Inlier screening and 3D point cloud registration method based on iterative reweighted voting mechanism

Abstract

The present application relates to a kind of based on iterative re-weighted voting mechanism interior point screening and three-dimensional point cloud registration method, belong to computer vision field.It includes: obtaining point cloud data, and initial corresponding set is generated based on FPFH algorithm;Compatibility graph is constructed for initial corresponding set, and the compatibility score between two points is calculated;Digging figure voter, search all ternary cycles in graph as voter, and score is obtained for each point by voting;Compatibility score obtained is sorted, and voter is weighted according to sorting result;Again, corresponding point is voted, and the voting score after re-weighted iteration is obtained;Repeat step S4 n times, and final voting score is used as input corresponding final confidence score;By OTSU threshold technique and final confidence score, internal set is obtained;By RANSAC algorithm, point cloud registration is carried out to the internal set obtained.The method has good generalization, simple and effective, strong robustness.

Description

Technical Field

[0001] This invention belongs to the field of computer vision, specifically relating to an interior point selection and 3D point cloud registration method based on an iterative reweighted voting mechanism. Background Technology

[0002] Point clouds are collections of three-dimensional points, each typically including coordinate information and other relevant attributes. Point cloud registration is an important research direction in point cloud data processing. By finding the mapping relationship between different point clouds from different perspectives, certain algorithms are used to align two or more point cloud datasets so that they have the optimal overlap relationship in the same coordinate system. With the development of technology, point cloud registration algorithms are widely used in fields such as autonomous driving, drones, high-precision maps, and image recognition. Currently, the performance of keypoint detectors and 3D local descriptors on real datasets is still limited, which leads to a large number of outliers in the initial correspondence set. In addition, subtle perturbations at the program level, such as clutter, occlusion, and limited overlap, may further reduce the initial ratio of the generated correspondence set. Finding the maximum initial correspondence set from the initial point cloud correspondence set with a large number of outliers is the core problem of point cloud registration. 3D point cloud feature registration has made great progress in the past few years, but finding the maximum initial correspondence set remains a challenging problem. Existing interior point selection methods can be divided into two types: geometry-based and learning-based methods. Geometry-based methods can be further divided into label-based and score-based methods. Since deep learning-based object recognition methods rely on large-scale datasets, but in real-world scenarios, the quantity and quality of datasets are difficult to guarantee. Therefore, we still adhere to using geometric methods for interior point selection and 3D point cloud registration.

[0003] This invention relates to a feature matching method based on voting, called iterative reweighted voting. This method mainly consists of two modules: voter definition and iterative reweighted voting. The main idea is to model the initial correspondence set as a graph, then use the graph elements as voters for all nodes, setting the high-scoring points as the inlier set, and using the resulting inlier set as input for point cloud registration. However, existing inlier selection methods still have some problems: their adaptability is weak, and they mostly only perform well on certain specific datasets; in initial sets with a large number of outliers, the ability of existing algorithms to find the largest initial inlier set remains limited. Furthermore, they lack robustness to common data nuances such as noise and limited overlap. Summary of the Invention

[0004] The technical problem to be solved by this invention is:

[0005] To avoid the shortcomings of existing technologies, this invention provides an interior point selection and 3D point cloud registration method based on an iterative reweighted voting mechanism, which solves the problem of poor robustness of existing interior point selection methods.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0007] A method for interior point selection and 3D point cloud registration based on an iterative reweighted voting mechanism is characterized by the following steps:

[0008] S1: Acquire point cloud data and generate an initial correspondence set based on the FPFH algorithm;

[0009] S2: Construct a compatibility graph for the initial correspondence set and calculate the compatibility score between two points;

[0010] S3: Discover graphical voters, search for all ternary cycles in the graph as voters, and vote for each point to get a score;

[0011] S4: Sort the obtained compatibility scores, and weight the voters according to the sorting results; vote again on the corresponding points to obtain the voting scores after reweighting iteration;

[0012] S5: Repeat step S4 n times, using the final voting score as the input for the corresponding final confidence score;

[0013] S6: Obtain the inner set using the OTSU thresholding technique and the final confidence score;

[0014] S7: Perform point cloud registration on the obtained internal set using the RANSAC algorithm.

[0015] A further technical solution of the present invention: the point cloud data includes images or maps acquired by unmanned vehicles or drones.

[0016] A further technical solution of the present invention: S1 includes the following steps:

[0017] S11: Use KdTree to find the K nearest neighbors of the keypoint R. Connect these (K+1) points pairwise to form K(K+1) / 2 pairs. For each pair, calculate a local coordinate system to estimate the relative normal vector deviation between the two pairs. Using p in a pair as an example... s As the source point of the local coordinate system, the coordinate system is determined according to the following formula:

[0018]

[0019] Where, n s For point p s The normal vector, n t For point pt The normal vector;

[0020] S12: After obtaining the local coordinate system, the features are described based on the local coordinate system, and the three parameters are obtained using formula (2); the triplet feature description vector composed of these three parameters is called the simplified point feature histogram SPFH:

[0021]

[0022] S13: Change the way the K nearest neighbor points in the neighborhood of key point R are combined, and connect the query point with the K nearest neighbor points in the neighborhood to form point pairs; calculate the SPFH of these K point pairs and perform a weighted summation to calculate the FPFH local feature descriptor of the key point:

[0023]

[0024] S14: For FPFH(p q Histogram statistical voting is performed to generate FPFH local feature descriptions of key points; based on the extracted feature points, FPFH is combined with a SAC-IA method, i.e. a greedy search, to establish preliminary correspondences between point clouds.

[0025] A further technical solution of the present invention: S2 includes the following steps:

[0026] S21: Evaluate c through rigid constraints i and c j Compatibility score between

[0027] Iterate through all points in the obtained point cloud, and for any two points c... i and c j First, calculate the distances between two points in the original point cloud and the target point cloud respectively, then calculate the difference between the two distances to obtain d(c i ,c j ), using d(c i ,c j Calculate the compatibility score S smp (c i ,c j );

[0028]

[0029]

[0030] S22: If s cmp (c i ,c j )>t cmp , t cmpThe threshold is set, and if the obtained compatibility score is greater than the set threshold, then c is applied. i and c j Connect the elements with an edge to construct a compatibility graph.

[0031] A further technical solution of the present invention: S3 includes the following steps:

[0032] S31: Iterate through all points in the compatibility graph and find all ternary cycles in the graph as voters; for three points c1, c2, c3, if the compatibility requirements are met, that is, the three points are connected to each other by an edge in the compatibility graph, then c1, c2, c3 form a ternary cycle V.

[0033] S32: Vote for each point according to the following formula to obtain the relevant score:

[0034]

[0035] f(c,v j ) = s cmp (c,c j1 )+s cmp (c,c j2 )+s cmp (c j1 ,c j2 (7)

[0036] Where, f(c,v) j ) represents the fractional contribution of a triple loop to point c, which is the sum of the compatibility scores of the three sides of the triangle.

[0037] A further technical solution of the present invention: S4 includes the following steps:

[0038] S41: Sort the scores obtained from each point using quicksort to get the ranking of the scores corresponding to c1, c2, and c3;

[0039] S42: Reweight the voters according to the following formula, assigning new voting weights to each triple loop:

[0040]

[0041]

[0042] Among them, r′, r′ i1 、r′ i2 These are the score rankings for each point for the i-th voter.

[0043] A further technical solution of the present invention: S6 specifically involves: calculating the threshold of each point's score using the OTSU thresholding technique; when the confidence score of a point is higher than the threshold, the point is identified as an inlier; when it is lower than the threshold, the point is considered an outlier, thus obtaining the inlier set.

[0044] A further technical solution of the present invention: S7 includes the following steps:

[0045] S71: Randomly select three points from the key points of the source point cloud S, because three points are the minimum number of points that can form a rigid body transformation matrix; find the corresponding three points in the target point cloud T based on the similarity of local feature descriptions to form three sets of matching point pairs.

[0046] S72: Calculate the rigid body transformation matrix based on these three sets of matching point pairs, and apply the transformation matrix to each point in the source point cloud S to generate the transformed point cloud S1;

[0047] S73: Find the number of all points in point cloud S1 and target point cloud T that meet the distance threshold requirement, and form a consistent point set for the transformation matrix;

[0048] S74: After several iterations, select the rigid body transformation matrix that creates the largest set of consistent points as the final output to complete the registration.

[0049] A further technical solution of the present invention: S74 also includes: setting a flag for exiting the iteration, such as when the size of the consistency point set is greater than a preset threshold, determining that the optimal registration transformation matrix has been obtained, and then cutting off the remaining iteration process to reduce time overhead.

[0050] An evaluation method for interior point selection and 3D point cloud registration based on an iterative reweighted voting mechanism is characterized by using rotation error (RE) and transformation error (TE) as evaluation indicators, and comparing RE and TE with corresponding thresholds respectively; the calculation formulas for RE and TE are as follows:

[0051]

[0052]

[0053] in, For rotation matrix, For translation matrix, t gt For the actual translation of the ground, R gt This represents the actual rotation of the ground.

[0054] The beneficial effects of this invention are as follows:

[0055] This invention provides an interior point selection and 3D point cloud registration method based on an iterative reweighted voting mechanism. This method mines voters from the graph and iteratively refines voter weights through a reweighting mechanism to reduce unreliable votes and improve voting reliability. Based on this, point cloud registration is performed on the obtained initial correspondence set. This method achieves excellent performance on both object-scale and scene-scale datasets. Even without training data, it achieves performance comparable to other deep learning-based algorithms, and its advantages are even more pronounced under low interior point ratios. Compared with existing interior point selection methods based on traditional methods, it has the following advantages:

[0056] 1) The method of this invention has good generalization ability. Voting takes place in a graph rather than in a three-dimensional spatial domain. This method achieves excellent performance on datasets at both object and scene scales.

[0057] 2) The method of the present invention is simple and effective. Even without training data, it can achieve competitive performance like several deep learning algorithms, and its advantages are even more pronounced under low internal ratios.

[0058] 3) The method of this invention is highly robust. In our voting process, not all voters are equal due to the reweighting process. This helps eliminate the side effects of unreliable voters, resulting in excellent accuracy and performance. Attached Figure Description

[0059] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0060] Figure 1 A diagram illustrating the method for implementing the present invention.

[0061] Figure 2 FPFH is a method for calculating local feature descriptions.

[0062] Figure 3 A flowchart of the method of the present invention.

[0063] Figure 4 Generate the flowchart of the inner set.

[0064] Figure 5 The performance of the test methods on the 3D feature matching datasets U3M and U3M-LO is as follows: (a) U3M(linear); (b) U3M(log); (c) U3M-LO(linear); (b) U3M-LO(log).

[0065] Figure 6 Feature matching results.

[0066] Figure 7 Point cloud registration result diagram. Detailed Implementation

[0067] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0068] This invention provides a method for interior point selection and 3D point cloud registration based on an iterative reweighted voting mechanism, the process of which is as follows: Figure 1 As shown. First, using the initial 3D feature correspondences as input, the compatibility score of each correspondence with other correspondences is calculated to construct a compatibility graph, and the ternary loops in the graph are used as voters. Then, the voters are iteratively reweighted and reweighted voting is performed to score the correspondences; the correspondence with the highest score is regarded as an interior point.

[0069] The following examples illustrate the interior point selection and 3D point cloud registration method based on an iterative reweighted voting mechanism provided by this invention. Figure 3 As shown:

[0070] (1) The specific process of generating the initial correspondence set based on the FPFH (Fast Point Feature Histograms) algorithm is as follows: Figure 2 As shown:

[0071] Using KdTree, find the K nearest neighbors of a keypoint R. Connect these (K+1) points pairwise to form K(K+1) / 2 pairs. For each pair, calculate a local coordinate system to estimate the relative normal vector deviation between the two pairs. Let p be a point in a pair. s As the source point of the local coordinate system, the coordinate system is determined according to the following formula:

[0072]

[0073] Where, n s For point p s The normal vector, n s For p t The normal vector.

[0074] After determining the local coordinate system, the features are described based on the local coordinate system. For example, the three parameters are obtained by formula (2). The feature description vector of this triplet is called the Simplified Point Feature Histogram (SPFH).

[0075]

[0076] Change the way the K nearest neighbor points in the neighborhood of key point R are combined, and combine the query point with the K nearest neighbor points (p) in the neighborhood. i Connect the points to form point pairs. Calculate the SPFH of these K point pairs and perform a weighted summation to calculate the keypoints (p). q The FPFH local feature descriptor.

[0077]

[0078] For FPFH(p q Histogram statistical voting is performed to generate FPFH local feature descriptions of key points. Based on the extracted feature points, FPFH is combined with a method called SAC-IA (Sample Consensus Initial Alignment), which is a greedy search, to establish preliminary correspondences between point clouds.

[0079] (2) Evaluate c through rigid constraints i and c j Compatibility score between cmp Iterate through all points in the resulting point cloud. For any two points c... i and c j First, calculate the distance between two points in the point cloud based on the vectors of two points in the original point cloud and the vectors of two points in the target point cloud. Then, obtain d(c) based on the difference between the two distances. i ,c j The compatibility score s is calculated using formula (5). cmp Among them, s cmp The value of α is between (0, 1). dist Set it to 10pr (pr is the point cloud resolution). c i and c j The vectors corresponding to the origin point cloud and the target point cloud.

[0080]

[0081]

[0082] If s cmp (c i ,c j )>t cmp , t cmp The threshold is set when the obtained compatibility score s cmp If it exceeds the set threshold, then it is c. iand c j Connect the elements with an edge to construct a compatibility graph.

[0083] (3) Discover graphic voters, searching for all ternary cycles in the graph as voters, such as... Figure 4 As shown, the specific steps for voting to obtain a score for each point include: looping through all points in the constructed compatibility graph and finding all ternary cycles in the graph as voters. For three points c1, c2, and c3, if all three points meet the compatibility requirements, that is, there are edges connecting all three points in the compatibility graph, then a ternary cycle is formed as a voter. Voting is performed on each point according to the following formula (7) to obtain the relevant score. Where f(c,v) j ) represents the fractional contribution of a triple loop to point c, which is the sum of the compatibility scores of the three sides of the triangle.

[0084]

[0085] f(c,v j ) = s cmp (c,c j1 )+s cmp (c,c j2 )+s cmp (c j1 ,c j2 (7)

[0086] (4) Sort the obtained compatibility scores and weight the voters according to the sorting results. Vote again for the corresponding points to obtain the reweighted voting scores. Sort the scores of each point to obtain the ranking of each point. Reweight the voters according to the following formula, r′, r′ i1 ,r′ i2 Let each point be ranked according to its score for the i-th voter. Each triple loop assigns a new voting weight, and the score s(c) for each point is calculated based on the new voting weight.

[0087]

[0088]

[0089] (5) Repeat step (4) n times, and use the final voting score as the input corresponding to the final confidence score.

[0090] (6) Obtain the inner set using the OTSU thresholding technique and the final confidence score. The threshold for each point's score is calculated using the OTSU thresholding technique. When the confidence score of a point is higher than the threshold, the point is identified as an inner point. When it is lower than the threshold, the point is considered an outlier, thus obtaining the inner point set.

[0091] (7) The obtained internal set is registered using the RANSAC (Random Sample Consensus) algorithm, and the rotation error RE and transformation error TE are calculated.

[0092] (7.1) Randomly select three points from the keypoints of the source point cloud S, because three points are the minimum number of points required to form a rigid body transformation matrix. In the target point cloud T, find the corresponding three points based on the similarity of local feature descriptions to form three sets of matching point pairs;

[0093] (7.2) Calculate the rigid body transformation matrix based on these three sets of matching point pairs, and apply the transformation matrix to each point in the source point cloud S to generate the transformed point cloud S1;

[0094] (7.3) Find the number of all points in point cloud S1 and target point cloud T that meet the distance threshold requirement (i.e., the distance is less than a certain threshold), and form the consistency point set of the transformation matrix;

[0095] (7.4) After iterating the above calculation process several times, select the rigid body transformation matrix that creates the largest set of consistent points as the final output to complete the registration. In addition, a flag can be set to exit the iteration, such as when the size of the set of consistent points is greater than a preset threshold, the optimal registration transformation matrix is ​​considered to have been obtained, and then the remaining iteration process is cut off to reduce time overhead.

[0096] (7.5) The corresponding rotation matrix is ​​obtained. Translation matrix The rotation error RE and translation error TE are calculated according to formulas (10) and (11), where R gt For the actual rotation of the ground, t gt This represents the actual translation of the ground. The calculated rotation and translation matrices are evaluated and compared with the corresponding thresholds. If RE ≤ 15 degrees and TE ≤ 30 cm, then the calculated rotation and translation matrices meet the requirements.

[0097]

[0098]

[0099] Overall, compared with existing interior point selection algorithms based on traditional methods, this invention has the following advantages:

[0100] This invention proposes a simple yet effective method for geometric integral interior point selection and 3D point cloud registration. Utilizing the proposed iterative reweighted voting mechanism, more reliable voters can be identified, and then the corresponding votes are sorted based on their scores to retrieve information.

[0101] The performance of the test method on the 3D feature matching datasets U3M and U3M-LO is shown. For each dataset, we present two plots with linear and logarithmic recall axes, as follows: Figure 5 As shown, this is to more clearly illustrate the performance difference when the K (i.e., top-K) value is large and small, respectively.

[0102] On both target-scale and scene-scale datasets, IR-GV achieves outstanding feature matching and 3D point cloud registration performance. It even surpasses several deep learning-based methods. For feature matching results such as... Figure 6 We found a significant difference in the voting scores assigned to inliers and outliers, as shown by the corresponding colors, indicating that IR-GV can accurately classify inliers and outliers. Regarding the registration results of the point cloud... Figure 7 We can see that IR-GV achieves more accurate registration than its competitors on the corresponding subset selected by IR-GV.

[0103] On the 3DMatch and 3DLoMatch datasets, as shown in Tables 1 and 2, our method outperforms all comparable methods in registration accuracy, including those using only geometry and deep learning methods. Even compared to deep learning methods, our geometry-based method is highly competitive, with the advantage of not requiring training data. This demonstrates the feasibility of our method in real-world applications. This gap is particularly pronounced on 3DLoMatch, where our method surpasses PointDSC by 3.54%.

[0104] The precision and recall results in Table 3 demonstrate that IR-GV has a greater gap with other RANSAC methods that require fewer iterations, especially on the 3DLoMatch dataset. Specifically, our method has high selectivity while achieving excellent precision and recall performance.

[0105] Table 1 shows the registration accuracy of the 3DMatch dataset under FPFH settings.

[0106]

[0107] Table 2 shows the registration accuracy on the 3DLoMatch dataset under FPFH settings.

[0108]

[0109]

[0110] Table 3 shows the performance of the RANSAC-based method for point cloud registration and feature matching on the 3DMatch and 3DLoMatch datasets.

[0111]

[0112] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention.

Claims

1. A method for interior point selection and 3D point cloud registration based on an iterative reweighted voting mechanism, characterized in that... The steps are as follows: S1: Acquire point cloud data and generate an initial correspondence set based on the FPFH algorithm; S2: Construct a compatibility graph for the initial correspondence set and calculate the compatibility score between two points; S2 includes the following steps: S21: Evaluate c through rigid constraints i and c j Compatibility score between Iterate through all points in the obtained point cloud, and for any two points c... i and c j First, calculate the distances between two points in the original point cloud and the target point cloud respectively, then calculate the difference between the two distances to obtain d(c i ,c j ), using d(c i ,c j Calculate compatibility score S smp ( c i ,c j ); （4） （5） S22: If s cmp (c i , c j ) > t cmp , t cmp A threshold is set; if the obtained compatibility score is greater than the set threshold, then... and Connect the nodes with an edge to construct a compatibility graph; S3: Discover graphical voters by searching for all ternary cycles in the graph as voters and voting for each point to obtain a score; S3 includes the following steps: S31: Loop through all points in the compatibility graph, finding all ternary cycles in the graph as voters; for three points... , , If all three points satisfy the compatibility requirements, meaning that there are edges connecting all three points in the compatibility graph, then , , This forms a ternary cycle V; S32: Vote for each point according to the following formula to obtain the relevant score: （6） （7） in, The fractional contribution of a triple loop to point c is the sum of the compatibility scores of the three sides of the triangle. S4: Sort the obtained compatibility scores and weight the voters according to the sorting results; vote again on the corresponding points to obtain the voting scores after reweighting iteration; S4 includes the following steps: S41: Sort the scores obtained from each point using quicksort to get... , , Corresponding score ranking; S42: Reweight the voters according to the following formula, assigning new voting weights to each triple loop: (8) (9) in, , , The first i Ranking of each voter's score at each point; S5: Repeat step S4 n times, using the final voting score as the input for the corresponding final confidence score; S6: Obtain the inner set using the OTSU thresholding technique and the final confidence score; S7: Perform point cloud registration on the obtained internal set using the RANSAC algorithm.

2. The method for interior point selection and 3D point cloud registration based on iterative reweighted voting mechanism according to claim 1, characterized in that, The point cloud data includes images or maps acquired by autonomous vehicles or drones.

3. The method for interior point selection and 3D point cloud registration based on iterative reweighted voting mechanism according to claim 1, characterized in that, S1 includes the following steps: S11: Use KdTree to find the K nearest neighbors of the keypoint R neighborhood. Connect these (K+1) points pairwise to form K(K+1) / 2 pairs. For each pair, calculate a local coordinate system to estimate the relative normal vector deviation between the two pairs. As the source point of the local coordinate system, the coordinate system is determined according to the following formula: （1） Where ns is the normal vector of point ps, n t Let be the normal vector of point pt; S12: After obtaining the local coordinate system, the features are described based on the local coordinate system, and the three parameters are obtained using formula (2); the triplet feature description vector composed of these three parameters is called the simplified point feature histogram SPFH: （2） S13: Change the way the K nearest neighbor points in the neighborhood of key point R are combined, and connect the query point with the K nearest neighbor points in the neighborhood to form point pairs; calculate the SPFH of these K point pairs and perform a weighted summation to calculate the FPFH local feature descriptor of the key point: （3） S14: For FPFH(p q Histogram statistical voting is performed to generate FPFH local feature descriptions of key points; based on the extracted feature points, FPFH is combined with a SAC-IA method, i.e. a greedy search, to establish preliminary correspondences between point clouds.

4. The method for interior point selection and 3D point cloud registration based on iterative reweighted voting mechanism according to claim 1, characterized in that, S6 specifically involves calculating the threshold for each point's score using the OTSU thresholding technique. When a point's confidence score is higher than the threshold, it is considered an inlier; when it is lower than the threshold, it is considered an outlier, thus obtaining the inlier set.

5. The method for interior point selection and 3D point cloud registration based on iterative reweighted voting mechanism according to claim 1, characterized in that, S7 includes the following steps: S71: Randomly select three points from the key points of the source point cloud S, because three points are the minimum number of points that can form a rigid body transformation matrix; find the corresponding three points in the target point cloud T based on the similarity of local feature descriptions to form three sets of matching point pairs. S72: Calculate the rigid body transformation matrix based on these three sets of matching point pairs, and apply the transformation matrix to each point in the source point cloud S to generate the transformed point cloud. ; S73: Locate the point cloud The number of all points in the target point cloud T that meet the distance threshold requirement constitutes the consistency point set of the transformation matrix; S74: After several iterations, select the rigid body transformation matrix that creates the largest set of consistent points as the final output to complete the registration.

6. The method for interior point selection and 3D point cloud registration based on iterative reweighted voting mechanism according to claim 5, characterized in that, S74 also includes: setting a flag for exiting the iteration, such as when the size of the consistency point set is greater than a preset threshold, determining that the optimal registration transformation matrix has been obtained, and then cutting off the remaining iteration process to reduce time overhead.

7. An evaluation method for the interior point selection and 3D point cloud registration method based on an iterative reweighted voting mechanism as described in any one of claims 1-6, characterized in that, Rotation error (RE) and conversion error (TE) are used as evaluation indicators, and their respective values ​​are compared with corresponding thresholds. The calculation formulas for rotation error (RE) and conversion error (TE) are as follows: （10） （11） in, For rotation matrix, For translation matrix, For the actual translation of the ground, This represents the actual rotation of the ground.

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