CN113256693A - Multi-view registration method based on K-means and normal distribution transformation - Google Patents
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Abstract
The invention provides a multi-view registration method based on K-means and normal distribution transformation, and relates to the technical field of three-dimensional reconstruction, mode identification and computer vision. According to the multi-view registration method based on K-means and normal distribution transformation, firstly, a clustering method idea is utilized to perform grid division on an integral three-dimensional object, and the mean value and covariance of point sets of all grid units are calculated. Assuming that each point in the data point cloud to be registered corresponds to a grid unit, and the probabilities of the corresponding points in the same grid unit all follow the same gaussian distribution, a probability and a function can be obtained. The method uses a first-order partial derivative to simplify a target function, and uses a lie algebra method to perform iterative optimization to obtain an optimal transformation relation of each frame of point cloud under the condition that the point cloud is mapped to a reference coordinate system, so as to finally obtain an accurate registration model. Experimental results show that the method has a good effect on multi-view registration in a three-dimensional space.
Description
Technical Field
The invention relates to the technical field of three-dimensional reconstruction, pattern recognition and computer vision, in particular to a multi-view registration method based on K-means and normal distribution transformation.
Background
Since the nineties of the twentieth century, with the rapid development of computers and sensor devices, it has become more and more convenient to obtain high-density and high-precision point cloud data, and point cloud registration has gradually become a hot problem in the research fields of computer vision, mobile robots, pattern recognition and the like. Due to the influence of the scanning scene range, the data acquired each time is incomplete, and the information of a complete object or scene cannot be reflected. The multi-view point cloud registration technology can register and fuse multi-frame point cloud data collected from different angles, so that a complete three-dimensional point cloud model of a target is obtained, and the method is further applied to the problems of target tracking, motion detection, scene reconstruction and the like, and the representative application of the method is embodied in the following aspects:
1) three-dimensional reconstruction
Three-dimensional reconstruction is a very fundamental but at the same time very important task in the field of computer vision. The technology acquires point cloud data of a target object or a scene to perform point cloud registration and fusion. In practical application, due to the reasons of view angle occlusion and the like, usually, only part of point cloud coordinates of an object or a scene can be acquired by each sensor acquisition, and multi-frame point cloud fusion can be realized by utilizing the existing three-dimensional point cloud data registration technology to complete the three-dimensional reconstruction process of a large scene or object. The complete three-dimensional reconstruction process typically requires several steps: the method comprises the processes of point cloud data acquisition, point cloud preprocessing, point cloud registration and fusion, data derivation, grid rendering and the like. Among them, point cloud registration and fusion are the most critical in the process.
2) Mobile robot map creation
With the rapid development of computer vision processing technology, the degree of intellectualization of the mobile robot is higher and higher, and the mobile robot is widely applied to industries such as family life, catering and the like. In the process of creating the map, the mobile robot needs to continuously obtain accurate attitude information, and the position and attitude information of the mobile robot can be accurately calculated by using a point cloud registration technology. After the laser radar of the robot acquires the point cloud information of the surrounding environment, the edge information of the map to be spliced is extracted to obtain point cloud data corresponding to the map, and then accurate map splicing parameters are calculated by using a point cloud registration technology to realize map splicing.
3) Automatic driving
An autopilot system generally includes five sub-modules, respectively: sensor, sensing, positioning, planning and control, point cloud registration technology can realize the positioning module. When the sensor generates point cloud data and inputs the point cloud data into the positioning system, multi-frame point clouds of the surrounding environment can be generated, the point cloud registration technology can perform registration and fusion on the point clouds, and a real-time map is generated and updated for subsequent use. Positioning plays a crucial role in the whole automatic driving system, and the point cloud registration technology is the key technology.
4) Medical image processing
With the continuous maturity of medical imaging equipment technology, more and more technologies can be used for acquiring human pathological information, and images of multiple human body modalities acquired by different technologies can reflect different pathological characteristics of patients. In practical clinical medical applications, a single-source modality image often provides only single information, and other pathological factors are not considered, which may cause a judgment result of a doctor to be wrong. To obtain more comprehensive information, point cloud registration techniques may fuse together multiple modality images acquired from different devices to obtain overall pathological information of the body to assist in treatment. In the medical field, functional images (for example) can capture human body functional information, such as metabolic transformation and the like, but the imaging mode has low resolution and cannot better reflect the morphological structure, tissues, organs and the like of the human body; whereas anatomical images (for example) have a high spatial resolution and sharp geometric properties, but do not show functional information of the human body. The point cloud registration technology can register two images with the same structure but reflecting different characteristics, thereby not only displaying various functional information of the human body, but also clearly displaying the morphological structure of the human body.
In conclusion, the point cloud registration technology and method have wide application prospects in various fields. At present, related documents already provide a plurality of effective point cloud registration methods, but most of the traditional registration methods are only suitable for solving the double-view-point cloud registration problem. In practical application, the multi-view point cloud registration problem is often faced. Compared with the double-view-point cloud registration problem, the multi-view-point cloud registration problem focuses more on the registration precision and the registration efficiency. Therefore, the method has important practical significance in researching the multi-view point cloud registration method with high registration accuracy and high efficiency.
Disclosure of Invention
Technical problem to be solved
Aiming at the defects of the prior art, the invention provides a multi-view registration method based on K-means and normal distribution transformation, and overcomes the defects of the existing multi-view registration method.
(II) technical scheme
In order to achieve the purpose, the invention is realized by the following technical scheme: the multi-view registration method based on K-means and normal distribution transformation comprises the following specific implementation steps:
1) establishing grid cells using clustering methodology
Because the cubic grid unit is difficult to divide in the three-dimensional space, and the method has the advantages of high convergence rate and good clustering effect, the invention provides the idea of using the clustering method to realize the division of the spherical grid unit of the data point cloud in the three-dimensional space to replace the cubic grid unit. Firstly, scanning the surrounding environment by using a laser scanner to obtain a three-dimensional point cloud, and obtaining an initial registration model through an initial rotation matrix and a translation vector. The initial centroid is determined by random spotting.
2) Determining the corresponding relation between each frame point cloud and the mass center to establish a grid unit
The target of the multi-view point cloud fine registration is to calculate accurate multi-view registration parameters, and the first frame is usually set as a reference frame so as to convert all point clouds into a coordinate system of the first frame point cloud, and the registration parameters of the first frame point cloud do not need to be calculated. And traversing all the frame numbers of the point clouds in sequence, and establishing the corresponding relation between all the points in each frame point cloud and the nearest neighbor centroid by adopting a tree-based nearest neighbor searching method. And fitting a spherical grid unit consisting of each centroid and nearest neighbor points into a Gaussian distribution function, and calculating a mean value and a covariance matrix through the internal points. The eigenvector and eigenvalue of the covariance matrix can express grid information, less than 3 points in the grid often cause the covariance matrix to have no inverse matrix, and grid units with less than 5 points are removed in the method. And establishing an objective function formula of the algorithm after re-determining the corresponding relation between the points and the rest grid units.
3) Obtaining accurate multi-view registration results
The first derivative and the partial derivative of the objective function are obtained, and the simplified objective function can be obtained. The simplified objective function contains a transformation matrix, and the addition calculation of the transformation matrix in the space is unclosed and needs to be mapped into lie algebra. The original optimization problem of the target function is converted into a convex optimization problem by using an exponential operator in a lie algebra, the convergence of the optimization method is expressed as second-order optimization, and the convergence speed is higher than that of the traditional gradient-based method. And calculating a Hessian matrix and a gradient vector updating transformation matrix, and transforming the three-dimensional point cloud of each frame into a global coordinate system to further obtain an accurate object model.
The calculation formula of the point set clustering method in the step 1) is as follows:
the cluster center obtained by the last iteration is represented, and the rotation matrix and the translation vector obtained by the last iteration are respectively obtained.
Step 2), fitting the grid units into a Gaussian distribution function, wherein the calculation formula of the mean value and the inverse covariance matrix is as follows:
in the inverse matrix calculation of the covariance, a minimum value is added in the method, a common covariance matrix comprises three singular values, when the three singular values are far larger than the common covariance matrix, the covariance matrix is singular, namely, a determinant is 0, inversion cannot be achieved, and the existence of the inverse matrix can be ensured by adding the minimum value.
The established objective function formula of the step 2) is as follows:
where a residual vector is represented, a detection factor is represented, which is often used to eliminate the effect of outliers, representing the inverse of the information matrix or covariance matrix.
Step 3), the formula of the objective function simplified by using a partial derivative and a first derivative is as follows:
wherein, the weight coefficient is represented, and the transformation matrix obtained after the last iteration is represented.
Step 3) the exponential operator using the lie algebra is that the simplified objective function formula is as follows:
wherein, a Hessian matrix is represented, b represents a gradient vector, c represents a constant, and the concrete representation of b and c is as follows:
setting a six-dimensional vector, which is a form of representing lie algebra on SE (3) space, and is expressed as a matrix as follows:
and step 3), the updating formula of the pair of the Hessian matrix and the gradient vector obtained by calculation is as follows:
ξ*＝-H-1b
using the calculated update for the transformation matrix:
the invention firstly utilizes a clustering method to perform grid division on the integral three-dimensional object and calculates the mean value and covariance of point sets of all grid units. Assuming that each point in the data point cloud to be registered corresponds to a grid unit, and the probabilities of the corresponding points in the same grid unit all follow the same gaussian distribution, a probability and a function can be obtained. The method uses a first-order partial derivative to simplify a target function, and uses a lie algebra method to perform iterative optimization to obtain an optimal transformation relation of each frame of point cloud under the condition that the point cloud is mapped to a reference coordinate system, so as to finally obtain an accurate registration model. Experimental results show that the method has a good effect on multi-view registration in a three-dimensional space.
(III) advantageous effects
The invention provides a multi-view registration method based on K-means and normal distribution transformation. The method has the following beneficial effects:
1. the clustering method is used for rapidly carrying out grid division on the original point cloud model in the three-dimensional space, and the polymerization degree is good.
2. The method adopts a Gaussian distribution function to fit the grid unit, utilizes a lie algebra to optimize a target function, uses second-order optimization, and has higher convergence speed than the traditional gradient-based method.
3. The registration error is small and a very accurate registration model can be obtained.
Drawings
FIG. 1 is a schematic flow chart of a multi-view registration method based on K-means and normal distribution transformation according to the present invention;
FIG. 2 is an information diagram of a data set disclosed in the present section of the multi-view registration method based on K-means and normal distribution transformation proposed in the present invention;
FIG. 3 is a data table of registration results of a K-means and normal distribution transformation based multi-view registration method and a public data set of a current mainstream registration method;
fig. 4 is a cross-sectional comparison result graph of the multi-view registration method based on K-means and normal distribution transformation, which is proposed by the present invention, and the current mainstream registration method in the public data set.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The specific embodiment is as follows:
referring to fig. 1, the multi-view registration method based on K-means and normal distribution transformation provided by the embodiment of the present invention is divided into three parts, and each part includes the following steps:
1) establishing a grid unit by using a clustering method, which comprises the following specific steps:
(1a) firstly, scanning a surrounding environment by using a laser scanner to obtain three-dimensional point cloud, and obtaining an initial registration model through an initial rotation matrix and a translation vector;
(1b) and determining the initial mass center of the clustering method through random point selection.
2) Determining the corresponding relation between all points in each frame of point set and grid units, and the specific steps are as follows:
(2a) traversing each frame of point cloud, establishing a corresponding relation between each point and a mass center based on a tree nearest neighbor searching method, and establishing a spherical grid unit for points near each mass center;
(2b) removing grid units with the number of points less than 5, and reestablishing the corresponding relation between each point and each grid unit;
(2c) and calculating a mean value and an inverse covariance matrix of the point sets in the grid units, and fitting each grid unit into a Gaussian distribution function. And fitting each point to a Gaussian distribution function, and accumulating to obtain a target function.
3) Optimizing an objective function, reducing the solving difficulty and obtaining an accurate multi-view registration result, and the method comprises the following specific steps:
(3a) the first derivative and the partial derivative are calculated for the objective function, and the objective function can be converted into the following form:
(3b) optimizing an objective function by using an exponential operator in a lie algebra, closing the addition calculation of a transformation matrix gamma in an SE (3) space, and converting the objective function into a target function after simplification:
wherein H denotes a Hessian matrix, b denotes a gradient vector, and c denotes a constant, which is specifically expressed as follows:
setting a six-dimensional vector xi ∈ R6Xi, a form representing lie algebra in SE (3) spaceΛExpressed in matrix form as follows:
(3c) xi after Hessian matrix and gradient vector are obtained through calculation*The update formula of (2) is as follows:
ξ*＝-H-1b
therefore, an updated rotation matrix and translation vector can be obtained, and the formula for updating the rotation matrix and the translation vector is as follows:
fig. 2 shows information of some of the currently 6 disclosed data sets, by which the registration results of the data sets can verify the effectiveness and robustness of the algorithm. Fig. 3 is a table showing the registration results of the present invention compared to the currently prevailing registration method on these 6 data sets, wherein bold font indicates the registration method with the best performance. Compared with the method, the method is respectively a multi-view registration method based on a motion average algorithm, a multi-view point cloud joint registration method, a multi-view registration method based on low-rank sparse matrix decomposition, a multi-view registration method based on a student-t mixed model and a multi-view registration (EMPMR) method based on expectation maximization. Fig. 4 shows the registration effect of the registration method of the present invention and the current mainstream in these public data sets and the cross section of the data sets, and the clearer the cross section is, the better the registration effect is. The initial result, the registration result of the using method, the registration result of the EMPRM method and the registration result of the method are shown.
Therefore, the registration method provided by the invention can obtain a very accurate registration model.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (7)
1. The multi-view registration method based on K-means and normal distribution transformation is characterized by comprising the following steps of:
1) establishing grid cells using clustering methodology
Because the cubic grid unit is difficult to divide in the three-dimensional space, and the method has the advantages of high convergence rate and good clustering effect, the invention provides the idea of using the clustering method to realize the division of the spherical grid unit of the data point cloud in the three-dimensional space to replace the cubic grid unit. Firstly, scanning the surrounding environment by using a laser scanner to obtain a three-dimensional point cloud, and obtaining an initial registration model through an initial rotation matrix and a translation vector. Determining an initial centroid through random point selection;
2) determining the corresponding relation between each frame point cloud and the mass center to establish a grid unit
The target of the multi-view point cloud fine registration is to calculate accurate multi-view registration parameters, and the first frame is usually set as a reference frame so as to convert all point clouds into a coordinate system of the first frame point cloud, and the registration parameters of the first frame point cloud do not need to be calculated. And traversing all the frame numbers of the point clouds in sequence, and establishing the corresponding relation between all the points in each frame point cloud and the nearest neighbor centroid by adopting a tree-based nearest neighbor searching method. And fitting a spherical grid unit consisting of each centroid and nearest neighbor points into a Gaussian distribution function, and calculating a mean value and a covariance matrix through the internal points. The eigenvector and eigenvalue of the covariance matrix can express grid information, less than 3 points in the grid often cause the covariance matrix to have no inverse matrix, and grid units with less than 5 points are removed in the method. Establishing a target function formula of the algorithm after re-determining the corresponding relation between the points and the rest grid cells;
3) obtaining accurate multi-view registration results
The first derivative and the partial derivative of the objective function are obtained, and the simplified objective function can be obtained. The simplified objective function contains a transformation matrix, and the addition calculation of the transformation matrix in the space is unclosed and needs to be mapped into lie algebra. The original optimization problem of the target function is converted into a convex optimization problem by using an exponential operator in a lie algebra, the convergence of the optimization method is expressed as second-order optimization, and the convergence speed is higher than that of the traditional gradient-based method. And calculating a Hessian matrix and a gradient vector updating transformation matrix, and transforming the three-dimensional point cloud of each frame into a global coordinate system to further obtain an accurate object model.
2. The K-means and normal distribution transformation based multi-view registration method of claim 1, wherein: step 1) the calculation formula of the clustering method used by the point set is as follows:
the cluster center obtained by the last iteration is represented, and the rotation matrix and the translation vector obtained by the last iteration are respectively obtained.
3. The K-means and normal distribution transformation based multi-view registration method of claim 1, wherein: step 2) fitting the grid cells into a Gaussian distribution function, wherein the mean value and covariance calculation formula is as follows:
in the calculation of the inverse matrix of the covariance, a minimum value is added in the method, a common covariance matrix comprises three singular values, if the three singular values are contained, the covariance matrix is singular, namely, the determinant is 0, so that inversion cannot be realized, and the existence of the inverse matrix can be ensured by adding a minimum value.
4. The K-means and normal distribution transformation based multi-view registration method of claim 1, wherein: the objective function formula established in step 2) is as follows:
where the residual vector is represented, the detection factor is represented, which is often used to eliminate the effect of outliers, the inverse of the covariance matrix or the information matrix.
5. The K-means and normal distribution transformation based multi-view registration method of claim 1, wherein: step 3), the formula of the objective function simplified by using the partial derivative and the first derivative is as follows:
wherein the content of the first and second substances,
the weight coefficient is represented by a weight coefficient,
representing the transformation matrix obtained after the last iteration.
6. The K-means and normal distribution transformation based multi-view registration method of claim 1, wherein: step 3) the exponential operator using the lie algebra is that the simplified objective function formula is as follows:
wherein H represents a Hessian matrix, b represents a gradient vector, c represents a constant, and the specific representation of H, b and c is as follows:
setting a six-dimensional vector xi ∈ R6Which represents a form of lie algebra on the SE (3) space, ξΛExpressed in matrix form as follows:
7. the K-means and normal distribution transformation based multi-view registration method of claim 1, wherein: step 3), calculating an updating formula of a Hessian matrix and gradient vectors, wherein the updating formula is as follows:
ξ*＝-H-1b
will calculate the xi*Update for the transformation matrix Γ:
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