LiDAR-Descriptor

Place recognition pipeline using LiDAR data from a publicly available dataset

The goal is to design a descriptor for LiDAR scans, implement a matching algorithm, and evaluate the system using standard performance metrics.

• descriptor: https://ieeexplore.ieee.org/document/7759060
• LiDAR scans: https://robots.engin.umich.edu/nclt/
• similarity measure as matching algorithm: https://dl.acm.org/doi/10.1109/IROS.2015.7353454

LiDAR-Based Place Recognition using M2DP

Overview

This project is part of exercise 3 of the Autonomous Mobile Robots Lecture (Winter 25/26) at TU Darmstadt. It implements a place recognition pipeline based on LiDAR data from the publicly available NCLT Dataset.

The goal is to:

• Design and implement a LiDAR scan descriptor.
• Implement a matching and retrieval algorithm.
• Detect loop closures.
• Evaluate performance using standard metrics (Precision-Recall, ROC, F1, Recall).

The descriptor used in this project is M2DP (Multi-view 2D Projection Descriptor).

Dataset

We use LiDAR data from the first three days of the NCLT dataset.

Each day consists of:

• A sequence of LiDAR scans (.bin files).
• Corresponding timestamps (extracted from filenames).
• Ground truth pose data (CSV file) providing timestamped robot positions $(x, y, z)$.

Methodology

1. M2DP Preprocessing

For each LiDAR scan:

1. Extract 3D points and remove invalid data.
2. Centroid Shift: Shift point cloud to its centroid.
3. PCA Alignment: Apply Principal Component Analysis to align the x-axis with the first and the y-axis with the second principal component. This ensures a consistent local coordinate frame.

2. M2DP Descriptor

For each scan:

• Projections: Generate $p \times q$ projection planes defined by azimuth $\theta$ and elevation $\phi$.
• 2D Histograms: Project points onto each plane, convert to polar coordinates, and build a histogram with $l$ radial and $t$ angular bins.
• SVD: Stack histograms into a matrix $A \in \mathbb{R}^{(l \cdot t) \times (p \cdot q)}$. Apply Singular Value Decomposition: $A = U\Sigma V^T$.
• Final Descriptor: Constructed as $d = [U[:,0], U[:,1]]$. Descriptors are $L_2$-normalized.

3. Loop Candidate Retrieval

For each scan $i$, compare its descriptor to all previous descriptors $j$:

• Time Separation: $t_i - t_j \geq \Delta t$
• Matching: Compute Euclidean distance. A loop candidate is defined if $|d_i - d_j| < \tau$.

4. Ground Truth Loop Definition

Defined independently of descriptors:

• Spatial Constraint: $|p_i - p_j| \leq r$
• Time Constraint: $t_i - t_j \geq \Delta t$ If a scan $j$ fulfills both, scan $i$ is marked as a Ground Truth (GT) loop.

Evaluation

We evaluate the system using:

1. Precision-Recall Curve
2. Average Precision (AP)
3. ROC Curve & AUC
4. F1 Score:

Visualization

The trajectory is visualized in 2D:

• Grey line: Robot trajectory.
• Red lines: Predicted loop closures.
• Green lines: Ground truth loop closures.

Key Parameters

Parameter	Description	Values
l	Radial bins	8
t	Angular bins	16
p, q	Projection angles	4, 4
τ	Descriptor threshold	0.025, 0.03, 0.035
Δt	Min. time separation	30 s
r	Spatial loop radius	1, 3, 5 m

Conclusion

This project demonstrates a complete LiDAR-based place recognition pipeline from geometric descriptor design to quantitative validation. It can be extended with Geometric Verification (ICP) or KD-tree acceleration for larger datasets.