LiDAR SLAM

Matching every point of every scan is slow. LiDAR SLAM systems like LOAM keep only the most useful points: edge points, where the surface bends sharply, and plane points, where it is flat. Matching edges to edges and planes to planes is fast and accurate.

Edge curvature threshold Build the map while driving

Curvature

For each scan point $\mathbf{p}_i$, LOAM compares it with its neighbors along the scan line. A point on a flat wall is nearly the average of its neighbors, while a corner point is not:

$$c_i = \frac{1}{\lvert S\rvert\,\lVert\mathbf{p}_i\rVert}\Big\lVert \sum_{j \in S} (\mathbf{p}_j - \mathbf{p}_i) \Big\rVert$$

Points with large $c$ become edge features and points with small $c$ become plane features. Edges are matched to lines in the map, and planes to planes, and the pose comes from minimizing those point-to-line and point-to-plane distances.

What to notice

Red points cluster at corners and object edges, and navy points cover flat walls. Raise the threshold and fewer points count as edges. Only a small fraction of the scan is kept, yet it is enough to pin down the pose. In 3D, LOAM and its successors such as LeGO-LOAM and LIO-SAM use the same idea, often adding an IMU to handle fast motion.