pcregistercpd

Register two point clouds using CPD algorithm

Syntax

tform = pcregistercpd(moving,fixed)

[tform,movingReg] = pcregistercpd(___)

[___,rmse] = pcregistercpd(___)

[___] = pcregistercpd(___,Name=Value)

Description

tform = pcregistercpd(moving,fixed) returns a transformation that registers a moving point cloud with a fixed point cloud using the CPD algorithm. The coherent point drift (CPD) algorithm [1] supports non-rigid transformations.

Note

The CPD algorithm is robust to noise, outlier and missing points, at the expense of speed. Consider downsampling point clouds using pcdownsample before using pcregistercpd to improve the efficiency of registration.

Alternatively, you can speed up the algorithm by using the extractFPFHFeatures (Lidar Toolbox) function to extract features before performing registration. For more details, see the Improve CPD Performance Using FPFH Descriptors example.

[tform,movingReg] = pcregistercpd(___) also returns the transformed point cloud that aligns with the fixed point cloud.

[___,rmse] = pcregistercpd(___) also returns the root mean square error of the Euclidean distance between the aligned point clouds.

[___] = pcregistercpd(___,Name=Value) specifies options using one or more name-value arguments in addition to any combination of arguments from previous syntaxes. For example, MaxIterations=20 stops the CPD algorithm after 20 iterations.

Examples

Align Two Point Clouds Using CPD Algorithm

Load point cloud data into the workspace. Extract the moving and the fixed point clouds from the point cloud data in workspace.

handData = load('hand3d.mat');
moving = handData.moving;
fixed = handData.fixed;

To improve the efficiency and accuracy of the CPD registration algorithm, downsample the moving and the fixed point clouds.

movingDownsampled = pcdownsample(moving,'gridAverage',0.03);
fixedDownsampled = pcdownsample(fixed,'gridAverage',0.03);

Display the downsampled point clouds before registration.

figure
pcshowpair(movingDownsampled,fixedDownsampled,'MarkerSize',50)
xlabel('X')
ylabel('Y')
zlabel('Z')
title('Point clouds before registration')
legend({'Moving point cloud','Fixed point cloud'},'TextColor','w')
legend('Location','southoutside')

Perform non-rigid registration using the CPD algorithm.

[tform,movingReg] = pcregistercpd(movingDownsampled,fixedDownsampled);

Display the downsampled point clouds after registration.

figure
pcshowpair(movingReg,fixedDownsampled,'MarkerSize',50)
xlabel('X')
ylabel('Y')
zlabel('Z')
title('Point clouds after registration')
legend({'Moving point cloud','Fixed point cloud'},'TextColor','w')
legend('Location','southoutside')

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.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: MaxIteration=20 stops the CPD algorithm after 20 iterations.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Transform — Type of transformation

"Nonrigid" (default) | "Rigid" | "Affine"

Type of transformation, specified as "Nonrigid", "Rigid", or "Affine".

Data Types: char | string

OutlierRatio — Expected percentage of outliers

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

Expected percentage of outliers with respect to a normal distribution, specified as a scalar in the range [0, 1). Increasing this value reduces the influence of outliers and noise.

Data Types: single | double

MaxIterations — Maximum number of iterations

20 (default) | positive integer

Maximum number of iterations before CPD stops, specified as a positive integer.

MaxIterations and Tolerance are both stopping conditions for the CPD algorithm. The algorithm stops when it satisfies either of the stopping conditions.

Data Types: single | double

Tolerance — Tolerance between consecutive CPD iterations

1e-5 (default) | scalar

Tolerance between consecutive CPD iterations, specified as a scalar. The algorithm stops when the absolute percentage change in the values of the log likelihood function measured between consecutive iterations reaches or falls below the specified tolerance value. Decreasing this value increases the likelihood of a better alignment.

MaxIterations and Tolerance are both stopping conditions for the CPD algorithm. The algorithm stops when it satisfies either of the stopping conditions.

Data Types: single | double

InteractionSigma — Interaction between points

2.0 (default) | positive scalar

Interaction between points, specified as positive scalar that represents standard deviation of a Gaussian filter. Typical values are in the range [1.5, 3]. Increasing this value increases interaction between the points in point cloud. As a result, you can observe coherent motion in the point cloud and every point undergoes the same displacement. Alternatively, decreasing this value reduces interaction between the points in point cloud. As a result, you can observe localized displacement of points and the output displacement field exhibits localized deformation.

Note

To use this name-value argument, Transform must be "Nonrigid".

Data Types: single | double

SmoothingWeight — Motion smoothing weight

3.0 (default) | positive scalar

Motion smoothing weight, specified as a positive scalar. Typical values are in the range [0.1,10]. Increase this value to produce a more coherent motion in the output displacement field.

Note

To use this name-value argument, Transform must be "Nonrigid".

Data Types: single | double

Verbose — Display progress information

false (default) | true

Display progress information, specified as a numeric or logical 0 (false) or 1 (true). To display the progress information, set Verbose to true.

Output Arguments

tform — Transformation

rigidtform3d object | affinetform3d object | displacement field

Transformation, returned as a rigidtform3d object, an affinetform3d object, or a displacement field. tform is a 3-D transformation that registers the moving point cloud, moving to the fixed point cloud, fixed. The output type depends on the value of the Transform argument.

Transform Value	tform
"Rigid"	rigidtform3d object
"Affine"	affinetform3d object
"Nonrigid"	Displacement field, a numeric matrix of same size and datatype as the Location property of the moving point cloud object, moving.

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 real number

Root mean square error, returned as a positive numeric scalar that represents the Euclidean distance between the aligned points. The aligned points is a result of the moving point cloud transformed by the tform output and the fixed point cloud. For each point in the fixed point cloud, the algorithm finds the closest point in the transformed point cloud, movingReg, then computes the Euclidean distance between the points, and then computes the rmse. A low rmse value indicates a more accurate registration. The rmse calculation is:

rmse = sqrt(sum(distance.^2,'all')/numel(distance));

Data Types: double

Algorithms

Both MaxIterations and Tolerance are used as stopping criteria. The algorithm stops when it satisfies either of the stopping conditions, i.e., when the number of iteration reaches MaxIterations or the absolute percentage change in log likelihood function is less than or equal to Tolerance.

References

[1] Myronenko, A., and X. Song. "Point Set Registration: Coherent Point Drift. "Proceedings of IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI)." Vol 32, Number 12, December 2010, pp. 2262–2275.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

• The name-value argument Transform must be compile-time constant.

Version History

Introduced in R2018b

R2022b: Returns new geometric transformation objects

Starting in R2022b, most Computer Vision Toolbox™ functions create and perform geometric transformations using the premultiply convention. Accordingly, for rigid and affine transformation types, the pcregistercpd function now returns tform as a rigidtform3d or affinetform3d object, which use the premultiply convention. Before, the function returned tform as a rigid3d or affine3d object, which use the postmultiply convention. For more information, see Migrate Geometric Transformations to Premultiply Convention.