CN111415377B - Incomplete point cloud registration method based on partial quality optimal transmission theory - Google Patents
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Abstract
The invention relates to an incomplete point cloud registration method based on a partial quality optimal transmission theory, and belongs to the field of image processing. The method comprises the following steps: s1: inputting two point clouds P and Q, aligning mass centers of the two point clouds after mass distribution to obtain new point clouds X and Y; s2: establishing a point cloud registration energy function, and solving an optimal transmission matrix between point clouds X and Y by using a partial quality optimal transmission theory; s3: according to the obtained optimal transmission plan, a relative transformation matrix T (R, T) between two point clouds is obtained by SVD decomposition; s4: repeating S2 to S3 until the F norms of the rotation matrix obtained twice are converged; s5: and applying the finally obtained transformation matrix T (R, T) to the point cloud Q to align the point clouds P and Q. The method and the device can overcome the defects of noise, abnormal points and the like existing in the current point cloud registration process, and particularly aim at large-scale abnormal points and defects in the point cloud.
Description
Technical Field
The invention belongs to the field of image processing, and relates to an incomplete point cloud registration method based on a partial quality optimal transmission theory.
Background
Due to the limitations of scanning technology, all information of a three-dimensional scene cannot be obtained. The process of reconstructing the data scanned at different angles into a three-dimensional object is called three-dimensional reconstruction. However, how to match the local information obtained from each scan together is called point cloud registration. A point cloud, also called a point set, refers to a set of points contained in a particular coordinate system. Typically, a point cloud is generated by a three-dimensional scanner to represent the outer surface of an object in three-dimensional space. The point cloud registration is widely applied in the fields of computer vision, pattern recognition, three-dimensional model sampling, geometric processing and the like, and is a process for aligning two point clouds. In addition, the point cloud matching also uses cultural relic reconstruction, medical image analysis, building reconstruction and camera pose estimation.
The point cloud is unstructured three-dimensional data, no connection relation exists between points, and no corresponding relation exists between the point clouds. The point cloud registration process is to find the corresponding relation between the target point cloud E and the source point cloud S, and find the mapping transformation of the target point cloud E and the source point cloud S according to the corresponding relation; and then transforming the source point cloud S according to the transformation parameters, and comparing the transformed source point cloud S with the target point cloud E through a proper similarity index. The difference in similarity between the point clouds and E is minimized, thereby allowing the best alignment of the point cloud E and the transformed S.
Rigid registration is a very challenging problem because point cloud data itself can be problematic, including: noise, outliers, missing. Noise is a point near the surface of a three-dimensional object that makes registration more difficult; outliers refer to points away from the surface of the three-dimensional object that would affect the result of registration if not discarded; due to the problems of the scanning technique, a partial point set is missing. In general, the algorithms for point cloud registration fall mainly into the following categories: iterative Closest Point (ICP) algorithms are the most common point cloud registration algorithms due to their simplicity and ease of computation. The ICP algorithm iteratively calculates corresponding points according to the thought of the nearest point, and then calculates transformation parameters for aligning two point clouds until local minimization is achieved; the method is characterized in that a point-to-point correspondence is established through a probability method, and the probability algorithm is better than the traditional ICP algorithm in performance, particularly in the process of noise, outliers and missing, unlike the ICP algorithm in which the correspondence points are one-to-one correspondence; another type of point cloud rigid registration method is a feature descriptor, and some useful corresponding relations are established according to the feature descriptor, so that coarse registration is completed, and then fine registration is completed by using algorithms such as ICP and the like.
Disclosure of Invention
In view of the above, the present invention aims to provide an incomplete point cloud registration method based on a partial quality optimal transmission theory.
In order to achieve the above purpose, the present invention provides the following technical solutions:
an incomplete point cloud registration method based on a partial quality optimal transmission theory comprises the following steps:
s1: inputting two point clouds P and Q, aligning mass centers of the two point clouds after mass distribution to obtain new point clouds X and Y;
s2: establishing a point cloud registration energy function, and solving an optimal transmission matrix sigma between the point clouds X and Y by using a partial quality optimal transmission theory;
s3: according to the obtained optimal transmission plan sigma, a relative transformation matrix T (R, T) between two point clouds is obtained by SVD decomposition;
s4: repeating S2 to S3 until the F norms of the rotation matrix obtained twice are converged;
s5: and applying the finally obtained transformation matrix T (R, T) to the point cloud Q to align the point clouds P and Q.
Optionally, in the step S1: two point clouds p= { P are input 1 ,p 2 ,…,p m Sum q= { Q 1 ,q 2 ,…,q n Performing quality allocation, wherein the detailed method adopts an equal allocation idea without considering other complex information such as introduced characteristics; the number of points in the point clouds P and Q is m and n, and the mass of each point in the point clouds P and Q is respectively:
optionally, in the step S1, a mass center of gravity B of the two-point cloud p And B q The method comprises the following steps of:
after aligning the mass center of gravity, obtaining a new point cloud X and a new point cloud Y, wherein the coordinates of the points are as follows:
optionally, in the step S2, a partial quality optimal transmission theory is used, and when a transmission plan is calculated, a range constraint spread function is used, so that the quality transmission of the point cloud is relaxed, and the quality conservation criterion is broken; the RG function is used for restraining the total quality of the transmission point cloud Y, so that the robustness of the algorithm under the conditions of a large number of abnormal points and loss is improved;
optionally, in the step S2, the optimal transmission theory is relaxed, the RG divergence function is used to relax the conservation law of quality, the concept of transmission cost is used to model the registration of two point clouds, the transmission cost is obtained by multiplying the distance between two points by the corresponding transmission plan, the adopted distance function is the square of euclidean distance between the two points, and the energy function of the registration of the point clouds is as follows:
s201: firstly, fixing a transformation matrix T (R, T) by using an alternating iterative algorithm, solving an optimal transmission plan sigma, approximately solving by an entropy regularization term, wherein epsilon is an entropy regularization term coefficient, and controlling the regularization degree; the point cloud registration energy function is rewritten as:
h (σ) is the entropy of the transmission plan, which is of the form:
s202: solving the point cloud registration problem is a convex optimization problem, and the optimal transmission plan is expressed as follows:
σ＝diag(exp(u/))Kdiag(exp(v/))
wherein the method comprises the steps ofu and v are two solving vectors of the dual problem of the point cloud registration energy function, the optimal transmission plan is solved by the two vectors, and the variables are replaced as follows:
a＝exp(u/),b＝exp(v/).
according to the dual criteria, the variables a, b are alternately iterated to solve the convex optimization problem, and the variable iterations are as follows:
using an RG function to restrict the total quality of point cloud transmission, and rewriting a transmission plan into:
π＝g·diag(exp(u/))Kdiag(exp(v/))
g is a scaling factor controlling overall transmission, solving the expression as follows:
representing the corresponding point division of the vector, when using the F function as the RG function presented herein, the corresponding operators are as follows:
the transmission plan is calculated by the above expression, and thus the solution of the transformation parameters T (R, T) is performed.
Optionally, in the step S3, after the transmission plan is obtained, a transformation matrix T (R, T) is left in the energy function to be solved, where the energy function is as follows:
s301: and (3) performing partial derivative on the energy function to obtain a translation vector:
s302: replacing the translation matrix t in the objective function, the objective function is rewritten as:
the above is replaced as followsAnd the constant term is omitted, the new energy function is:
obtaining the minimum value of the energy function when the trace is maximized; using the trace feature tr (AB) =tr (BA), we get:for->Singular value SVD decomposition to obtain UAV T And again using the trace features, we get: />Let w=v T RU，V t R, U are orthogonal matrices, and W is also an orthogonal matrix; w_j is each column in W, the utilization characteristics: />All elements W in the matrix ij Not more than 1; when W is ii When=1, tr (AV T RU) reaches a maximum value, resulting in the following equation:
I＝W＝V T RU
the display solution for deriving the rotation matrix is as follows:
R＝VCU T ,C＝diag(1,...,det(VU T ))。
optionally, in step S4, the steps S2 and S3 are iterated until the F norms of the rotation matrices R and R0 obtained by solving twice are smaller than a certain threshold, and then the solution is considered to be converged at this time, so as to obtain an accurate translational rotation matrix.
Optionally, in the step S5, the obtained transformation matrix T (R, T) is applied to the original point cloud Q, so as to complete the registration of the point clouds P and Q.
The invention has the beneficial effects that: the method and the device find the limitation of the traditional optimal transmission theory under abnormal and missing conditions while completing the energy function modeling of the point cloud registration by using the transmission cost of the optimal transmission theory, and firstly propose to use the partial quality optimal transmission theory to complete the accurate and robust registration between the two point clouds.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objects and other advantages of the invention may be realized and obtained by means of the instrumentalities and combinations particularly pointed out in the specification.
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For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in the following preferred detail with reference to the accompanying drawings, in which:
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 (a) is an initialization point cloud; FIG. 2 (b) is an initialized quality allocation for point clouds P and Q; FIG. 2 (c) is a depth map of the transmission matrix calculated; FIG. 2 (d) is a point cloud registration result;
fig. 3 is an initialization point cloud input in the present embodiment: fig. 3 (a) is a noise case; FIG. 3 (b) is an outlier case; FIG. 3 (c) is a deletion case;
fig. 4 is a result of the point cloud registration of the present embodiment: fig. 4 (a) is fig. 3 (a): registering the result under the noise condition; fig. 4 (b) is fig. 3 (b): registering results under the condition of abnormal points; fig. 4 (c) is fig. 3 (c): registering the result in the absence;
FIG. 5 (a) is a point cloud for the case of noise, outliers, and missing in this embodiment; FIG. 5 (b) is a graph of the results after registration of 5 (a);
FIG. 6 is a registration result of the embodiment under more point cloud models; fig. 6 (a) is a registration result of fish; fig. 6 (b) is the registration result of fu; fig. 6 (c) is a registration result of face;
fig. 7 (a) shows Stanford Lounge Data of the present embodiment as a true scan; fig. 7 (b) is a graph of the results after registration of 7 (a);
fig. 8 (a) shows Apoll SouthBay data of the present embodiment as a true scan; fig. 8 (b) is a graph of the results after registration of 8 (a);
fig. 9 (a) is a Buddha Head data of the real scan of the present embodiment; fig. 9 (b) is a graph of the results after 9 (a) registration.
Detailed Description
Other advantages and effects of the present invention will become apparent to those skilled in the art from the following disclosure, which describes the embodiments of the present invention with reference to specific examples. The invention may be practiced or carried out in other embodiments that depart from the specific details, and the details of the present description may be modified or varied from the spirit and scope of the present invention. It should be noted that the illustrations provided in the following embodiments merely illustrate the basic idea of the present invention by way of illustration, and the following embodiments and features in the embodiments may be combined with each other without conflict.
Wherein the drawings are for illustrative purposes only and are shown in schematic, non-physical, and not intended to limit the invention; for the purpose of better illustrating embodiments of the invention, certain elements of the drawings may be omitted, enlarged or reduced and do not represent the size of the actual product; it will be appreciated by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The same or similar reference numbers in the drawings of embodiments of the invention correspond to the same or similar components; in the description of the present invention, it should be understood that, if there are terms such as "upper", "lower", "left", "right", "front", "rear", etc., that indicate an azimuth or a positional relationship based on the azimuth or the positional relationship shown in the drawings, it is only for convenience of describing the present invention and simplifying the description, but not for indicating or suggesting that the referred device or element must have a specific azimuth, be constructed and operated in a specific azimuth, so that the terms describing the positional relationship in the drawings are merely for exemplary illustration and should not be construed as limiting the present invention, and that the specific meaning of the above terms may be understood by those of ordinary skill in the art according to the specific circumstances.
The invention relates to an incomplete point cloud registration method based on a partial quality optimal transmission theory, belonging to the fields of computational geometry, computer vision, medical image analysis and the like. The method comprises the following steps: s1: inputting two point clouds P and Q, aligning mass centers of the two point clouds after mass distribution to obtain new point clouds X and Y; s2: establishing a point cloud registration energy function, and solving an optimal transmission matrix sigma between the point clouds X and Y by using a partial quality optimal transmission theory; s3: according to the obtained optimal transmission plan sigma, a relative transformation matrix T (R, T) between two point clouds is obtained by SVD decomposition; s4: repeating S2 to S3 until the F norms of the rotation matrix obtained twice are converged; s5: and applying the finally obtained transformation matrix T (R, T) to the point cloud Q to align the point clouds P and Q. As shown in fig. 1, the point cloud registration method specifically includes the following steps:
step 1, two point clouds p= { P are input 1 ,p 2 ,…,p m Sum q= { Q 1 ,q 2 ,…,q n The quality allocation is performed as in fig. 2 (a), and as in fig. 2 (b), the detailed method adopts the idea of uniform allocation, and does not consider other complex information such as introduced characteristics. The number of points in the point clouds P and Q is m and n, and the mass of each point in the point clouds P and Q is respectively:
mass center of gravity of two-point cloudB p And B q The method comprises the following steps of:
after aligning the mass center of gravity, obtaining a new point cloud X and a new point cloud Y, wherein the coordinates of the points are as follows:
and 2, when the conventional optimal transmission theory solves the point cloud registration problem under the condition of abnormal points and missing, the transmission plan solving inaccuracy is caused in order to meet the initial edge probability distribution. The method is characterized by firstly proposing to use a partial quality optimal transmission theory, and when a transmission plan is calculated, using a range constraint divergence function to relax the quality transmission of the point cloud, breaking the quality conservation criterion, and ensuring the transmission quality of the point cloud to be as shown in fig. 2 (c). And the RG function is used for restraining the total quality of the transmission point cloud Y, so that the robustness of the algorithm under the conditions of a large number of abnormal points and missing is improved.
The conventional optimal transmission theory uses RG divergence function to relax the conservation law of quality, uses the concept of transmission cost to model the registration of two point clouds, uses the distance between two points multiplied by the corresponding transmission plan, and uses the distance function as the square of Euclidean distance between the two points, and the point cloud registration energy function is as follows:
using an alternate iterative algorithm, firstly fixing a transformation matrix T (R, T), solving an optimal transmission plan sigma, approximately solving through an entropy regularization term, wherein epsilon is an entropy regularization term coefficient, and controlling the regularization degree. The point cloud registration energy function can be rewritten as:
h (σ) is the entropy of the transmission plan, which is of the form:
solving the point cloud registration problem is a convex optimization problem, and the optimal transmission plan can be expressed as follows:
σ＝diag(exp(u/))Kdiag(exp(v/))
wherein the method comprises the steps ofu and v are two solution vectors of the dual problem of the point cloud registration energy function, the optimal transmission plan can be solved by the two vectors, and the variables are replaced as follows:
a＝exp(u/),b＝exp(v/).
according to the dual criteria, the variables a, b are alternately iterated to solve the convex optimization problem, and the variable iterations are as follows:
using the RG function to constrain the total quality of point cloud transmissions, the transmission plan can be rewritten as:
π＝g·diag(exp(u/))Kdiag(exp(v/))
g is a scaling factor controlling overall transmission, solving the expression as follows:
representing the corresponding point division of the vector, when using the F function as the RG function presented herein, the corresponding operators are as follows:
from the above expression, a transmission plan such as 2 (d) can be calculated, so that the solution of the transformation parameters T (R, T) is performed.
Step 3, after the transmission plan is obtained, the transmission plan is removed from the registration energy function, and then the function of point cloud registration becomes:
and (3) performing partial derivative on the energy function to obtain a translation vector:
replacing the translation matrix t in the objective function, the objective function may be rewritten as:
the above is replaced as followsAnd the constant term is omitted, the new energy function is:
when maximizing traceTo obtain a minimum of the energy function. Using the trace feature tr (AB) =tr (BA), we get:for->Singular value SVD decomposition to obtain UAV T And again using the trace features, one can get: />Let w=v T RU，V t R, U are orthogonal matrices, so W is also an orthogonal matrix. W_j is each column in W, the utilization characteristics: />All elements W in the matrix ij Not more than 1. When W is ii When=1, tr (AV T RU) reaches a maximum value, the following equation is obtained:
I＝W＝V T RU
the display solution for deriving the rotation matrix is as follows:
R＝VCU T ,C＝diag(1,...,det(VU T ))
and step 4, iterating the steps S2 and S3 until F norms of the rotation matrixes R and R0 obtained by solving twice are smaller than a certain threshold value, and considering that the solving is converged at the moment, so as to obtain an accurate translation rotation matrix.
And 5, applying the obtained transformation matrix T (R, T) to the original point cloud Q, thereby completing the registration of the point clouds P and Q. The result is shown in FIG. 2 (d).
In order to verify the robustness of the method in abnormal point cloud registration, a Stanford Bunny dataset is particularly adopted, and registration results of point clouds under different conditions are demonstrated: different initialization point clouds are respectively input, and the angle difference between the two point clouds is 50 degrees: FIG. 3 (a) is an initialization point cloud for noise conditions; FIG. 3 (b) is an initialization point cloud for the outlier case; fig. 3 (c) is an initialization point cloud in the absence. Fig. 4 (a) is the registration result of fig. 3 (a); fig. 4 (b) is the registration result of fig. 3 (b); fig. 4 (c) is the registration result of fig. 3 (c);
to verify the robustness of the method in various cases, the stanfordung with noise, outliers and missing is input as in fig. 5 (a), and fig. 5 (b) is a post-registration result graph.
More well-known point cloud models are used such as: fish, fu, face. The registration results for the various models under different abnormal conditions are shown in fig. 6. Fig. 6 (a) is a registration result of fish; fig. 6 (b) is the registration result of fu; fig. 6 (c) is a registration result of face;
in order to prove that the method is not only suitable for point cloud data of artificial abnormal points, missing points and noise, three kinds of actually scanned point cloud data are adopted, for example, 7 (a) is Stanford Lounge Data which is actually scanned in the embodiment; fig. 7 (b) is a graph of the results after 7 (a) registration. Fig. 8 (a) shows Apoll SouthBay data of the present embodiment as a true scan; fig. 8 (b) is a graph of the results after registration of 8 (a); fig. 9 (a) is a Buddha Head data of the real scan of the present embodiment; fig. 9 (b) is a graph of the results after 9 (a) registration;
through the above, in the traditional point cloud data, by manually adding different abnormal conditions, the simulation of various abnormal points, missing points and noise points and the data scanned in the real kinect or lidar are achieved, so that the method has the best effect in coping with the point clouds which deteriorate in various degrees.
Finally, it is noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the present invention, which is intended to be covered by the claims of the present invention.
Claims (7)
1. An incomplete point cloud registration method based on a partial quality optimal transmission theory is characterized by comprising the following steps of: the method comprises the following steps:
s1: inputting two point clouds P and Q, aligning mass centers of the two point clouds after mass distribution to obtain new point clouds X and Y;
s2: establishing a point cloud registration energy function, and solving an optimal transmission matrix sigma between the point clouds X and Y by using a partial quality optimal transmission theory;
s3: according to the obtained optimal transmission plan sigma, a relative transformation matrix T (R, T) between two point clouds is obtained by SVD decomposition;
s4: repeating S2 to S3 until the F norms of the rotation matrix obtained twice are converged;
s5: applying the finally obtained transformation matrix T (R, T) to the point cloud Q, and registering the point clouds P and Q;
in the step S2, the optimal transmission theory is relaxed, the RG divergence function is used to relax the mass conservation rule, the concept of transmission cost is used to model the registration of two point clouds, the transmission cost is obtained by multiplying the distance between two points by the corresponding transmission plan, the adopted distance function is the square of the euclidean distance between the two points, and the point cloud registration energy function is as follows:
s201: firstly, fixing a transformation matrix T (R, T) by using an alternating iterative algorithm, solving an optimal transmission plan sigma, approximately solving by an entropy regularization term, wherein epsilon is an entropy regularization term coefficient, and controlling the regularization degree; the point cloud registration energy function is rewritten as:
h (σ) is the entropy of the transmission plan, which is of the form:
s202: solving the point cloud registration problem is a convex optimization problem, and the optimal transmission plan is expressed as follows:
σ＝diag(exp(u/))Kdiag(exp(v/))
wherein the method comprises the steps ofu and v are two solving vectors of the dual problem of the point cloud registration energy function, the optimal transmission plan is solved by the two vectors, and the variables are replaced as follows:
a＝exp(u/),b＝exp(v/).
according to the dual criteria, the variables a, b are alternately iterated to solve the convex optimization problem, and the variable iterations are as follows:
using an RG function to restrict the total quality of point cloud transmission, and rewriting a transmission plan into:
π＝g·diag(exp(u/))Kdiag(exp(v/))
g is a scaling factor controlling overall transmission, solving the expression as follows:
representing the corresponding point division of the vector, when using the F function as the RG function presented herein, the corresponding operators are as follows:
the transmission plan is calculated by the above expression, and thus the solution of the transformation parameters T (R, T) is performed.
2. The partial quality optimal transmission theory-based incomplete point cloud registration method according to claim 1, wherein the method comprises the following steps: in the step S1: two point clouds p= { P are input 1 ,p 2 ,…,p m Sum q= { Q 1 ,q 2 ,…,q n Performing quality allocation, wherein the detailed method adopts an equal allocation idea without considering other information of the introduced features; the number of points in the point clouds P and Q is m and n, and the mass of each point in the point clouds P and Q is respectively:
3. the partial quality optimal transmission theory-based incomplete point cloud registration method according to claim 1, wherein the method comprises the following steps: in the step S1, the mass center of gravity B of the two-point cloud p And B q The method comprises the following steps of:
after aligning the mass center of gravity, obtaining a new point cloud X and a new point cloud Y, wherein the coordinates of the points are as follows:
4. the partial quality optimal transmission theory-based incomplete point cloud registration method according to claim 1, wherein the method comprises the following steps: in the step S2, a partial quality optimal transmission theory is used, and when a transmission plan is calculated, a range constraint spread function is used, so that the quality transmission of the point cloud is relaxed, and the quality conservation criterion is broken; the RG function is used for restraining the total quality of the transmission point cloud Y, so that the robustness of the algorithm under the conditions of a large number of abnormal points and loss is improved;
5. the partial quality optimal transmission theory-based incomplete point cloud registration method according to claim 1, wherein the method comprises the following steps: in the step S3, after the transmission plan is obtained, the transformation matrix T (R, T) is left in the energy function to be solved, and the energy function is as follows:
s301: and (3) performing partial derivative on the energy function to obtain a translation vector:
s302: replacing the translation matrix t in the objective function, the objective function is rewritten as:
the above is replaced as followsAnd the constant term is omitted, the new energy function is:
obtaining the minimum value of the energy function when the trace is maximized; using the trace feature tr (AB) =tr (BA), we get:for->Singular value SVD decomposition to obtain UAV T And again using the trace features, we get: />Let w=v T RU，V t R, U are orthogonal matrices, and W is also an orthogonal matrix; w_j is each column in W, the utilization characteristics: />All elements W in the matrix ij Not more than 1; when W is ii When=1, tr (AV T RU) reaches a maximum value, resulting in the following equation:
I＝W＝V T RU
the display solution for deriving the rotation matrix is as follows:
R＝VCU T ,C＝diag(1,...,det(VU T ))。
6. the partial quality optimal transmission theory-based incomplete point cloud registration method according to claim 1, wherein the method comprises the following steps: in the step S4, the steps S2 and S3 are iterated until the F norms of the rotation matrices R and R0 obtained by solving twice are smaller than a certain threshold, and then the solution is considered to be converged at this time, so as to obtain an accurate translation rotation matrix.
7. The partial quality optimal transmission theory-based incomplete point cloud registration method according to claim 1, wherein the method comprises the following steps: in the step S5, the obtained transformation matrix T (R, T) is applied to the original point cloud Q, and the registration of the point clouds P and Q is completed.
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