Point Cloud Registration

Point-cloud registration finds the rigid transform — rotation and translation — that best aligns two overlapping point clouds. It is the core geometric primitive behind mapping, scan stitching, and the front-end of lidar-odometry.

The classic recipe

Iterative Closest Point (ICP) alternates two steps until convergence:

1. **Correspondence** — for each source point, find its nearest target point. 2. **Alignment** — solve for the transform that minimizes the residual (point-to-point or, faster-converging, point-to-plane).

Variants improve every part of this loop: better correspondences (normals, features), robust losses (to reject outliers), and voxel or KD-tree acceleration so the nearest-neighbour search is not the bottleneck.

In practice

Real systems seed ICP with a coarse global alignment or an IMU prior so it converges to the right basin. When registration runs every frame against a sliding local map, it becomes lidar-odometry — same math, tighter time budget.