CN113192111B - Three-dimensional point cloud similarity registration method - Google Patents
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Abstract
The invention discloses a three-dimensional point cloud similarity 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 an initial value of a size factor and an initial value of a rotation matrix and an initial value of a translation vector in rigid body transformation by using a similar registration optimization model; obtaining a plurality of values by using a size factor, and carrying out rigid registration and iteration by using each value to obtain an optimal rotation matrix and a translation vector corresponding to each value; and carrying out 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 similar registration method can effectively inhibit the influence of external points and noise and improve the accuracy of similar registration.
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 a large number of noise points and outliers are contained in three-dimensional point cloud data.
Background
The three-dimensional image acquisition device can only obtain three-dimensional data of one side surface of the object at a time, and in order to obtain the whole three-dimensional data of the object, three-dimensional data are required to be obtained from multiple angles and registered. For the three-dimensional point cloud registration problem, not only rotation and translation transformation exists between the point clouds to be registered, but also scale transformation is often included, and the problem is similar registration. Since similar registration problems exist in a large number of data such as medical images, satellite telemetry images, etc., similar registration is a very important class of registration problems. Most of the existing similar registration methods have problems of application limitation or poor precision, such as that by using Ying et al, scale factors are combined into an iterative closest point (Iterative closest point, ICP) algorithm, the registration problem is converted into a constraint optimization problem on a 7D nonlinear space, and a singular value decomposition (Singular value decomposition, SVD) method is adopted to iteratively solve the optimization problem. However, this algorithm is difficult to apply in similar registration of actual point cloud data where there is a lot of noise and outliers.
Most of the existing three-dimensional point cloud similar registration algorithms have poor registration accuracy and application limitation, such as poor registration accuracy for three-dimensional point clouds containing a large amount of noise and external points. Due to the physical limitation of the point cloud data acquisition equipment, noise and other factors, a large amount of noise and outliers exist in the acquired point cloud, so that similar registration accuracy of the point cloud is affected, 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 problems to be solved by the invention are realized by the following technical scheme:
the invention provides a three-dimensional point cloud similarity 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 an initial value of a size factor and an initial value of a rotation matrix and an initial value of a translation vector in rigid body transformation by using the similar registration optimization model;
s3: obtaining a plurality of values by using the size factors, and carrying out 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 carrying out 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 one embodiment of the present invention, the S1 includes:
s11: acquiring shape point cloudsAnd model Point cloud->Wherein N is p N is the number of points in the shape point cloud q Points of the model point cloud;
s12: according to the shape point cloud and the model point cloud, a three-dimensional point cloud similar registration optimization model based on a pseudo Huber loss function is established:
s.t.R T R＝I 3 ，det(R)＝1
wherein s is a scale factor, R is a rotation matrix, t is a translation vector, and p i M is the three-dimensional coordinate of the ith point in the shape point cloud c(i) Is the ith point p in the shape point cloud i Optimal corresponding points in the model point cloud, b is an outlier threshold value, I 3 Representing a 3-order identity matrix;
s13: setting the maximum iteration number k of rigid body registration max Maximum number of iteration n of scale factor refinement max Minimum value epsilon of mean square error between point clouds after rigid body transformation min And a mean square error minimum value epsilon s of the similarity transformation min And let the initial value k=1 of the number of rigid registration iterations, and the initial value n=1 of the number of scale factor refinement iterations.
In one 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 similarity transformation:
wherein s is a scale factor, R is a rotation matrix, and t is a translation vector;
s22: calculating and obtaining an initial value of a size factor by using the model point cloud M and the shape point cloud P after similar transformation:
wherein p is g And m g The center of gravity, P, of the shape point cloud P and the model point cloud M respectively w And m w The centroids of the shape point cloud P and the model point cloud M are respectively;
s23: calculating and obtaining an initial value R of the rotation matrix R by using a principal component analysis method 0 An initial value t of the translation vector t 0 。
In one embodiment of the present invention, the S3 includes:
s31: using expressionsLet n=1, according to the initial value s of the size factor 0 Obtaining multiple values->
S32: for the plurality of valuesCarrying out rigid transformation solving on the shape point cloud P and the model point cloud M to obtain each value +.>Corresponding optimal rotation matrix and optimal translation vector。
In one embodiment of the present invention, the S32 includes:
s321: according to the current valueCalculating the spatial correspondence between the shape point cloud P and the model point cloud M after the similar transformation of the kth iteration +.>The method meets the following conditions:
wherein i=1, 2, …, N p The initial value of k is 1, c k (i) Representing the c-th in the model point cloud in the kth iteration k (i) Points, m j Is p i Corresponding points in the model point cloud M;
s322: according to the spatial correspondence obtained after the kth iterationCalculating relative rigid transformation R of shape point cloud P and model point cloud M between two iterations * 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 transformation R * And t * Updating rigid body transformation R for the kth iteration k And t k ：
R k ＝R * R k-1 ，t k ＝R * t k-1 +t * ；
S324: calculate the kth iterationRigid body transformation R k And t k Mean square error of the back shape point cloud Q and the model point cloud M:
s325: determining epsilon k ≤ε min Or k is greater than or equal to k max If not, making k+1 and returning to step S321 for iteration, if yes, determining the current rigid body transformation matrix R k And t k Is the optimal rigid transformation of the shape point cloud and the model point cloud after the similar transformation, wherein epsilon min Is the minimum value of the mean square error, k of the shape point cloud and the model point cloud after rigid body transformation max Registering the maximum iteration number for the rigid body;
s326: repeating the steps S321 to S325 to obtain the residual valueThe corresponding optimal rotation matrix and optimal translation vector.
In one embodiment of the present invention, the S4 includes:
s41: calculating the mean square error for each set of similarity transformations:
wherein,representing squaring the binary norms;
s42: at the position ofFinding out and obtaining the mean square error epsilon s l Size factor s at minimum l min Corresponding mean square error epsilon s l Rotation matrix and translation vector;
s43: determining epsilon s l ≤εs min Or n is greater than or equal to n max Whether it is true or not,if not, return to S31, let n+1, S 0 Is the mean square error epsilon S in step S42 l Size factor s at minimum l min Iterating, if yes, outputting the scale factor s calculated by the current iteration l min And their corresponding rotation matrices and translation vectors.
Another aspect of the present invention provides a storage medium having stored therein a computer program for performing the steps of the three-dimensional point cloud similarity registration method of any of the above embodiments.
Yet another aspect of the present invention provides an electronic device comprising a memory having a computer program stored therein and a processor implementing the steps of the three-dimensional point cloud similar registration method as in any of the above embodiments when the computer program in the memory is invoked by the processor.
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 inhibition effect on noise and external points, 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 block flow diagram of a three-dimensional point cloud similarity registration method provided by an embodiment of the 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 describe the technical means and effects adopted by the invention to achieve the preset aim, the following describes a three-dimensional point cloud similar registration method according to the invention in detail with reference to the attached drawings and the detailed description.
The foregoing and other features, aspects, and advantages of the present invention will become more apparent from the following detailed description of the preferred embodiments when taken in conjunction with the accompanying drawings. The technical means and effects adopted by the present invention to achieve the intended 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 intended to limit the technical scheme of the present invention.
It should be noted that in this document relational terms such as first and second, and the like are 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. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that an article or apparatus 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 one … …" does not exclude the presence of other like elements in an article or apparatus that comprises the element.
Referring to fig. 1 and fig. 2, 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. The three-dimensional point cloud similarity 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;
the step S1 specifically comprises the following steps:
s11: acquiring shape point cloudsAnd model Point cloud->Wherein N is p Points N being the shape point cloud P m Points of model point cloud M, N p ∈N，N m E, 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 the 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 factors are found, the similar registration problem is converted into a rigid body registration problem. Typically three-dimensional point cloud rigid body registration includes two things: (1) establishing a corresponding relation between two point clouds; (2) solving a rigid body transformation between the two point clouds.
Given shape point cloudAnd model Point cloud->Assuming that there is a certain mapping relationship C: p→m from the shape point cloud P to the model point cloud M, and a similarity transformation relationship T from the shape point cloud P to the model point cloud M, the following similarity metric function can be defined:
J(T(P),C(P))，
the point cloud similar registration process can be seen as an optimization problem as follows:
where s is the scale factor, R is the rotation matrix, and t is the translation vector.
In the embodiment, a pseudo Huber loss function 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 registration results is restrained, and the accuracy of similar registration is improved.
The pseudo-Huber loss function is a smoothed version of the Huber function, which has continuous conductivity and can effectively suppress the influence 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 a/2, while for larger values of a the loss function may approximate a straight line with a slope of b, which is thus insensitive to noise and outliers.
For the problem of similar registration of the three-dimensional point cloud with noise and external points, the noise and the 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 using the pseudo Huber loss function to establish the objective function of similar registration, so that the registration efficiency and accuracy are improved. Thus, for two point clouds P and M containing noise and outliers, a similar registration optimization model based on the pseudo Huber loss function can be built as follows:
s.t.R T R＝I 3 ，det(R)＝1
wherein s is a scale factor, R is a rotation matrix, t is a translation vector, and p i M is the three-dimensional coordinate of the ith point in the shape point cloud c(i) Is the ith point p in the shape point cloud i Optimal corresponding points in the model point cloud, b is an outlier threshold value, I 3 Representing the identity matrix of order 3.
Thus, the three-dimensional point cloud similarity registration problem is converted into a minimization optimization problem of a nonlinear objective function.
S13: setting the maximum iteration number k of rigid body registration max Maximum number of iteration n of scale factor refinement max Minimum value epsilon of mean square error between point clouds after rigid body transformation min And a mean square error minimum value epsilon s of the similarity transformation min And let the initial value k=1 of the number of rigid registration iterations, and the initial value n=1 of the number of scale factor refinement iterations.
S2: obtaining an initial value of a size factor and an initial value of a rotation matrix and an initial value of a translation vector in rigid body transformation 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 similarity transformation:
wherein s is a scale factor, R is a rotation matrix, t is a translation vector, and N m Points in the model point cloud M;
s22: and calculating by using the model point cloud M and the shape point cloud P after similar transformation to obtain an initial value of the size factor.
In the similarity transformation of the point clouds, for the same point cloud, the relative distance between the center of gravity and the center of mass is changed proportionally, and under the similarity transformation of different scale factors, the relative distance ratio is the scale factor. Because the position of the center of gravity and the centroid changes due to the influence of noise and external points, and the result is inaccurate, the embodiment obtains the initial value of the scale factor by calculating the distance ratio of the center of gravity and the centroid of the three-dimensional point cloud, and then carries out refined solution on the scale factor in an iterative mode.
Giving a model point cloud M, wherein the point cloud after similarity transformation is P, and the centers of gravity of the shape point cloud P and the model point cloud M are assumed to be P respectively g And m g The mass centers are p respectively w And m w It is possible to obtain:
wherein,r i is the distance from 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 using a principal component analysis method 0 An initial value t of the translation vector t 0 。
Specifically, the present embodiment employs principal component analysis (Principal component analysis, PCA) to solve for the initial values of the rigid body transformation. Firstly, calculating covariance matrixes and mean values of two three-dimensional point clouds to be registered, using the covariance matrixes to obtain feature vectors, then using the mean value as an origin, using the feature vectors as coordinate axes to establish three-dimensional coordinate systems of the two three-dimensional point clouds to be registered, and obtaining initial values R of a rotation matrix R in rigid transformation by aligning the three-dimensional coordinate systems 0 Initial value t of translation vector t 0 。
S3: obtaining a plurality of values by using the size factors, and carrying out 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 embodiment adopts a rough-to-fine mode to iteratively solve the scale factor s. And carrying out rigid body transformation solving on each value through a plurality of values corresponding to the given scale factors, and solving the optimal similarity transformation through error comparison. After the 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 solution to rigid body transformation is focused. Given the initial value R of rigid body transformation 0 And t 0 Then, the present embodiment solves the optimal rigid body transformation by an iterative method.
The step S3 specifically comprises the following steps:
s31: using expressionsLet n=1, according to the initial value s of the size factor 0 Obtaining multiple values->
At the beginning of scale factor refinement iteration, according to the initial value s of the scale factor s 0 Obtaining a set of values arranged in an arithmetic progression, wherein the first value isThe last value is +.>The difference between adjacent values is->Thereby obtaining m values.
For example, in the first iteration, n=1, where the first value is 0 and the last value is 2s 0 The difference between adjacent values isThus obtaining 20 numerical values arranged in an arithmetic progression.
S32: for the plurality of valuesCarrying out rigid transformation solving on the shape point cloud Q and the model point cloud M to obtain each value +.>The corresponding optimal rotation matrix and optimal translation vector.
Specifically, step S32 includes:
s321: according to the current valueCalculating the spatial correspondence between the shape point cloud P and the model point cloud M after the similar transformation of the kth iteration +.>The method meets the following conditions:
wherein i=1, 2, …, N p The initial value of k is 1, c k (i) Representing the c-th in the model point cloud in the kth iteration k (i) Points, m j Is p i Corresponding points in the model point cloud M;
specifically, for the solution of the spatial correspondence between the shape point cloud P and the model point cloud M in the above formula, the embodiment is implemented by using a Delaunay triangulation-based nearest point search algorithm. Random scattered points in the three-dimensional space are connected by straight line segments to form a tightly adjacent tetrahedron set which is free from overlapping and gaps in space, and the vertex of each tetrahedron is the original scattered point. The shape point cloud P is triangulated by Delaunay, which must meet two basic criteria, namely the empty circle property and the maximized minimum angle property. On the basis, a triangular partition search strategy is adopted to find a model point cloudShape point cloud after similarity transformation +.>Corresponding points in (a).
S322: according to the spatial correspondence obtained after the kth iterationCalculating relative rigid transformation R of shape point cloud P and model point cloud M between two iterations * And t * The calculation formula is as follows:
wherein R is * Representing the relative rotation matrix between two adjacent iterations, t * Representing the relative translation matrix between two adjacent iterations.
The LM (Levenberg Marquarelt) algorithm is an algorithm for solving function extremum in an iterative mode, and the algorithm is high in convergence speed. In the embodiment, the LM algorithm is adopted to carry out optimization solution on the upper part, and the LM algorithm is utilized to obtain the relative rigid body transformation R of the shape point cloud P and the model point cloud M between two iterations * And t * 。
S323: using said relative rigid body transformation R * And t * Updating rigid body transformation R for the kth iteration k And t k ：
R k ＝R * R k-1 ，t k ＝R * t k-1 +t * ；
S324: computing the rigid body transformation R of the kth iteration k And t k Mean square error of the back shape point cloud P and the model point cloud M:
s325: determining epsilon k ≤ε min Or k is greater than or equal to k max If not, let k=k+1 and return to step S321 for iteration, if yes, determine the current rigid transformation matrix R k And t k Is the optimal rigid transformation of the shape point cloud and the model point cloud after the similar transformation, wherein epsilon min Is the minimum value of the mean square error, k of the shape point cloud and the model point cloud after rigid body transformation max Registering the maximum iteration number for the rigid body;
specifically, the above steps are repeated to obtain the valueWhen the corresponding optimal rotation matrix and optimal translation vector are adopted, the iteration number is k, the initial value is 1, and after k iterations, if epsilon k ≤ε min Or k is greater than or equal to k max If true, determining the current rigid body transformation matrix R k And t k To take the value +.>Corresponding optimal rotationA translation matrix and an optimal translation vector.
S326: repeating the steps S321 to S325 to obtain the residual valueThe corresponding optimal rotation matrix and optimal translation vector.
Specifically, for the remainderAccording to the iterative process from step S321 to step S325, the respective corresponding optimal rotation matrix and optimal translation vector can be obtained.
S4: and carrying out scale factor refinement iteration according to the optimal rotation matrix and the 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: calculating the mean square error for each set of similarity transformations:
wherein,
s42: at the position ofFinding out and obtaining the mean square error epsilon s l Minimum value s l Corresponding mean square error epsilon s l Rotation matrix and translation vector;
s43: determining epsilon s l ≤εs min Or n is greater than or equal to n max If not, returning to S31 to let n+1, S 0 Is the mean square error epsilon S in step S42 l Size factor s at minimum l min Iterating, if yes, outputting the scale factor s calculated by the current iteration l min And corresponding rotational momentArrays and translation vectors.
Specifically, after carrying out similar transformation solving on all values corresponding to the current scale factors, obtaining a mean square error corresponding to each value, and finding out and obtaining a mean square error epsilon s l Minimum value s l min Corresponding mean square error epsilon s l Rotation matrix and translation vector, if εs is satisfied l ≤εs min Or n is greater than or equal to n max Then the current value s l min The corresponding rigid transformation and translation vector are the final rotation matrix and translation vector of the point cloud matching calculated by the three-dimensional point cloud similarity registration method of the embodiment.
If εs is not satisfied l ≤εs min Or n is greater than or equal to n max Returning to S31, let n=n+1, S 0 Replaced by the mean square error epsilon S in step S42 l Size factor s at minimum l min And (5) performing iteration. For example, at the time of scale factor refinement iteration, return to S31 at this time, take n=2, S 0 Taking s l min Performing iterative processing until εs is satisfied l ≤εs min Or n is greater than or equal to n max 。
In summary, aiming at the problem of similar registration under the condition that the three-dimensional point cloud data contains a large amount of noise and outliers, 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 scale consistency, converts a similar registration problem into a rigid registration problem, iteratively solves a rigid transformation matrix and a translation vector according to a scale factor value interval, and finally gives an optimal rigid transformation and scale factor. According to the three-dimensional point cloud similar registration method, the pseudo Huber loss function has an inhibition effect on noise and external points, so that the similar registration accuracy can be effectively improved.
Yet another embodiment of the present invention provides a storage medium having stored therein a computer program for performing the three-dimensional point cloud similar registration method steps described in the above embodiments. In a further aspect, 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 according to the above embodiment. In particular, the integrated modules described above, implemented in the form of software functional modules, may be stored in a computer readable storage medium. The software functional module is stored in a storage medium and includes instructions for causing an electronic device (which may be a personal computer, a server, or a network device, etc.) or a processor (processor) to perform part of the steps of the methods described in the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (Random Access Memory, RAM), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
The foregoing is a further detailed description of the invention in connection with the preferred embodiments, and it is not intended that the invention be limited to the specific embodiments described. It will be apparent to those skilled in the art that several simple deductions or substitutions may be made without departing from the spirit of the invention, and these should be considered to be within the scope of the invention.
Claims (3)
1. A method for three-dimensional point cloud similarity registration, comprising:
s1: obtaining a shape point cloud and a model point cloud, establishing a similar registration optimization model and initializing parameters;
s2: obtaining an initial value of a size factor and an initial value of a rotation matrix and an initial value of a translation vector in rigid body transformation by using the similar registration optimization model;
s3: obtaining a plurality of values by using the size factors, and carrying out 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: according to the optimal rotation matrix and translation vector corresponding to each value, carrying out scale factor refinement iteration to obtain the optimal scale factor and the final rotation matrix and translation vector,
the S1 comprises the following steps:
s11: acquiring shape point cloudsAnd model Point cloud->Wherein N is p N is the number of points in the shape point cloud m Points of the model point cloud;
s12: according to the shape point cloud and the model point cloud, a three-dimensional point cloud similar registration optimization model based on a pseudo Huber loss function is established:
s.t.R T R＝I 3 ，det(R)＝1
wherein s is a scale factor, R is a rotation matrix, t is a translation vector, and p i M is the three-dimensional coordinate of the ith point in the shape point cloud c(i) Is the ith point p in the shape point cloud i Optimal corresponding points in the model point cloud, b is an outlier threshold value, I 3 Representing a 3-order identity matrix;
s13: setting the maximum iteration number k of rigid body registration max Maximum number of iteration n of scale factor refinement max Minimum value epsilon of mean square error between point clouds after rigid body transformation min And a mean square error minimum value epsilon s of the similarity transformation min And let the initial value k=1 of the rigid registration iteration number, the initial value n=1 of the scale factor refinement iteration number,
the step S2 comprises the following steps:
s21: performing similarity transformation on the model point cloud M to obtain a shape point cloud P after similarity transformation:
wherein s is a scale factor, R is a rotation matrix, and t is a translation vector;
s22: calculating and obtaining an initial value of a size factor by using the model point cloud M and the shape point cloud P after similar transformation:
wherein p is g And m g The center of gravity, P, of the shape point cloud P and the model point cloud M respectively w And m w The centroids of the shape point cloud P and the model point cloud M are respectively;
s23: calculating and obtaining an initial value R of the rotation matrix R by using a principal component analysis method 0 An initial value t of the translation vector t 0 ，
The step S3 comprises the following steps:
s31: using expressionsLet n=1, according to the initial value s of the size factor 0 Obtaining multiple values->
S32: for the plurality of valuesCarrying out rigid transformation solving on the shape point cloud P and the model point cloud M to obtain each value +.>The corresponding optimal rotation matrix and optimal translation vector,
the S32 includes:
s321: according to the current valueCalculating the spatial correspondence between the shape point cloud P and the model point cloud M after the similar transformation of the kth iteration +.>The method meets the following conditions:
wherein i=1, 2, …, N p The initial value of k is 1, c k (i) Representing the c-th in the model point cloud in the kth iteration k (i) Points, m j Is p i Corresponding points in the model point cloud M;
s322: according to the spatial correspondence obtained after the kth iterationCalculating relative rigid transformation R of shape point cloud P and model point cloud M between two iterations * 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 transformation R * And t * Updating rigid body transformation R for the kth iteration k And t k ：
R k ＝R * R k-1 ，t k ＝R * t k-1 +t * ；
S324: computing the rigid body transformation R of the kth iteration k And t k Mean square error of the back shape point cloud Q and the model point cloud M:
s325: determining epsilon k ≤ε min Or k is greater than or equal to k max If not, making k+1 and returning to step S321 for iteration, if yes, determining the current rigid body transformation matrix R k And t k Is the optimal rigid transformation of the shape point cloud and the model point cloud after the similar transformation, wherein epsilon min Is the minimum value of the mean square error, k of the shape point cloud and the model point cloud after rigid body transformation max Registering the maximum iteration number for the rigid body;
s326: repeating the steps S321 to S325 to obtain the residual valueThe corresponding optimal rotation matrix and optimal translation vector,
the step S4 comprises the following steps:
s41: calculating the mean square error for each set of similarity transformations:
wherein,
s42: at the position ofFinding out and obtaining the mean square error epsilon s l Size factor s at minimum lmin Corresponding mean square error epsilon s l Rotation matrix and translation vector;
s43: determining epsilon s l ≤εs min Or n is greater than or equal to n max If not, returning to S31 to let n+1, S 0 Replaced by the mean square error epsilon S in step S42 l Size factor s at minimum lmin Iterating, if yes, outputting the scale factor s calculated by the current iteration lmin And their corresponding rotation matrices and translation vectors.
2. A storage medium having stored therein a computer program for performing the steps of the three-dimensional point cloud similarity registration method of claim 1.
3. An electronic device comprising a memory and a processor, the memory having stored therein a computer program, the processor implementing the steps of the three-dimensional point cloud-like registration method of claim 1 when the computer program in the memory is invoked by the processor.
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