:
wherein p isgAnd mgThe center of gravity, P, of the shape point cloud P and the model point cloud M, respectivelywAnd mwRespectively the centroids of the shape point cloud P and the model point cloud M;
s23: calculating and obtaining an initial value R of the rotation matrix R by utilizing a principal component analysis method0And an initial value t of the translation vector t0。
4. The three-dimensional point cloud similar registration method according to claim 3, wherein the S3 includes:
s31: using expressions
Let n equal to 1, according to the initial value s of the size factor0Obtaining a plurality of values
S32: for the plurality of values
Carrying out rigid transformation solving on the shape point cloud P and the model point cloud M to obtain each value
A corresponding optimal rotation matrix and an optimal translation vector.
5. The three-dimensional point cloud similar registration method according to claim 4, wherein the S32 includes:
s321: according to the current value
Calculating the space corresponding relation between the shape point cloud P after the similarity transformation of the kth iteration and the model point cloud M
Satisfies the following conditions:
wherein, i is 1,2, …, NpK has an initial value of 1, ck(i) Representing the c-th in the model point cloud in the k-th iterationk(i) Point, mjIs piCorresponding points in the model point cloud M;
s322: according to the spatial corresponding relation obtained after the k-th iteration
Calculating relative rigid body transformation R between two iterations of shape point cloud P and model point cloud M*And t*The calculation formula is as follows:
wherein R is*Representing the relative rotation matrix between two adjacent iterations, t*Representing a relative translation matrix between two adjacent iterations;
s323: using said relative rigid body to transform R*And t*Updating rigid body transformation R of kth iterationkAnd tk：
Rk＝R*Rk-1，tk＝R*tk-1+t*；
S324: computing rigid body transformations R for the kth iterationkAnd tkMean square error of the post-shape point cloud Q and the model point cloud M:
s325: judging epsilonk≤εminOr k is not less than kmaxIf not, making k +1 and returning to step S321 for iteration, if yes, determining the current rigid body transformation matrix RkAnd tkFor optimal rigid transformation of the similarity transformed shape point cloud and model point cloud, where εminIs the minimum mean square error, k, of the shape point cloud and the model point cloud after rigid body transformationmaxRegistering the maximum iteration times for the rigid body;
s326: repeating the steps S321 to S325 to obtain the residual value
A corresponding optimal rotation matrix and an optimal translation vector.
6. The three-dimensional point cloud similar registration method according to claim 5, wherein the S4 includes:
s41: the mean square error of each set of similarity transforms is calculated:
wherein the content of the first and second substances,
s42: in that
Finding out and obtaining mean square error epsilon slMinimum size factor slminAnd corresponding mean square error slA rotation matrix and a translation vector;
s43: judging ε sl≤εsminOr n is more than or equal to nmaxIf the determination is not true, the process returns to S31 to let n +1, S0Instead, the mean square error ε S in step S42lMinimum size factor slminIteration is carried out, if so, the scale factor s solved by the current iteration is outputlminAnd its corresponding rotational matrix and translation vector.
7. A storage medium, characterized in that the storage medium has stored therein a computer program for executing the steps of the three-dimensional point cloud similarity registration method of any one of claims 1 to 6.
8. An electronic device, characterized by comprising a memory and a processor, wherein the memory stores a computer program, and the processor realizes the steps of the three-dimensional point cloud similar registration method according to any one of claims 1 to 6 when the processor calls the computer program in the memory.
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