3D Multi-Layered Normal Distribution Transform for Fast and Long Range Scan Matching

Ulaş, Cihan; Temeltaş, Hakan

doi:10.1007/s10846-012-9780-8

Cited by 54 publications

(29 citation statements)

References 15 publications

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“…Next, it computes the normal vector n of the fitting plane by principal component analysis (PCA) as shown in Fig. 3 [6]. It uses the eigenvector corresponding to the smallest eigenvalue of covariance matrix C as n , and then it obtains a plane which includes m as follows.…”

Section: A Flatness Evaluation Methodsmentioning

confidence: 99%

“…Fig. 2 is an example when  is set to 6 10  . The radius of ellipsoids standing for distributions are Mahalanobis distance of 1.8.…”

Section: Methodsmentioning

confidence: 99%

“…Flatness evaluation method computes MSE of distance between reference points and the fitting plane to evaluate the flatness of the partial point cloud in a cell. The black points are reference points, and the red point is the mean point.TT  n p n m(6) where p is an arbitrary point on the plane. Finally, it computes the MSE of distances.…”

mentioning

confidence: 99%

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A Method of Generating Multi-Scale Disc-Like Distributions for NDT Registration Algorithm

Hong¹,

Lee²

2016

IJMERR

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Thick distributions whose mass centers are hanging in the air is one reason lowering the accuracy of Normal Distributions Transform (NDT). This paper proposes a method to solve this problem. The proposed method is transforming reference point cloud to disc-like distributions fitting the structure of point cloud. The subdivision of cells is based on octree, and it subdivides point cloud by different sizes of cells. By Principal Component Analysis (PCA), it finds fitting plane for the partial reference point cloud in each cell. It compares the Mean Square Error (MSE) to the threshold value  to evaluate the flatness of the partial point cloud. If the cloud is not flat, the corresponding cell is subdivided to smaller cells, and those cells subdivide the cloud once more. The proposed method recursively subdivides reference point cloud until no more partial point cloud is possible to be subdivided. The experiment evaluates the loss of data and the error related to  . In addition, the flat distributions transformed from reference point cloud is shown. 

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Section: A Flatness Evaluation Methodsmentioning

confidence: 99%

“…Fig. 2 is an example when  is set to 6 10  . The radius of ellipsoids standing for distributions are Mahalanobis distance of 1.8.…”

Section: Methodsmentioning

confidence: 99%

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A Method of Generating Multi-Scale Disc-Like Distributions for NDT Registration Algorithm

Hong¹,

Lee²

2016

IJMERR

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“…Figure 21 shows the pseudocode of the point-to-probability distribution scan matching. The point-to-probability distribution scan matching obtains the score and the Jacobian function between the point and the probability distribution and then derives the optimal state variables through nonlinear optimization (like the conventional NDT scan matching [15,16,19]), where the state variables, (x), are the results of error correction through scan matching between the map and the point cloud. However, unlike the NDT scan matching, which can be directly matched with probability distributions in a grid, the FRPDM does not have a fixed grid, and a data association process is required for matching between the point and the probability distribution.…”

Section: Map Matching Algorithmmentioning

confidence: 99%

Free-Resolution Probability Distributions Map-Based Precise Vehicle Localization in Urban Areas

Kim

Jee

2020

Sensors

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We propose a free-resolution probability distributions map (FRPDM) and an FRPDM-based precise vehicle localization method using 3D light detection and ranging (LIDAR). An FRPDM is generated by Gaussian mixture modeling, based on road markings and vertical structure point cloud. Unlike single resolution or multi-resolution probability distribution maps, in the case of the FRPDM, the resolution is not fixed and the object can be represented by various sizes of probability distributions. Thus, the shape of the object can be represented efficiently. Therefore, the map size is very small (61 KB/km) because the object is effectively represented by a small number of probability distributions. Based on the generated FRPDM, point-to-probability distribution scan matching and feature-point matching were performed to obtain the measurements, and the position and heading of the vehicle were derived using an extended Kalman filter-based navigation filter. The experimental area is the Gangnam area of Seoul, South Korea, which has many buildings around the road. The root mean square (RMS) position errors for the lateral and longitudinal directions were 0.057 m and 0.178 m, respectively, and the RMS heading error was 0.281°.

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“…The 3D-NDT algorithm was proposed and compared with the ICP algorithm in reference [13]. Another improved NDT algorithm, the Multi-Layered Normal Distributions Transform (ML-NDT) algorithm was mentioned in reference [14]. The NDT algorithm and the other improved algorithms have been applied in point cloud classification [15], mobile robotic mapping [16] and path planning [17].…”

Section: Introductionmentioning

confidence: 99%

The Pose Estimation of Mobile Robot Based on Improved Point Cloud Registration

Miao

Liu

et al. 2016

International Journal of Advanced Robotic Systems

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Due to GPS restrictions, an inertial sensor is usually used to estimate the location of indoor mobile robots. However, it is difficult to achieve high-accuracy localization and control by inertial sensors alone. In this paper, a new method is proposed to estimate an indoor mobile robot pose with six degrees of freedom based on an improved 3D-Normal Distributions Transform algorithm (3D-NDT). First, point cloud data are captured by a Kinect sensor and segmented according to the distance to the robot. After the segmentation, the input point cloud data are processed by the Approximate Voxel Grid Filter algorithm in different sized voxel grids. Second, the initial registration and precise registration are performed respectively according to the distance to the sensor. The most distant point cloud data use the 3D-Normal Distributions Transform algorithm (3D-NDT) with large-sized voxel grids for initial registration, based on the transformation matrix from the odometry method. The closest point cloud data use the 3D-NDT algorithm with small-sized voxel grids for precise registration. After the registrations above, a final transformation matrix is obtained and coordinated. Based on this transformation matrix, the pose estimation problem of the indoor mobile robot is solved. Test results show that this method can obtain accurate robot pose estimation and has better robustness.

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3D Multi-Layered Normal Distribution Transform for Fast and Long Range Scan Matching

Cited by 54 publications

References 15 publications

A Method of Generating Multi-Scale Disc-Like Distributions for NDT Registration Algorithm

A Method of Generating Multi-Scale Disc-Like Distributions for NDT Registration Algorithm

Free-Resolution Probability Distributions Map-Based Precise Vehicle Localization in Urban Areas

The Pose Estimation of Mobile Robot Based on Improved Point Cloud Registration

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