Module 3: Coarse Registration
3.1 What is Coarse Registration?
In point cloud registration, we have two point clouds: a source cloud and a target cloud. Coarse registration aims to estimate an initial rotation and translation so that the source cloud roughly aligns with the target cloud. This initial alignment does not need to be perfect, but it must be good enough for the subsequent fine registration to succeed.
Why can’t we use ICP directly for coarse registration? Because ICP easily gets stuck in local minima. If the two clouds start far apart, ICP will fail. Therefore we need a robust coarse registration method.
The most popular coarse registration method is RANSAC (Random Sample Consensus). Its core idea is: from the candidate matches obtained by feature matching, repeatedly pick a small random subset of matches, compute a transformation, and count how many other matches are inliers. Finally, select the transformation with the largest number of inliers.
3.2 Basic Procedure
Assume we have already obtained a set of candidate correspondences via feature matching (e.g., using FPFH or FCGF):
where \(p_i\) comes from the source cloud and \(q_i\) from the target cloud. Many of these matches are outliers. RANSAC’s task is to find the correct transformation despite the outliers.
RANSAC algorithm (repeat \(N\) times):
- Randomly select 3 matches which must not be collinear.
- Compute a transformation \(R, t\) from these 3 point pairs (method in Section 3.3).
-
Count inliers: For each match \((p_i, q_i)\), check the error after
transformation:
\[ \| R p_i + t - q_i \| < \tau \]If the error is smaller than threshold \(\tau\), this match is considered an inlier.
- Keep the best transformation: If the current number of inliers is larger than the previous best, update the best transformation.
After all iterations, recompute the final transformation using all inliers that gives the coarse registration result.
3.3 How to Compute a Transformation from 3 Point Pairs?
3.4 Operating instructions
When the initial relative pose is unknown, global registration provides a robust starting point. It utilizes RANSAC to filter out erroneous matches and estimate a transformation matrix that brings both datasets into a shared coordinate system.
| Parameter | Meaning | Adjustment Guide |
|---|---|---|
| Voxel Size (m) | Downsampling before RANSAC to speed up correspondence search. | Use the same or slightly larger than feature extraction voxel size. Larger → faster but less accurate initial alignment. |