CN112509018A - Quaternion space optimized three-dimensional image registration method - Google Patents

Quaternion space optimized three-dimensional image registration method Download PDF

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CN112509018A
CN112509018A CN202011397111.2A CN202011397111A CN112509018A CN 112509018 A CN112509018 A CN 112509018A CN 202011397111 A CN202011397111 A CN 202011397111A CN 112509018 A CN112509018 A CN 112509018A
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CN112509018B (en
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王耀南
武子杰
朱青
毛建旭
张辉
江一鸣
唐永鹏
聂静谋
林杰
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Abstract

The invention provides a three-dimensional image registration method based on quaternion space optimization. The quaternion space optimized three-dimensional image registration method utilizes the normal vector characteristics of point cloud to decouple the association of rotation and translation, and then utilizes the mechanism iteration of cyclic histogram search to search the optimal transformation, so as to register the three-dimensional images with different visual angles. The invention provides a brand-new point cloud registration method system, which can decouple rotation and translation, greatly improve algorithm efficiency, can be applied to more comprehensive three-dimensional image registration, can obtain more accurate registration effect and has extremely high algorithm adaptability.

Description

Quaternion space optimized three-dimensional image registration method
Technical Field
The invention relates to the field of image registration, in particular to a quaternion space optimized three-dimensional image registration method.
Background
With the rapid development of artificial intelligence and science and technology, the image acquisition equipment can obtain more and more accurate point cloud images with more and more huge data volume. The point cloud registration is a key part in a three-dimensional reconstruction technology, and the relative coordinates of three-dimensional images with different visual angles are fused into an absolute coordinate system to realize accurate three-dimensional model reconstruction. In intelligent manufacturing systems such as aerospace, automobile industry, large ships and the like, model reconstruction based on a three-dimensional machine vision algorithm is always an efficient research method. The processing and detection of the complex special-shaped curved surface both need a high-precision image registration algorithm.
Currently, Iterative Closest Point (Iterative Closest Point) algorithm is one of the most widely used Point cloud registration algorithms, and it confirms the corresponding Point set and calculates the optimal transformation step through Iterative alternative optimization until the algorithm converges. The algorithm is simple and the algorithm complexity is not high. However, the corresponding relation of the point set is very strict and a good initial position of the point cloud posture is needed, so a coarse registration-fine registration system based on the iteration closest point is developed, an additional manually designed descriptor algorithm is used for obtaining a good initialization, and the iteration closest point algorithm is used for final optimization.
At present, the algorithm is limited in practical application no matter the algorithm is an iterative closest point algorithm or a rough registration-precise registration system taking the iterative closest point algorithm as a base stone, and the algorithm can only be applied to a type of three-dimensional point cloud data with specific characteristics. The traditional feature extraction algorithm for describing the subtype usually has strict requirements on the corresponding relation of points, is very sensitive to parameter selection and has poor robustness. In the registration process, different algorithms can only ensure a relatively optimal solution while being applied to a specific object.
The traditional Iterative Closest Point (Iterative Closest Point) algorithm needs harsh Point cloud implicit corresponding relation and can realize registration only in a certain small Point cloud space initial pose range, but the algorithm is difficult to be effective due to noise, large transformation and the like during actual industrial curved surface reconstruction. A coarse registration-fine registration system based on an iterative closest point algorithm and other algorithms needs a good manually designed local descriptor extraction feature, and a traditional feature extraction algorithm for describing a subtype usually has strict requirements on a corresponding relation of points, is very sensitive to parameter selection and has poor robustness. In the registration process, certain requirements are also set for the types of point cloud features, and good matching and wide adaptability of industrial landing cannot be realized. Different algorithms can only guarantee one relative optimal solution when being applied to a specific object.
Disclosure of Invention
The invention provides a three-dimensional image registration method for quaternion space optimization, and aims to solve the technical problems of low adaptability and registration accuracy and poor robustness of the existing image point cloud registration algorithm in the background technology.
In order to achieve the above object, the present invention provides a quaternion space optimized three-dimensional image registration method, which decouples the rotation and translation relationship between point clouds to be registered by using the normal vector characteristics of the point clouds, and then performs registration on three-dimensional images of different viewing angles by using iterative search optimal transformation of a circular histogram search mechanism, specifically comprising the following steps:
s1, acquiring three-dimensional point cloud coordinates of adjacent view scenes, and acquiring an X coordinate of a source point cloud and a coordinate of a target point cloud Y;
step S2, solving to obtain a candidate rotation vector group converted from the X coordinate of the source point cloud to the coordinate of the target point cloud Y, and obtaining a candidate rotation mode and a translation mode of the corresponding relation point;
step S3, according to the candidate rotation mode and translation mode in the step S1, rotation and translation are carried out on the source point cloud X to obtain a transformed point set, and a point pair set of which the point pair relationship in a certain error range in the obtained point set and the subset of the target point cloud Y is solved;
step S4, solving a rotation mode and a translation mode between point pair sets with small point pair relation errors by using singular value decomposition;
and S5, performing rotation average on the source point cloud X by using the rotation mode and the translation mode in the step S4 to realize registration between the source point cloud X and the target point cloud Y.
Preferably, the step S1 is specifically: acquiring three-dimensional point cloud coordinates of adjacent view scenes, acquiring X coordinates of source point cloud and coordinates of target point cloud Y, and setting quaternion expression Q of local coordinate systems of X and YxAnd Qy(ii) a The method specifically comprises the following steps:
constructing a local coordinate system L for each point in X and Y in a three-dimensional point cloudi：
Figure BDA0002815608880000031
Wherein n is1、n2And n3Forming a linear independent vector group of the three-dimensional point cloud; n is3＝n1×n2，n1Is the normal vector of the point, n2A second bit vector that is a linearly independent set of the point perpendicular to the normal vector; obtaining quaternion expression of local coordinate system of three-dimensional point cloud X and Y respectively, and marking as QxAnd Qy；
Preferably, in the step S1, a linear independent point normal vector n of the three-dimensional point cloud is obtained1The concrete is as follows:
at point P0Get P0Is in the neighborhood of radius r1All point sets S inl1＝{Pi|||Pi–P0||≤r1}, constructing a matrix Cl:
Figure BDA0002815608880000032
K is the set of points Sl1Number of points, use oddSingular value decomposition algorithm decomposition matrix Cl＝UDVTD is a diagonal matrix, U and V are unitary matrices, and a characteristic value lambda of diagonal elements in the sorted D is obtained1>λ2>λ3And corresponding feature vector N1、N2、N3(ii) a Maximum value lambda1Corresponding feature vector N1Is taken as the normal vector n of the point1；
Obtaining a linear independent point normal vector n of the three-dimensional point cloud2The method specifically comprises the following steps:
at point P0Get P0Is in the neighborhood of radius r2<r<r3All point sets S inl2＝{Pi|r2≤||Pi–P0|| ≤r3Get the distance at the normal vector n1Point P where the directional component is maximummaxFrom P0Point of direction PmaxThe component of the vector of (a) in the direction perpendicular to the normal vector n1 is set as the second bit vector n of the local coordinate system2(ii) a Corresponding to n2＝ns-(ns·n1)*n1(ii) a Symbol-representing a vector dot product, a product symbol, nsIs a point set vector.
Preferably, the step S2 specifically includes the following steps:
step S21, Slave QxAnd QySolving a candidate rotation vector group T;
step S22, performing density clustering of the candidate rotation vector group T by using a histogram search mechanism to obtain the candidate rotation vector group T in a spatial domain with a certain density rangenew(ii) a And calculating to obtain the candidate rotation mode and translation mode of the corresponding relation point in the unit space domain.
Preferably, in step S21, the solving of the candidate rotation vector group T is specifically: will be part of the coordinate system
Figure BDA0002815608880000033
In terms of identity matrix
Figure BDA0002815608880000034
Calculating a rotational quaternion Q for a referencexAnd QyDividing Q by quaternionxEach rotational quaternion of (1) and QyEach rotation quaternion in the four-element system is divided by quaternion to obtain each QxTo each QyUnidirectional rotation mapping of elements.
Preferably, the step S22 is specifically: through density clustering based on a histogram search mechanism, an alpha% space domain interval of a certain density range is obtained and is marked as a new candidate rotation vector group TnewPerforming the following steps; obtaining a corresponding relation point pair corresponding to the candidate rotation in the unit space domain and recording the corresponding relation point pair as AiAnd Bi(ii) a The candidate rotation in the space domain is averaged to obtain QRAnd then solve for translation tR；
Preferably, the step S22 specifically includes the following steps:
taking the first N dimensions of the T vectors of the candidate rotation vector group as a new screening group NT＝{ntiAnd corresponds to T one by one;
to NTScreening N-dimensional histogram, setting M groups for each dimension to form N-dimensional density indication number group D ═ DiD is MNA size N-dimensional array whose values represent N in the regionTThe number of (D) is recorded as the density value in the unit area, at MNWithin one region, D ═ DiSorting, and taking the density value d of unit areaiN in the first alpha% region of size orderingTα＝{ntiThe rotation vector groups corresponding to the parts one by one form a new candidate rotation vector group Tnew；
By new candidate rotation vector group TnewObtaining a corresponding relation point pair corresponding to the candidate rotation in the unit space domain and recording the corresponding relation point pair as AiAnd Bi；
The candidate rotation in the space domain is averaged to obtain QRThe candidate rotation vector group T ═ qi}，QR＝ argmax qTMq，
Figure BDA0002815608880000041
k is the number of vectors of the vector group T, qiIs point pair AiAnd BiCorresponding QxTo QyThe rotation relation of (1) is directly obtained by quaternion division, and q is qiForming a matrix;
solving for translation tR: corresponding relation point set AiAnd BiThe particle difference of (a) is translation tR：
Figure BDA0002815608880000042
Figure BDA0002815608880000043
Preferably, the step S3 is specifically: applying the currently obtained average rotation Q to the source point cloud XRAnd translating tRObtaining a converted Source Point cloud XTObtaining X under the transformationTCandidate source cloud subset a ofiTransformed point set aizSolving the transformed point set aizWith the target point cloud subset BiPoint pair set A with certain error range eta% of point pair relationizAnd BizEta% is the density range; when the error is less than xi, the point set A is setizAnd BizXi is the error range value as the registration data of the three-dimensional point clouds X and Y, otherwise, the step S22 is returned, and the candidate rotation vector group is set to be Tnew；
Preferably, the step S3 specifically includes the following steps:
acting on the current mean rotation QRTranslation of tRAt candidate source cloud subset AiSolving the transformed point set aizWith the target point cloud subset BiIs smaller than the error of the point pair set AizAnd Biz；
Figure BDA0002815608880000051
Accordingly, the rotation belongs to a quaternion multiplication operation;
solving eta% point pair set A with smaller error of Euclidean distance measurementizAnd BizThe Euclidean distance error is defined as that two points (x)1y1z1) And (x)2y2z2) Then the error of the point pair is
Figure BDA0002815608880000052
Figure BDA0002815608880000053
When the error is less than xi, the point set A is setizAnd BizAs registration data of the three-dimensional point clouds X and Y, otherwise, returning to step S22, the candidate rotation vector group is set to Tnew。
Preferably, the step S4 is specifically: solving for A using singular value decompositionizAnd BizA rotation R and a translation t between A and BizMove to BizAnd realizing the registration between the three-dimensional point clouds X and Y.
The technical effects which can be achieved by adopting the invention are as follows: according to the invention, a novel point-to-point local coordinate system is constructed, the space pose of a single point can be separated from the overall description, and a quaternion method is adopted for description to construct a candidate rotation quaternion vector group, so that the optimal rotation can be searched by a circular histogram search mechanism. The method and the system have the advantages that a brand-new point cloud registration method system is provided, rotation and translation can be decoupled, algorithm efficiency is greatly improved, the method and the system can be applied to more comprehensive three-dimensional image registration, more accurate registration effect can be achieved, and high algorithm adaptability is achieved.
By introducing the normal vector description method, the algorithm can be solved by intrinsic decoupling rotation and translation, the defects of the traditional feature description sub-algorithm are overcome, and meanwhile, the application range of the algorithm is greatly expanded by optimization of a histogram mechanism, so that the algorithm can process most point cloud data, the robustness of the algorithm is further improved, errors in the registration process are reduced, and the registration efficiency is improved.
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FIG. 1 is a flow chart of a quaternion space optimized three-dimensional image registration method of the present invention;
fig. 2 is a diagram illustrating a histogram-based search mechanism according to a preferred embodiment of the quaternion space optimized three-dimensional image registration method of the present invention, where dimension N is 2.
Detailed Description
In order to make the technical problems, technical solutions and advantages to be solved by the present invention clearer, the following detailed description is made with reference to the accompanying drawings and specific embodiments.
Aiming at the existing problems, the invention provides a quaternion space optimized three-dimensional image registration method.
As shown in fig. 1, which is a flowchart of the method of the present invention, a method for registering a three-dimensional image based on quaternion space optimization of a cyclic histogram search mechanism includes the following steps:
step S1: acquiring three-dimensional point cloud coordinates of adjacent view scenes, acquiring X coordinates of a source point cloud and coordinates of a target point cloud Y, setting X and Y, and constructing a local coordinate system L for each point in the source point cloud X and the target point cloud Y acquired from the three-dimensional point cloudi：
In the embodiment, a 3D contour scanning sensor is adopted to obtain two three-dimensional point clouds of adjacent visual angles;
Figure BDA0002815608880000061
wherein n is1、n2And n3A set of linearly independent vectors forming a three-dimensional point cloud. n is3＝n1×n2，n1Is the normal vector of the point, n2A second bit vector that is a linearly independent set of the points perpendicular to the normal vector. Obtaining quaternion expression of local coordinate system of three-dimensional point cloud X and Y respectively, and marking as QxAnd Qy。
Obtaining a linear independent point normal vector n of the three-dimensional point cloud1The method specifically comprises the following steps:
at point P0Get P0All point sets S within the neighborhood radius r1l1＝{Pi|||Pi–P0||≤r1}, constructing a matrix Cl:
Figure BDA0002815608880000062
K is the set of points Sl1Using singular value decomposition algorithm to decompose the matrix ClObtaining a characteristic value lambda1> λ2>λ3And corresponding feature vector N1、N2、N3. Eigenvector N corresponding to maximum value λ 11Is taken as the normal vector n of the point1。
Obtaining a linear independent point normal vector n of the three-dimensional point cloud2The method specifically comprises the following steps:
at point P0Get P0Is in the neighborhood of radius r2<r<r3All point sets S in12＝{Pi|r2≤||Pi–P0||≤r3Get the distance at the normal vector n1Point P where the directional component is maximummaxFrom P0Point of direction PmaxIn a direction perpendicular to the normal vector n1The component of the direction is set as a second bit vector n of the local coordinate system2. Corresponding to n2＝ns-(ns·n1)*n1. Symbol-representing a vector dot product, a product symbol, nsIs a point set vector.
In this example, r is1＝0.01，r2＝0.03，r3＝0.04。
Step S2: solving to obtain a candidate rotation vector group converted from the X coordinate of the source point cloud to the coordinate of the target point cloud Y, and obtaining a candidate rotation mode and a translation mode of the corresponding relation point; the method specifically comprises the following steps:
step S21, Slave QxAnd QySolving a candidate rotation vector group T;
in the local coordinate system
Figure BDA0002815608880000071
In terms of identity matrix
Figure BDA0002815608880000072
Is a baseQuasi-computing rotational quaternion QxAnd QyDividing Q by quaternionxEach rotational quaternion of (1) and QyEach of the rotational quaternions in (1) is subjected to quaternion division. Get each QxTo each QyUnidirectional rotation mapping of elements.
Step S22, performing density clustering of a histogram search mechanism on the candidate rotation vector group T to obtain a candidate rotation vector group in a spatial domain within a certain density range; calculating to obtain candidate rotation modes and translation modes of corresponding relation points in the unit space domain;
the method specifically comprises the following steps: through density clustering based on a histogram search mechanism, alpha% space domain interval of a certain density range is obtained and is marked as a new candidate rotation vector group TnewPerforming the following steps; obtaining the corresponding relation point pair corresponding to the candidate rotation in the unit space domain and marking as AiAnd Bi(ii) a The candidate rotation in the space domain is averaged to obtain QRAnd then solve for translation tR；
The method comprises the following steps:
step S221, calculating an alpha% space domain interval of a certain density range through density clustering based on a histogram search mechanism, and recording as a new candidate rotation vector group TnewPerforming the following steps;
taking the first N dimensions of the T vectors of the candidate rotation vector group as a new screening group NT＝{ntiAnd corresponds to T one by one;
to NTScreening N-dimensional histogram, setting M groups for each dimension to form N-dimensional density indication number group D ═ DiD is MNA size N-dimensional array whose values represent N in the regionTThe number of (D) is recorded as the density value in the unit area, at MNWithin one region, D ═ DiSorting, and taking the density value d of unit areaiN in the first alpha% region of size orderingTα＝{ntiThe rotation vector groups corresponding to the parts one by one form a new candidate rotation vector group Tnew；
In this embodiment, the following concrete steps are performed: of the candidate rotational vector group T, by a histogram-based search mechanismDensity clustering, selecting the first N dimensions (N is less than or equal to 4) of the T vectors of the candidate rotation vector group, carrying out N-dimensional histogram screening, setting M groups in each dimension, and performing M-dimensional histogram screening on the M groupsNIn the first alpha% of the regions with the largest number (i.e., the highest density of the unit region) of the plurality of regions, the rotation vector groups in the first alpha% of the regions are grouped into a new rotation vector candidate group, which is denoted as a new rotation vector candidate group TnewIn (1).
In this example, N is 2, M is 1000, and usually one tenth of the average point number of the point clouds X and Y.
Alpha is taken as 50.
And (2) taking the first 2 dimensions of the candidate rotation vector group T vector, performing two-dimensional histogram screening, and screening the areas with the first 50% of points, wherein the rotation vectors represented by the points are marked as a new candidate rotation vector group. As shown in fig. 2, the solid line frame represents the screening process that has passed through the first 50% of the maximum density per unit area, and the broken line represents the discarded area.
Step S222, passing new candidate rotation vector group TnewObtaining the corresponding relation point pair corresponding to the candidate rotation in the unit space domain, and marking as AiAnd Bi(ii) a The candidate rotation in the space domain is averaged to obtain QRAnd then solve for translation tR；
The candidate rotation in the space domain is averaged to obtain QRThe candidate rotation vector group T ═ qi}，QR＝ argmax qTMq，
Figure RE-GDA0002900061750000081
k is the number of vectors of the vector group T, qiIs point pair AiAnd BiCorresponding QxTo QyThe rotation relation of (1) is directly obtained by quaternion division, and q is qiA matrix of compositions; to obtain QR. And solve for translation tR。
Corresponding point relation point set AiAnd BiThe particle difference of (a) is translation tR：
Figure BDA0002815608880000082
And solving for translation tR。
Step S3: according to the candidate rotation mode and translation mode in step S1, rotation and translation are applied to the source point cloud X to obtain a transformed point set, and a point pair set in which the point pair relationship in the obtained point set and the subset of the target point cloud Y is within a certain error range is solved.
The method specifically comprises the following steps: applying the currently obtained average rotation Q to the source point cloud XRAnd translating tRObtaining a converted Source Point cloud XTObtaining X under the transformationTCandidate source cloud subset a ofiTransformed point set aizSolving the transformed point set aizWith the target point cloud subset BiPoint pair set A with certain error range eta% of point pair relationizAnd Biz(ii) a When the error is less than xi, the point set A is setizAnd BizXi is the error range value as the registration data of the three-dimensional point clouds X and Y, otherwise, the step S22 is returned to, the candidate rotation vector group is set to be Tnew。
The method specifically comprises the following steps:
step S31, applying the current average rotation QRTranslation of tRAt candidate source cloud subset AiSolving the transformed point set aizWith the target point cloud subset BiIs smaller than the error of the point pair set AizAnd Biz。
Figure BDA0002815608880000083
Accordingly, the rotation belongs to a quaternion multiplication operation. Solving eta% point pair set A with smaller error of Euclidean distance measurementizAnd BizThe Euclidean distance error is defined as two points (x)1y1z1) And (x)2y2z2) Then the error of the point pair is
Figure BDA0002815608880000084
Step S32, when the error is less than xi, the point set A is setizAnd BizAs registration data of the three-dimensional point clouds X and Y, otherwise, returning to the step S22 to select rotation candidatesVector group set to Tnew。
In this example, η is 60, and ξ is 0.001.
Step S4, solving a rotation mode and a translation mode between point pair sets with small point pair relation errors by using singular value decomposition;
solving a always corresponding point set A by singular value decompositionizAnd BizA rotation R and a translation t between A and BizMove to BizAnd realizing the registration between the three-dimensional point clouds X and Y. The singular value decomposition algorithm is to solve the obtained optimal point pair relation AizAnd BizTransformation of (A)izIs aizCorresponding point sets in the original point cloud X.
And S5, performing rotation average on the source point cloud X by using the rotation mode and the translation mode in the step S4 to realize registration between the source point cloud X and the target point cloud Y.
The invention provides a quaternion space optimized three-dimensional image registration method based on a cyclic histogram search mechanism. The method and the system have the advantages that a brand-new point cloud registration method system is provided, rotation and translation can be decoupled, algorithm efficiency is greatly improved, the method and the system can be applied to more comprehensive three-dimensional image registration, more accurate registration effect can be achieved, and high algorithm adaptability is achieved.
According to the invention, by introducing a normal vector description method, the algorithm can be used for solving intrinsic decoupling rotation and translation, the application range of the algorithm is greatly expanded by optimizing a histogram mechanism while the defects of the traditional feature description sub-algorithm are overcome, so that the algorithm can process most point cloud data, the robustness of the algorithm is further improved, errors in the registration process are reduced, and the registration efficiency is improved.
The theory of the invention is that the overall optimal rotation is represented based on the rotation density maximum group, after initial preprocessing (denoising and the like), in the invention, the point characteristics on the aimed complex irregular curved surface (reference fan blade curved surface) are highly similar and difficult to identify, and the rotation search is carried out according to the normal vector (the normal vector of the blade is necessarily existed and the normal vector of each point is different), in this case, the optimal rotation of the normal vector between two point clouds is converted into a candidate, and the optimal density maximum group is necessarily existed (the conversion between each real corresponding point pair of the rotation true value group _ truth is consistent and highly similar, thereby forming a condition that the true rotation is used as the center, the number of candidate rotation vectors in the minimum space area is the most, and the true rotation is unique.
The method gets rid of the feature extraction constraint of the traditional feature descriptor, does not need to process the situation of highly similar features, realizes registration by utilizing the characteristics of normal vector features, can obtain good effect in the registration of various models, and is particularly suitable for models with advantages which are difficult to obtain by other methods such as a complex special-shaped curved surface.
The histogram density search is a tool, other clustering methods can still find the optimal density maximum group, but the methods are often huge in calculation amount and cannot be applied to the industrial scene, the number of model points is large (past 10000 points or more), and a part of sparse points are discarded in the histogram density search each time. The truth group must be a high density group, thus ensuring that the screening leaves the optimal transformation. The optimization of the histogram mechanism reduces the calculation amount and improves the speed of the algorithm.
The invention can make the registration more accurate and the adaptability better by the search theory of the rotation translation and the large density. The four-element number is a representation method, and the histogram is a search tool, so that the calculation amount is greatly reduced, and the accuracy of the original algorithm is not lost.
The foregoing is a preferred embodiment of the present invention, and it should be noted that it is obvious to those skilled in the art that various modifications and improvements can be made without departing from the principle of the present invention, and these modifications and improvements should be construed as the protection scope of the present invention.

Claims (10)

1. A quaternion space optimized three-dimensional image registration method is characterized in that rotation and translation relations between point clouds to be registered are decoupled by utilizing normal vector features of the point clouds, then the optimal search transformation of mechanism iteration of cyclic histogram search is utilized, and three-dimensional images of different visual angles are registered, and the method specifically comprises the following steps:
s1, acquiring three-dimensional point cloud coordinates of adjacent view scenes, and acquiring an X coordinate of a source point cloud and a coordinate of a target point cloud Y;
step S2, solving to obtain a candidate rotation vector group converted from the X coordinate of the source point cloud to the coordinate of the target point cloud Y, and obtaining a candidate rotation mode and a translation mode of the corresponding relation point;
step S3, according to the candidate rotation mode and translation mode in the step S1, rotation and translation are applied to the source point cloud X to obtain a transformed point set, and a point pair set of which the point pair relation in a certain error range in the obtained point set and the subset of the target point cloud Y is solved;
step S4, solving a rotation mode and a translation mode between point pair sets with small point pair relation errors by using singular value decomposition;
and S5, performing rotation average on the source point cloud X by using the rotation mode and the translation mode in the step S4 to realize registration between the source point cloud X and the target point cloud Y.
2. The quaternion space optimized three-dimensional image registration method according to claim 1, wherein the step S1 specifically comprises: acquiring three-dimensional point cloud coordinates of adjacent view scenes, acquiring X coordinates of source point cloud and coordinates of target point cloud Y, and setting quaternion expression Q of local coordinate systems of X and YxAnd Qy(ii) a The method specifically comprises the following steps:
constructing a local coordinate system L for each point in X and Y in a three-dimensional point cloudi：
Figure FDA0002815608870000011
Wherein n is1、n2And n3Forming a linear independent vector group of the three-dimensional point cloud; n is3＝n1×n2，n1Is the normal vector of the point, n2A second bit vector that is a linearly independent set of the point perpendicular to the normal vector; obtaining quaternion expression of local coordinate systems of the three-dimensional point cloud X and the three-dimensional point cloud Y respectively and marking as QxAnd Qy。
3. The quaternion space optimized three-dimensional image registration method according to claim 2, wherein in step S1, a linear independent point normal vector n of the three-dimensional point cloud is obtained1The method specifically comprises the following steps:
at point P0Get P0Is in the neighborhood of radius r1All point sets S inl1＝{Pi|||Pi–P0||≤r1}, constructing a matrix Cl:
Figure FDA0002815608870000021
K is the set of points Sl1Using singular value decomposition algorithm to decompose the matrix Cl＝UDVTD is a diagonal matrix, U and V are unitary matrices, and a characteristic value lambda of diagonal elements in the sorted D is obtained1>λ2>λ3And corresponding feature vector N1、N2、N3(ii) a Maximum value lambda1Corresponding feature vector N1Is taken as the normal vector n of the point1；
Obtaining a linear independent point normal vector n of the three-dimensional point cloud2The method specifically comprises the following steps:
at point P0Get P0Is in the neighborhood of radius r2<r<r3All point sets S inl2＝{Pi|r2≤||Pi–P0||≤r3Get the distance at the normal vector n1Point P where the directional component is maximummaxFrom P0Point of direction PmaxThe component of the vector of (a) in the direction perpendicular to the normal vector n1 is set as the second bit of the local coordinate systemVector n2(ii) a Corresponding to n2＝ns-(ns·n1)*n1(ii) a Symbol-representing a vector dot product, a product symbol, nsIs a point set vector.
4. The quaternion space optimized three-dimensional image registration method according to claim 2, wherein the step S2 specifically comprises the steps of:
step S21, Slave QxAnd QySolving a candidate rotation vector group T;
step S22, performing density clustering of the candidate rotation vector group T by using a histogram search mechanism to obtain the candidate rotation vector group T in a spatial domain with a certain density rangenew(ii) a And calculating to obtain the candidate rotation mode and translation mode of the corresponding relation point in the unit space domain.
5. The method according to claim 4, wherein in step S21, the solving of the candidate rotation vector group T specifically comprises: will be a local coordinate system
Figure FDA0002815608870000022
In terms of identity matrix
Figure FDA0002815608870000023
Calculating a rotational quaternion Q for a referencexAnd QyDividing Q by quaternionxEach rotational quaternion of (1) and QyEach rotation quaternion in the four-element system is divided by quaternion to obtain each QxTo each QyUnidirectional rotation mapping of elements.
6. The quaternion space optimized three-dimensional image registration method according to claim 4, wherein the step S22 specifically comprises: through density clustering based on a histogram search mechanism, alpha% space domain interval of a certain density range is obtained and is marked as a new candidate rotation vector group TnewPerforming the following steps; to obtainThe corresponding relation point pair corresponding to the candidate rotation in the unit space domain is marked as AiAnd Bi(ii) a The candidate rotation in the space domain is averaged to obtain QRAnd then solve for translation tR。
7. The quaternion space optimized three-dimensional image registration method according to claim 6, wherein the step S22 specifically comprises the steps of:
taking the first N dimensions of the T vectors of the candidate rotation vector group as a new screening group NT＝{ntiAnd corresponds to T one by one;
to NTAnd (4) carrying out N-dimensional histogram screening, setting M groups for each dimension, and forming an N-dimensional density indication array D ═ DiD is MNA size N-dimensional array whose values represent N in the regionTThe number of (D) is recorded as the density value in the unit area, at MNWithin one region, D ═ DiSorting, and taking the density value d of unit areaiN in the first alpha% region of size orderingTα＝{ntiThe rotation vector groups corresponding to the parts one by one form a new candidate rotation vector group Tnew；
By new candidate rotation vector group TnewObtaining a corresponding relation point pair corresponding to the candidate rotation in the unit space domain and recording the corresponding relation point pair as AiAnd Bi；
The candidate rotation in the space domain is averaged to obtain QRThe candidate rotation vector group T ═ qi}，QR＝argmaxqTMq，
Figure FDA0002815608870000031
k is the number of vectors of the vector group T, qiIs point pair AiAnd BiCorresponding QxTo QyThe rotation relation of (1) is directly obtained by quaternion division, and q is qiA matrix of compositions;
solving for translation tR: corresponding relation point set AiAnd BiThe particle difference of (a) is translation tR：
Figure FDA0002815608870000032
Figure FDA0002815608870000033
8. The quaternion space optimized three-dimensional image registration method according to claim 6, wherein the step S3 specifically comprises: applying the currently obtained average rotation Q to the source point cloud XRAnd translating tRObtaining a converted Source Point cloud XTObtaining X under the transformationTCandidate source cloud subset a ofiTransformed point set aizSolving the transformed point set aizWith the target point cloud subset BiPoint pair set A with certain error range eta% of point pair relationizAnd BizEta% is the density range; when the error is less than xi, the point set A is setizAnd BizXi is the error range value as the registration data of the three-dimensional point clouds X and Y, otherwise, the step S22 is returned to, the candidate rotation vector group is set to be Tnew。
9. The method for registering quaternion space optimized three-dimensional images as claimed in claim 8, wherein the step S3 specifically comprises the following steps:
acting on the current mean rotation QRTranslation of tRAt candidate source cloud subset AiSolving the transformed point set aizWith the target point cloud subset BiIs smaller than the error of the point pair set AizAnd Biz；
Figure FDA0002815608870000041
Accordingly, the rotation belongs to a quaternion multiplication operation;
solving eta% point pair set A with smaller error of Euclidean distance measurementizAnd BizThe Euclidean distance error is defined as two points (x)1 y1 z1) And (a)x2 y2 z2) Then the error of the point pair is
Figure FDA0002815608870000042
Figure FDA0002815608870000043
When the error is less than xi, the point set A is setizAnd BizAs registration data of the three-dimensional point clouds X and Y, otherwise, returning to step S22, the candidate rotation vector group is set to Tnew。
10. The quaternion space optimized three-dimensional image registration method according to claim 8, wherein the step S4 specifically comprises: solving for A using singular value decompositionizAnd BizA rotation R and a translation t between A and BizMove to BizAnd realizing the registration between the three-dimensional point clouds X and Y.
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