LiDAR Sampling: Methods and Algorithms

• LiDAR Sampling is a set of methodologies and algorithms focused on selecting optimal point subsets to balance efficiency with high-fidelity 3D data acquisition.
• It integrates spatial, photometric, and uncertainty-driven strategies to support robust reconstruction, semantic segmentation, and localization.
• Adaptive, task-driven sampling methods reduce data and computational requirements while maintaining or improving geometric precision and photometric detail.

LiDAR Sampling is the set of methodologies, theoretical foundations, and practical algorithms for selecting, acquiring, or retaining subsets of LiDAR point cloud, depth, or time-of-flight samples to achieve specific objectives such as efficient storage, robust reconstruction, semantic segmentation, registration, or real-time operation. LiDAR sampling spans problems of spatial, photometric, task-driven, adaptive, and hardware-based selection at both acquisition and processing stages, and is an active area at the intersection of computational geometry, signal processing, and optimization.

1. Principles and Taxonomy of LiDAR Sampling

LiDAR sampling strategies can be categorized by the operational domain (spatial, photometric/color, temporal, range, or spectral), guiding priors (uniformity, entropy, localizability, uncertainty), and the modality of operation (pre-acquisition/on-device, post-acquisition/algorithmic, or hybrid):

• Spatial Uniformity: Traditional approaches (Random Sampling, voxel grid, normal-space) treat each spatial location equivalently, seeking uniform or edge-aware geometric coverage. Voxel grid methods bin points in regular 3D grids; normal-space sampling emphasizes regions with high surface normal variation (Lim et al., 11 Jan 2026).
• Photometric/Color-Driven Sampling: When aligned RGB is available (as in RGB-LiDAR fusion), color-stratified approaches (e.g., PRISM) allocate sampling density based on chromatic diversity, enhancing structural and textural feature retention at the cost of geometric uniformity (Lim et al., 11 Jan 2026).
• Polar or Cylindrical Balancing: In scenes with strong range-dependent density gradients (e.g., automotive), random sampling under-represents distant objects; balanced strategies (e.g., PCB-RS) partition space in polar-cylindrical cells and enforce quota-balanced selection across cells to equalize sampling across distance and angle (Han et al., 2022).
• Task-Adaptive and Uncertainty-Driven: For resource-constrained applications or downstream learning, adaptive sampling dynamically selects points to minimize uncertainty or maximize task utility (e.g., depth completion, classification, localization error). Approaches include ensemble-variance-based selection (Gofer et al., 2020), learning-based mask generation (Shomer et al., 2023), and task-optimal Bayesian experiment design (Belmekki et al., 2021).
• Localizability and Observability: In SLAM and continuous-time odometry, points are prioritized based on their contribution to preserving observability of translation/rotation or information along all pose degrees of freedom (e.g., CTE-MLO) (Shen et al., 2024).
• Spectral and Multispectral Subsampling: For single-photon and multi-wavelength systems, tailored spatial-spectral patterns (e.g., blue-noise codes) minimize aliasing and acquisition time while enabling robust Bayesian multi-surface reconstruction (Tachella et al., 2019, Belmekki et al., 2021).

2. Sampling Algorithms and Mathematical Foundations

LiDAR sampling algorithms formalize the mapping from dense inputs or sensing budgets to sample subsets via quantized, randomized, or optimization procedures:

• PRISM (Color-Stratified Sampling): LiDAR points $p_i=(x_i, y_i, z_i, c_i)$, $c_i\in[0,1]^3$ are binned into quantized RGB bins $b_i=\lfloor255 c_i\rfloor$. The maximal per-bin quota $k^*$ is chosen so that $$\sum_{b\in B}\min(n_b, k^*) \approx r_{\text{target}} N$$, distributing higher quota to color-diverse regions and yielding point sets $P_{\text{out}}$ with elevated color entropy $$H=-\sum_{b}(m_b/|P_{\text{out}}|)\log(m_b/|P_{\text{out}}|)$$ (Lim et al., 11 Jan 2026).
• PCB-RS (Polar Cylinder Balanced RS): Points are partitioned in $(r,\theta,z)$, and each cell is allocated $S_i\approx M/K$ samples, ensuring coverage across all spatial bands, mitigating fore-ground bias, and empirically achieving significant gains in far-field semantic segmentation (Han et al., 2022).
• Superpixel-Guided Sampling: For depth map reconstruction, the domain is partitioned into superpixels (e.g., via SLIC), one sample is acquired per superpixel centroid, and dense output is reconstructed via zero-order interpolation and log-bilateral filtering. Sample budget directly determines the spatial segmentation, enabling high-fidelity reconstruction with extreme sparsity (e.g., 1/1200 density) (Wolff et al., 2019).
• Ensemble Variance and Probability-Matching: Uncertainty is estimated per-pixel from an ensemble of predictors; sampling probability at each location is set proportional to predictive variance, and next samples are drawn i.i.d. according to this distribution (probability matching). Staged iteration with retraining/adaptation prevents redundancy and oversampling (Gofer et al., 2020).
• Prior-Based and Task-Driven Sampling: Learned predictors generate future depth or uncertainty maps, which are then used by a CNN (e.g., SampleDepth) to produce soft sampling masks. The mask is optimized end-to-end w.r.t. final task loss (e.g., depth-completion RMSE), enforcing a hard sample budget constraint (Shomer et al., 2023).
• Localizability Metrics: The point cloud is scored by its contribution to observability of 6-DOF pose, via eigendecomposition of the registration Jacobian block–matrices, and minimal quotas are imposed per principal direction to guarantee trajectory estimation robustness (Shen et al., 2024).

3. Sampling in Task-Optimized and Adaptive Frameworks

Adaptive sampling frameworks operate in a closed loop, incorporating prior measurements, uncertainty estimates, or task-specific criteria:

• Task-Based Bayesian Adaptive Sampling: Iterative frameworks use Bayesian posterior computations (e.g., of parameter uncertainty, class label, or depth) to define a pixel-level importance map $$m_n^{(i)}=h_r(\hat\theta_n^{(i-1)},\epsilon_n^{(i-1)})$$ (Belmekki et al., 2021). New batches of shots are allocated to the $N_s$ pixels that promise maximal reduction in uncertainty or error, subject to hardware scanning constraints (pixel-wise or SPAD array). Stopping is typically based on RMSE convergence or uncertainty plateau.
• Adaptive Neighbor and Object-Aware Sampling: In detection pipelines (e.g., ALIGN), DBSCAN clustering yields cluster-cores per object. Surrounding neighborhoods are densely sampled within spatial–semantic constraints (using camera mask projection). Dynamic query balancing further allocates the remaining sampling budget between foreground (object) and background regions to minimize either under- or over-coverage in occluded or crowded scenarios (Baek et al., 20 Dec 2025).
• Simultaneous Diffusion Sampling in Generative Enhancement: In conditional LiDAR densification, multiple views are synthesized from the input scan and jointly sampled using diffusion models. Every reverse step fuses multi-view projections to enforce geometric consistency, achieving improved scene completion, inpainting, or beam densification (Faulkner et al., 2024).

4. Sampling for Efficient, Robust, and High-Precision LiDAR

Sampling is closely coupled to operational constraints—computational, memory, or hardware—in high-rate or precision-critical systems:

• Continuous-Time Estimation and Localizability-Aware Downsampling: In multi-LiDAR odometry (MLO), per-point localizability is computed, and only points that collectively span all 6-DOFs with sufficient Fisher information are retained. This reduces per-frame point counts by ≥2× and improves runtime by 2–5× without sacrificing accuracy (Shen et al., 2024).
• Sparse and Blue-Noise Subsampling in Multispectral SPAD LiDAR: Acquisition is governed by spatial–spectral masks $G\in\{0,1\}^{N_r\times N_c\times L}$ enabling only a subset of bands per pixel. Blue-noise patterns uniformly distribute samples, maximizing true detection and minimizing intensity error; Bayesian RJ-MCMC reconstructs multi-surface, multi-spectral scenes from such codes at dramatically reduced acquisition cost (Tachella et al., 2019).
• Asynchronous and Two-Photon Sampling in TOF LiDAR: Asynchronous electrical (single-comb) or two-photon (dual-comb) approaches leverage under-sampling combined with pulse timing reconstruction to vastly improve data-utilization and rate. Asynchronous sampling achieves 1 MHz update rates and ∼8 μm precision (Dong et al., 2024); two-photon methods extend alias-free acquisition limits by 12× and permit ultra-low data bandwidth multi-kHz operation with sub-100 nm precision using microcontroller timing (Wright et al., 2021).

5. Quantitative Impact and Empirical Benchmarks

Table: Representative Performance Across LiDAR Sampling Strategies

Strategy	Setup	Efficiency / Accuracy Gain	Benchmarking Context
PRISM (color-stratified)	1% compression, quant. bins	+2.2–3.8 bits ΔH, ≈1.4% ratio, 0.35–1.53 m CD	Toronto-3D, ETH3D, Paris-CARLA (Lim et al., 11 Jan 2026)
Superpixel-guided adaptive	0.08%–0.45% sampling	3–4× fewer samples at same RMSE, preserves edges	Synthia, NYU-Depth-v2 (Wolff et al., 2019)
PCB-RS (balanced)	Cylinder grid, urban driving	+2.8–4.6 pt mIoU far-field vs. RS, improved balance	SemanticKITTI, POSS (Han et al., 2022)
Ensemble-variance PM	KITTI depth, B=1024 (~1%)	4–10× sample reduction at fixed accuracy	KITTI depth completion (Gofer et al., 2020)
CTE-MLO (localizability)	Multi-LiDAR odometry, NTU VIRAL	2–5× runtime drop, no ATE loss	Odometry, mapping (Shen et al., 2024)
Blue-noise subsampling	Multispectral SPAD, W=2 of 32 bands	97.7-100% detection, 3.9 mm RMSE, 4–8× less time	Middlebury art, blocks+leaves (Tachella et al., 2019)
Asynchronous LiDAR sampling	Femtosecond comb, TOF	1 MP/s, 8 µm Allen dev., real-time	Micrometer metrology (Dong et al., 2024)
Two-photon dual-comb	Cross-pol. combs, stopwatch counter	sub-100 nm, >10⁴x data reduction, alias-free @12×	Distance metrology (Wright et al., 2021)

Empirical studies converge that adaptive, color- or uncertainty-aware, and domain-tailored sampling can reduce data, bandwidth, acquisition time, and computational requirements by factors ranging from 3× to 100× for a given task error threshold, while maintaining or exceeding geometric, photometric, or semantic fidelity relative to uniform or naïve strategies.

6. Limitations, Trade-offs, and Practical Considerations

• Granularity and Fidelity Trade-offs: Aggressive binning (color, spatial) or synthetic view generation (diffusion) may degrade geometric or textural details in feature-rich scenes or at range extremes. Hybrid schemes (e.g., color + spatial stratification) may be required for high-precision geodesy (Lim et al., 11 Jan 2026).
• Computational Budget: Adaptive and uncertainty-based strategies incur M×K multiplicative factor in compute (ensemble size x stages), mitigated via parallelism, subsampling in the predictor, or lighter-weight models (Gofer et al., 2020, Shomer et al., 2023).
• Hardware Constraints: Sequential or large-array scanning modes affect the spatial degrees of freedom for task-based adaptive sampling, and parallel arrays may skip fine structures (Belmekki et al., 2021).
• Robustness and Generalization: Domain-specific sampling (e.g., polar-cylinder balance) assumes certain spatial distributions (e.g., radial decay in automotive point clouds), which may not generalize to arbitrary scene types (Han et al., 2022).
• End-to-End Optimization: Integration with downstream tasks (depth completion, object detection, place recognition) often necessitates joint optimization and cross-validation to ensure that sample distributions align with end-task performance sensitivities (Shomer et al., 2023, Baek et al., 20 Dec 2025, Stathoulopoulos et al., 2024).
• Annotation and Training Data: For supervised approaches (e.g., deep colorization, sampling mask learning), sufficient annotated data in the target LiDAR modality is required to generalize the sampling policy (Ha et al., 4 May 2025).

7. Integration in Modern LiDAR Processing Pipelines

LiDAR sampling is integral to a range of contemporary computational pipelines:

• 3D Reconstruction and Completion: Adaptive spatial and color-guided sampling enhances sparse-to-dense conversion, supporting high-fidelity 3D mesh or surface recovery at lower acquisition or storage cost (Wolff et al., 2019, Savkin et al., 2023).
• Perception (Semantic Segmentation, Detection): Balanced and locality-preserving downsampling enables networks to maintain performance across all spatial ranges, aiding minority-class and far-field object recognition (Han et al., 2022, Baek et al., 20 Dec 2025).
• Odometry, SLAM, and Localization: Localizability-aware and descriptor-space–optimized sampling reduces memory and compute loads for continuous mapping and robust place recognition, particularly in long-duration and resource-constrained robotics (Shen et al., 2024, Stathoulopoulos et al., 2024).
• High-Precision and Multispectral Metrology: TOF under asynchronous and dual-comb regimes leverages pulse timing or spectral code selection, pushing spatial resolution to micrometer and sub-micrometer scales with real-time operation (Dong et al., 2024, Wright et al., 2021, Tachella et al., 2019).
• Generative Filling and Densification: Simultaneous diffusion sampling and learned upsampling restore missing, occluded, or low-resolution scans while enforcing geometric coherence across multiple views (Faulkner et al., 2024, Savkin et al., 2023).

LiDAR sampling thus remains a pivotal, highly optimized stage in the pipeline for efficient, accurate, and scalable 3D scene understanding and reconstruction (Lim et al., 11 Jan 2026, Wolff et al., 2019, Shen et al., 2024, Stathoulopoulos et al., 2024, Han et al., 2022, Shomer et al., 2023, Faulkner et al., 2024, Baek et al., 20 Dec 2025, Belmekki et al., 2021, Tachella et al., 2019, Dong et al., 2024, Wright et al., 2021, Ha et al., 4 May 2025, Savkin et al., 2023).