Range image

A range image is a 2D projection of a 3D LiDAR sweep. For a spinning LiDAR, the natural projection is cylindrical: each column corresponds to an azimuth angle and each row to a laser ring (elevation), and each pixel stores the measured depth — often alongside intensity and the ring index. A point with azimuth $\phi$ and elevation $\theta$ maps to

for a $W \times H$ image. This works because a spinning LiDAR is effectively a rotating 1D sensor array — the range image simply recovers the sensor’s native 2D structure that gets flattened into an unordered point list. Concretely, a 64-beam sensor gives $H = 64$ rows, and the horizontal resolution follows from the azimuth step (an angular step of $0.2°$ would give $W = 360/0.2 = 1800$ columns).

Why the representation is so useful

• Cheap neighborhoods: a point’s neighbors sit in adjacent pixels, so normals and local curvature can be estimated from neighboring pixels without any 3D nearest-neighbor search.

• Projective data association: SuMa renders its surfel map into a synthetic range image $\hat{\mathcal{R}}$ from the current pose estimate; the scan point at pixel $(u,v)$ is matched to the rendered surfel at the same pixel, and the pose is refined with a point-to-plane objective

  $$\mathbf{T}^* = \arg\min_{\mathbf{T}} \sum_k \big(\mathbf{n}_k^\top (\mathbf{T}\mathbf{p}_k - \hat{\mathbf{p}}_k)\big)^2 .$$

  Pixel-to-pixel lookup replaces k-d tree search — dramatically faster, and GPU-friendly since rendering is the association step.

• 2D deep learning on LiDAR: RangeNet++ runs an encoder-decoder CNN on range images for real-time semantic segmentation. SuMa++ uses those per-pixel labels to filter dynamic objects out of registration — points labeled car, person, or bicycle are simply excluded from the ICP correspondence set, $\mathcal{P}_{\text{ICP}} = \{p_k \mid \text{label}(p_k) \notin \mathcal{C}_{\text{dynamic}}\}$ — and to weight correspondences whose labels agree.

• Compactness: a full sweep becomes a dense image, convenient for compression, visibility checks, and occlusion reasoning — rendering the map from a pose immediately tells you what should be visible from there.

Common pitfalls

• Quantization collisions: multiple 3D points can land in one pixel (keep the nearest), and angular resolution means the same pixel covers a growing physical area with range — neighborhood-based normals get noisy far from the sensor.
• Row geometry is hardware, not math: real spinning LiDARs have non-uniformly spaced beam elevations, so indexing rows by the sensor’s ring index is more faithful than the linear-in-$\theta$ formula above.
• One viewpoint per sweep: the projection assumes all points were captured from a single pose; motion during the sweep must be compensated (de-skewing) before projection, or the image is smeared.
• Solid-state LiDARs break the model: irregular, non-repeating scan patterns (e.g., Livox-style) do not map cleanly onto an image grid — one reason the direct point-cloud methods (FAST-LIO2 lineage) took over as those sensors spread.

Why it matters for SLAM

The range image is the bridge between LiDAR processing and the mature toolbox of image processing and CNNs. An entire branch of LiDAR SLAM — SuMa’s projective ICP, SuMa++‘s semantic filtering, learned descriptors and loop-closure networks operating on range views — depends on it. Knowing when a method operates on raw point clouds (LOAM, FAST-LIO2) versus range images (SuMa family) tells you a lot about its speed profile, hardware requirements, and sensor assumptions.

Related

• SuMa — surfel SLAM built on projective ICP over range images
• SuMa++ — semantic segmentation of range images for dynamic filtering
• LiDAR — sensor fundamentals
• ICP — the registration algorithm that projective lookup accelerates
• LOAM — the contrasting branch that works on the raw point list