pcregisterndt

Register two point clouds using NDT algorithm

Syntax

tform = pcregisterndt(moving,fixed,gridStep)

[tform,movingReg] = pcregisterndt(moving,fixed,gridStep)

[___,rmse] = pcregisterndt(moving,fixed,gridStep)

[___] = pcregisterndt(moving,fixed,gridStep,Name,Value)

Description

tform = pcregisterndt(moving,fixed,gridStep) returns the rigid transformation that registers the moving point cloud with the fixed point cloud. The point clouds are voxelized into cubes of size gridStep.

The registration algorithm is based on the normal-distributions transform (NDT) algorithm [1] [2]. Best performance of this iterative process requires adjusting properties for your data. To improve accuracy and efficiency of registration, consider downsampling the point clouds by using pcdownsample before using pcregisterndt.

[tform,movingReg] = pcregisterndt(moving,fixed,gridStep) also returns the transformed point cloud that aligns with the fixed point cloud.

[___,rmse] = pcregisterndt(moving,fixed,gridStep) also returns the root mean square error of the Euclidean distance between the aligned point clouds, using any of the preceding syntaxes.

[___] = pcregisterndt(moving,fixed,gridStep,Name,Value) uses additional options specified by one or more Name,Value pair arguments.

Examples

Align Two Point Clouds Using NDT Algorithm

Load point cloud data.

ld = load('livingRoom.mat');
moving = ld.livingRoomData{1};
fixed = ld.livingRoomData{2};
pcshowpair(moving,fixed,'VerticalAxis','Y','VerticalAxisDir','Down')

To improve the efficiency and accuracy of the NDT registration algorithm, downsample the moving point cloud.

movingDownsampled = pcdownsample(moving,'gridAverage',0.1);

Voxelize the point cloud into cubes of sidelength 0.5. Apply the rigid registration using the NDT algorithm.

gridStep = 0.5;
tform = pcregisterndt(movingDownsampled,fixed,gridStep);

Visualize the alignment.

movingReg = pctransform(moving,tform);
pcshowpair(movingReg,fixed,'VerticalAxis','Y','VerticalAxisDir','Down')

Input Arguments

moving — Moving point cloud

pointCloud object

Moving point cloud, specified as a pointCloud object.

fixed — Fixed point cloud

pointCloud object

Fixed point cloud, specified as a pointCloud object.

gridStep — Size of voxels

positive scalar

Size of the 3-D cube that voxelizes the fixed point cloud, specified as a positive scalar.

Data Types: single | double

Name-Value Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: 'MaxIterations',20 stops the NDT algorithm after 20 iterations.

InitialTransform — Initial rigid transformation

rigid3d object

Initial rigid transformation, specified as the comma-separated pair consisting of 'InitialTransform' and a rigid3d object. The initial rigid transformation is useful when you provide an external coarse estimation.

The rigid3d object contains a translation that moves the center of the moving point cloud to the center of the fixed point cloud.

OutlierRatio — Percentage of outliers

0.55 (default) | scalar in the range [0, 1)

Expected percentage of outliers with respect to a normal distribution, specified as the comma-separated pair consisting of 'OutlierRatio' and a scalar in the range [0, 1). The NDT algorithm assumes a point is generated by a mixture of a normal distribution for inliers and a uniform distribution for outliers. A larger value of 'OutlierRatio' reduces the influence of outliers.

Data Types: single | double

MaxIterations — Maximum number of iterations

30 (default) | nonnegative integer

Maximum number of iterations before NDT stops, specified as the comma-separated pair consisting of 'MaxIterations' and a nonnegative integer.

Data Types: single | double

Tolerance — Tolerance between consecutive NDT iterations

[0.01 0.5] (default) | 2-element vector

Tolerance between consecutive NDT iterations, specified as the comma-separated pair consisting of 'Tolerance' and a 2-element vector with nonnegative values. The vector, [Tdiff Rdiff], represents the tolerance of absolute difference in translation and rotation estimated in consecutive NDT iterations. Tdiff measures the Euclidean distance between two translation vectors. Rdiff measures the angular difference in degrees. The algorithm stops when the difference between estimated rigid transformations in the most recent consecutive iterations falls below the specified tolerance value.

Data Types: single | double

Verbose — Display progress information

false (default) | true

Display progress information, specified as the comma-separated pair consisting of 'Verbose' and a logical scalar. Set Verbose to true to display progress information.

Data Types: logical

Output Arguments

tform — Rigid transformation

rigid3d object

Rigid transformation, returned as a rigid3d object. tform describes the rigid 3-D transformation that registers the moving point cloud, moving, to the fixed point cloud, fixed.

movingReg — Transformed point cloud

pointCloud object

Transformed point cloud, returned as a pointCloud object. The transformed point cloud is aligned with the fixed point cloud, fixed.

rmse — Root mean square error

positive number

Root mean square error, returned as a positive number. rmse is the Euclidean distance between the aligned point clouds.

Algorithms

Tips

• For ground vehicle point clouds, you can improve performance and accuracy by removing the ground using pcfitplane or segmentGroundFromLidarData before registration. For details on how to do this, see the helper function, helperProcessPointCloud in the Build a Map from Lidar Data (Automated Driving Toolbox) example.

• To merge more than two point clouds, you can use pccat function instead of the pcmerge function.

NDT Registration Overview

The NDT registration is based on normal distributions rather than other types of registration which match points or lines in order to find the transformation between two point clouds. The NDT approach uses statistical models with 3-D boxes, called voxels.

To register two point clouds, a moving point cloud and a fixed point cloud, using the NDT approach, the algorithm performs the following:

1. Computes the normal distributions for the fixed point cloud by dividing the area covered by the point cloud scan into 3-D boxes of constant size, referred to as "voxels". Each voxel contains a set of points. The algorithm computes the mean and covariance matrix for the points in each voxel.

2. Starting with an initial guess of the transformation, the algorithm aligns the moving point cloud to the fixed point cloud. It then finds the sum of the statistical likelihood of each aligned point to be located in the voxel that surrounds the point (in the moving point cloud), based on the normal distribution of the fixed point cloud.

3. To improve the registration, the algorithm maximizes the probability score of the moving point cloud on the normal distributions of the fixed point cloud. This is done by iteratively optimizing angular and translational estimations.

4. Repeats the alignment of the moving point cloud with the fixed piont cloud using the new transformation from the previous step and then repeats the optimization.

5. The algorithm stops once the maximum iterations or the tolerance parameters, are met. The tolerance is a measure of how much the angular and translational estimations change from one iteration to another.

Compatibility Considerations

The pcregisterndt function returns a rigid3d object

Behavior changed in R2020a

Starting in R2020a, the pcregisterndt function returns a rigid3d object. Prior to R2020a, the function returned an affine3d object.

References

[1] Biber, P., and W. Straßer. “The Normal Distributions Transform: A New Approach to Laser Scan Matching.” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Las Vegas, NV. Vol. 3, November 2003, pp. 2743–2748.

[2] Magnusson, M. “The Three-Dimensional Normal-Distributions Transform — an Efficient Representation for Registration, Surface Analysis, and Loop Detection.” Ph.D. Thesis. Örebro University, Örebro, Sweden, 2013.

Extended Capabilities

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