Registration using Normal Distribution Transformation

In this post, I am going to experiment the PCL Normal Distribution Transformation (NDT) algorithm for registration of two clouds.

Experiment description:

Two Kinects are oppositely located and both facing to a box of size ~18x40cm on a table. One Kinect is called target and the other is called source. Therefore, our aim is to register source cloud with target cloud, or in other word find a transformation that best align source cloud and target cloud.
Both source and target clouds have been cropped based on region of interest for faster processing and fewer background noise. In addition, source cloud (coloured with green) has been down-sampled to 1/10 of its original density.

As mentioned at PCL official tutorial (link), these parameters are set according to different application:

The Transformation Epsilon(TE) parameter defines minimum, allowable, incremental change of the transformation vector, [x, y, z, roll, pitch, yaw] in meters and radians respectively. Once the incremental change dips below this threshold, the alignment terminates.

The Step Size(SS) parameter defines the maximum step length allowed by the More-Thuente line search. This line search algorithm determines the best step length below this maximum value, shrinking the step length as you near the optimal solution. Larger maximum step lengths will be able to clear greater distances in fewer iterations but run the risk of overshooting and ending up in an undesirable local minimum.

The Resolution parameter(RP) defines the voxel resolution of the internal NDT grid structure. This structure is easily searchable and each voxel contain the statistical data, mean, covariance, etc., associated with the points it contains.

I've adjusted these parameters individually and cross compared the results of registration.

TE: 0.01, SS:0.01, RP:0.1

TE: 0.01, SS:0.01, RP:0.2

TE: 0.01, SS:0.01, RP:0.3

TE: 0.01, SS:0.05, RP:0.1

TE: 0.01, SS:0.05, RP:0.3

From above results we can conclude:
1) If the clouds were jointing together rather than aligning, we can increase the RP in order to include more points for each voxel structure.
2) For large SS parameter, the registration converge faster while small SS parameter gives finer alignment.

At the end of experiment, I found that the algorithm is more robust to regular object in the scene. Since the above experiment all includes my head during registration. If I let myself out of the scene, the registration can be done much better and faster for reasonable parameters. Here is the result without my head in the scene: