---
kind: concept
slug: surfel-mapping
title: Surfel mapping
summary: >-
  Surfel mapping merges each new observation into a map of oriented points or discs. Covers SuMa and SuMa++, which align LiDAR scans to surfels and use labels to drop moving-object surfels (KITTI, author-reported), and ConceptFusion, which fuses language-aligned features into a posed point map with no alignment step.
tags: [slam, lidar, mapping, semantic-mapping, dynamic-objects, feature-fusion, open-vocabulary]
papers: ["2105.11320", "2302.07241"]
related: [simultaneous-localization-and-mapping, iterative-closest-point, semantic-segmentation, lidar-inertial-odometry, gaussian-splatting, open-vocabulary-segmentation]
status: draft
updated_at: 2026-10-31
---

## Overview

A surfel is a small oriented disc with a position, a normal and a radius. A
surfel map stores the scene as a set of these, and each one also carries
timestamps and a stability score [arxiv:2105.11320 §III-B]. A new LiDAR scan
is aligned to the map by ICP, and the scan is then merged into the map
[arxiv:2105.11320 §III]. SuMa adds loop closure and pose-graph optimisation on
top of this loop [arxiv:2105.11320 §III-B].

The variants differ in what each map element carries and in whether a new frame
is aligned to the map before it is merged. SuMa and SuMa++ align each LiDAR scan
to the surfel map and keep a stability score per surfel. ConceptFusion takes
camera poses as given, merges per-pixel features into its map, and keeps only an
accumulated confidence per point [arxiv:2302.07241 §3.1] [arxiv:2302.07241 eq. 2].
Two cards list this concept. The LiDAR systems come from one paper; the point
map comes from a second paper, whose card does not call its map surfels. Other
surface-based maps are not covered here.

## Variants

### Geometric surfel mapping (SuMa)

The baseline keeps the surfel map and the align-then-merge loop, with no
semantic labels [arxiv:2105.11320 §III-B]. Each surfel's stability is a
log-odds value updated by a binary Bayes filter, so a surfel can be
trusted more or less over time [arxiv:2105.11320 §III-B].

The paper reports this baseline as a clear failure on moving-object scenes.
On KITTI highway sequence 35 the relative translational error is 26.8%,
author-reported [arxiv:2105.11320 tab. I]. On the odometry training sequences
00 to 10, the average is 0.83% [arxiv:2105.11320 tab. II]. The baseline has no
card of its own; it is compared through the [SuMa++ card](/papers/2105.11320).

### Naive removal of movable surfels (SuMa_nomovable)

This baseline deletes every surface of a movable class from the map. The
paper uses it to show that removal alone is not enough. Parked cars help scan
registration, and wrong labels delete static surfels [arxiv:2105.11320 §IV-B].
On the odometry sequences the average relative translational error is 9.24%,
and the paper says it diverges on the urban sequences [arxiv:2105.11320 tab. II].
On the highway sequence it does well, at 1.22% [arxiv:2105.11320 tab. I].
Card: [SuMa++: Efficient LiDAR-based Semantic SLAM](/papers/2105.11320).

### Semantic surfel mapping with dynamic filtering (SuMa++)

SuMa++ puts semantics into three steps of the loop [arxiv:2105.11320 §III]:

1. **Label refinement.** Each scan gets per-point labels from a segmenter on
   its spherical projection. The label image is then eroded at object
   boundaries and refilled from consistent neighbours [arxiv:2105.11320 §III-C]
   [arxiv:2105.11320 §III-D] [arxiv:2105.11320 alg. 1].
2. **Stability update.** When a surfel's stored label disagrees with the new
   label and its class is movable, the stability update is penalised. Static
   classes such as vegetation are not penalised [arxiv:2105.11320 §III-E]
   [arxiv:2105.11320 §IV-C].
3. **Semantic ICP.** Each residual gets a semantic compatibility weight on top
   of the robust weight, so moving objects count less in the pose estimate
   [arxiv:2105.11320 §III-F] [arxiv:2105.11320 eq. 6].

On the odometry training sequences the average relative translational error
is 0.70%, author-reported, against 0.83% for SuMa [arxiv:2105.11320 tab. II].
On highway sequence 35 it is 1.11%, against 26.8% for SuMa
[arxiv:2105.11320 tab. I]. The paper reports these for the full system and
does not isolate the semantic ICP weights [arxiv:2105.11320 §IV].
Card: [SuMa++: Efficient LiDAR-based Semantic SLAM](/papers/2105.11320).

### Point-map feature fusion without alignment (ConceptFusion)

This variant builds its map from posed RGB-D frames and fuses a per-pixel
feature into it, where SuMa fuses a label. Each pixel's feature goes into the
map point it projects to, weighted by a confidence that falls off with radial
distance from the camera [arxiv:2302.07241 §3.1] [arxiv:2302.07241 eq. 1]. That
confidence accumulates over observations [arxiv:2302.07241 eq. 2]. Points are
merged when their positions and normals are close, using PointFusion's defaults
of 5 cm and 20 degrees [arxiv:2302.07241 app. A3]. Outdoors the paper uses
LeGO-LOAM odometry on lidar [arxiv:2302.07241 app. A3]. The paper describes no
step that aligns each frame to the map, and no stability score per point
[arxiv:2302.07241 §3.1].

The headline result is open-vocabulary retrieval, not mapping error. On UnCoCo
structured text queries it reports 0.446 3D mIoU, against 0.289 for supervised
OpenSeg-3D [arxiv:2302.07241 tab. 1]. These numbers score retrieval of map
regions from queries, so they cannot be set against the KITTI trajectory errors
above [arxiv:2105.11320 tab. II]. Feature extraction is a separate cost: the
paper reports 10 to 15 s per image on an RTX 3090 [arxiv:2302.07241 §3]. Card:
[ConceptFusion: Open-set Multimodal 3D Mapping](/papers/2302.07241).

## When to use which

| Situation | Use | Why |
|---|---|---|
| No labelled training data, or no segmenter you can train or run | Geometric surfel mapping (SuMa) | SuMa++ needs a labelled set and a trained segmenter [arxiv:2105.11320 §IV]. Without labels only the geometric form applies. |
| LiDAR-only sequences with many moving vehicles, labels available | Semantic surfel mapping (SuMa++) | The gain on highway sequence 35 is large and author-reported [arxiv:2105.11320 tab. I]. The motivation is that moving objects give wrong associations [arxiv:2105.11320 §III-E]. |
| Tempted to delete all movable surfels with no further filtering | Do not use naive removal (SuMa_nomovable) alone | Diverges on the urban odometry sequences [arxiv:2105.11320 tab. II]. Its highway result is good, so the failure is scene-dependent [arxiv:2105.11320 tab. I]. |
| Tight per-scan latency | Budget for the segmenter | On the paper's GPU, segmentation takes about 75 ms and surfel mapping about 48 ms per scan, up to 190 ms with loop closures [arxiv:2105.11320 §IV]. |
| Map must answer text, image or audio queries with no training | Point-map feature fusion (ConceptFusion) | Queries are cosine scores against the fused features, with no training [arxiv:2302.07241 §3.3]. The paper reports no trajectory error for this map [arxiv:2302.07241 §4]. |

The LiDAR results are KITTI only [arxiv:2105.11320 §IV]. For other sensors or
environments they do not transfer by themselves. The ConceptFusion results
come from tabletop scenes and are not on the same benchmark [arxiv:2302.07241 §4.1].

## Implementation sketch

The loop below is the common core. The marked lines are where the variants
differ. The semantic steps follow the paper's Algorithm 1 and Equations 1, 6
and 8, with the code's details noted below.

```pseudocode
# One scan of surfel mapping  [arxiv:2105.11320 §III]
# Input:  scan points, surfel map, previous pose
#         (semantic variant also takes per-point labels)
# Output: pose of the scan, updated surfel map

def process_scan(scan, surfel_map, pose_prev, labels=None):
    # Spherical projection to a vertex map and a normal map  [arxiv:2105.11320 §III-B]
    vertices, normals = project_and_normals(scan)
    # Semantic variant only: clean the labels  [arxiv:2105.11320 §III-D]
    if labels is not None:
        labels = refine_labels(labels, vertices)
    # Frame-to-model ICP; semantic variant adds label weights  [arxiv:2105.11320 §III-F]
    pose = icp_to_surfels(vertices, normals, surfel_map, pose_prev, labels)
    # Merge the scan and update each surfel's stability  [arxiv:2105.11320 §III-E]
    surfel_map.integrate(scan, labels, pose)
    return pose
```

The stability update is a log-odds step. Its penalty term applies only when the
label disagrees and the class is movable [arxiv:2105.11320 §III-E]
[arxiv:2105.11320 eq. 1].

```pseudocode
# Stability log-odds update for one surfel  [arxiv:2105.11320 eq. 1]
# odds(p) = log(p / (1 - p))

def update_stability(log_odds, compat, prior, penalty_applies):
    # compat = p_stable times two exponential terms in angle and distance  [eq. 1]
    log_odds += odds(compat) - odds(prior)
    # Movable surfel whose label conflicts with the scan  [arxiv:2105.11320 §III-E]
    if penalty_applies:
        log_odds -= penalty  # value not stated in the paper
    return log_odds
```

For ConceptFusion the same merge step runs with the pose given and a feature
vector in place of the label. The alignment line is absent [arxiv:2302.07241 §3.1].

Implementation notes, from comparing the paper with the released code
(MIT, [PRBonn/semantic_suma](https://github.com/PRBonn/semantic_suma)):

- The paper leaves the penalty value p_penalty unstated. The code subtracts a
  constant of 1.0 in log-odds, and only for movable classes whose label
  differs from the scan's label [arxiv:2105.11320 §III-E].
- The paper's angle term uses the angle between normals. The code uses the
  sine of that angle, which is the length of the cross product of the two
  normals [arxiv:2105.11320 §III-E].
- The code clamps the compatibility probability and caps log-odds, and it
  invalidates surfels below a threshold. The paper does not describe these
  steps [arxiv:2105.11320 §III-E].
- Most numeric settings are not stated in the paper, including the
  stability priors, the Huber threshold, the ICP limits and the flood-fill
  tolerance [arxiv:2105.11320 §III-D] [arxiv:2105.11320 §III-F]. The released
  configuration gives defaults for the KITTI setting. Treat them as defaults,
  not as tuned values.

## Contradictions

None known. The paper reports the baseline's effect differently by sequence
set: naive removal of movable surfels does well on highway sequence 35 and
diverges on the urban odometry sequences [arxiv:2105.11320 tab. I]
[arxiv:2105.11320 tab. II]. This is one paper's result, not a disagreement
between papers. The two families report different tasks, query mIoU and KITTI
trajectory error, so their numbers are not comparable [arxiv:2302.07241 tab. 1]
[arxiv:2105.11320 tab. II].

## Papers

- [SuMa++: Efficient LiDAR-based Semantic SLAM](/papers/2105.11320): surfel LiDAR mapping with semantic labels that remove moving-object surfels from the map and weight the scan alignment; reports author-reported KITTI results and compares against SuMa and naive removal.
- [ConceptFusion: Open-set Multimodal 3D Mapping](/papers/2302.07241): fuses CLIP-aligned per-pixel features into a posed point map that is queried by text, image, click and audio; reports author-reported UnCoCo tabletop query results against supervised baselines.