Point Cloud Event Representation

• Point cloud-based event representation is a computational paradigm that encodes asynchronous event streams as high-fidelity point sets, preserving temporal precision and sparsity.
• It employs hierarchical grouping, frequency-domain analysis, and adaptive coding to extract spatiotemporal features for tasks like recognition, regression, and registration.
• This representation achieves real-time deployment with reduced computation and memory usage by leveraging permutation-invariant architectures and efficient sampling techniques.

Point cloud-based event representation is a computational paradigm for encoding, processing, and analyzing asynchronous event streams, such as those produced by event cameras or physical experiments, in high-dimensional, temporally precise point sets. By treating each event as a point in a structured space (typically $\mathbb{R}^n$), this representation naturally accommodates sparsity, permutation-invariant architectures, and continuous-time modeling, offering significant efficiency and fidelity advantages over traditional frame- or voxel-based approaches. Recent advances in deep learning exploit point cloud structures to abstract local and global spatial-temporal features, compress large event datasets, and perform real-time recognition, regression, and registration tasks.

1. Formal Definition and Construction of Event Point Clouds

In the context of event cameras, the native output is a time-ordered stream of events, each defined by spatial coordinates, timestamp, and polarity: $$\mathcal{E} = \{\,e_i = (x_i,y_i,t_i,p_i)\mid i=1,\dots,n\}$$ where $(x,y)$ are pixel coordinates, $t$ is the timestamp, and $p\in\{+1,-1\}$ is the polarity of brightness change. Unlike frame or voxel binning, point cloud methods preserve the raw event order and attributes, forming a $(2S\text{–}1T\text{–}1P)$ point cloud. For collider physics, the event representation $X = \{x_1,\dots,x_M\} \subset \mathbb{R}^n$ (where each $x_i$ is a particle with measured features) enables invariant and flexible architectures (Onyisi et al., 2022).

Event clouds are often downsampled or temporally sliced before processing. A consecutive or windowed subset of $T$ events forms the working set: $$\mathcal{EC} = \{\,e_j=(x_j,y_j,t_j,p_j)\mid j\in J, |J|=T\} \in \mathbb{R}^{T\times4}$$ Further refinements include rasterization (per-pixel&per-slice aggregation of statistical cues such as mean timestamp, polarity sum, event count) (Chen et al., 2022, Yin et al., 2023, Zhou et al., 6 Dec 2025), polarity attribute embedding (Seleem et al., 5 Feb 2025), or normalization for registration tasks (Lin et al., 2023).

2. Grouping, Sampling, and Feature Abstraction

Hierarchical architectures operate by iteratively grouping and downsampling point clouds. Typical modules include:

• Differentiation Farthest Point Sampling (D-FPS): Learnable scaling $\alpha$ emphasizes spatial/temporal/polarity dimensions for centroid selection (Ren et al., 30 Dec 2024).
• Feature-based k-NN (EF-KNN): Groups neighbors by proximity in learned feature space rather than Euclidean coordinates.
• Coordinates Evolution Strategy (CES): Updates centroid positions to the local mean of grouped events.
• Statistical Aggregation: Per-group features are standardized and concatenated for further abstraction.

These pipelines enable progressive reduction in point count while enriching feature dimensionality, facilitating efficient feature extraction even over long event sequences (Ren et al., 30 Dec 2024, Ren et al., 2023).

3. Frequency-Domain and Advanced Feature Extraction

To leverage the temporal structure of event clouds, frequency-domain modules perform 1D discrete Fourier transforms (DFT) on feature sequences:

$X[k] = \sum_{n=0}^{N-1} x[n]\,e^{-j2\pi kn/N}$

Frequency-aware modules apply learnable complex filters $V$ to the spectrum and reconstruct filtered representations via inverse FFT and pointwise nonlinearity: $$\widehat X = V \odot X, \qquad \tilde x = \sigma(\mathrm{iFFT}(\widehat X))$$ Spatial and temporal frequency modules replace dense convolutional or attention blocks, reducing complexity from $\mathcal{O}(d^2)$ to $\mathcal{O}(d\log d)$ for feature dimensionality $d$, with measured multiply-accumulate (MAC) reductions up to 20$\times$ (Ren et al., 30 Dec 2024).

Recent architectures, such as EventMamba (Ren et al., 9 May 2024), further introduce implicit and explicit temporal aggregation via attention or State-Space Models (SSM), capturing long-term dependencies with minimal computation, outperforming LSTM or self-attention-based approaches.

4. Point Cloud Event Coding and Compression

High-throughput streams necessitate efficient coding methods. Event data is mapped into 3D (spatial+temporal) voxel grids, with polarity as an attribute, enabling:

• Single-point cloud joint coding: Embeds polarity directly into the voxel attribute, facilitating adaptive lossy/lossless coding (DL-JEC) (Seleem et al., 5 Feb 2025).
• Block-wise encoding: 3D event blocks (e.g., $64^3$ voxels) are processed via autoencoder architectures, optimizing rate-distortion trade-offs with hyperprior-based entropy models.
• Adaptive voxel binarization: Top-$k$ selection tailored to classification, count, or quality objectives.
• Compressed-domain learning: Classifiers operate directly on latent representations, mitigating decompression artifacts (Seleem et al., 22 Jul 2024).

Empirical results show up to 50% reduction in bit rate at iso-distortion and denoising effects that improve downstream classification accuracy under lossy coding.

5. Applications: Recognition, Regression, Registration

Point cloud-based event representations enable high-performing models across varied domains:

• Action and gesture recognition: Hierarchical point cloud networks (TTPOINT (Ren et al., 2023), FECNet (Ren et al., 30 Dec 2024), EventMamba (Ren et al., 9 May 2024)) achieve SOTA accuracy with minimal computational resources, outperforming or matching frame-based methods while operating on sparse inputs.
• Human pose estimation: Rasterized event point clouds combined with statistical and edge-enhanced tokens (Event Temporal Slicing Convolution, Event Slice Sequencing) deliver high accuracy with real-time latency (Zhou et al., 6 Dec 2025, Chen et al., 2022).
• Deblurring: Multi-modal fusion networks (MTGNet (Lin et al., 16 Dec 2024)) leverage temporally fine-grained point cloud features and spatially dense voxel/image backbones for best-of-both performance.
• Event-to-point cloud registration: Event-Points-to-Tensor (EP2T) transforms irregular point clouds into grid-shaped tensors, enabling robust pose alignment under challenging conditions (Lin et al., 2023).
• Collider event classification: Point cloud architectures (Deep Sets, EdgeConv) provide permutation-invariant classification models with significant accuracy gains over feature-engineered methods (Onyisi et al., 2022).

6. Computational Characteristics and Efficiency

Compared to frame- and voxel-based approaches, point cloud representations:

• Preserve high temporal resolution: Events are encoded at native timestamps with minimal discretization, enabling accurate modeling of rapid motions and sparsity (Ren et al., 30 Dec 2024, Lin et al., 16 Dec 2024).
• Exploit sparsity for efficiency: Hierarchical feature extraction (point-based, graph-based, or continuous sparse convolution (Jack et al., 2020)) operates on far fewer data points, drastically reducing latency, memory, and computation.
• Permit flexible adaptivity: Grouping and sampling modules, adaptive binarization, and frequency-domain transformations allow task-specific optimization (classification, coding, regression).
• Achieve real-time deployment: In practical benchmarks, modern networks process tens of thousands of events in under 10 ms and fit within sub-1 million parameter footprints (Ren et al., 9 May 2024, Chen et al., 2022).

7. Limitations, Extensions, and Future Directions

Despite their strengths, point cloud representations face challenges:

• Polarity integration: Early methods ignored polarity, but recent architectures encode it as an attribute or use dual-clouds for joint coding (Ren et al., 30 Dec 2024, Seleem et al., 5 Feb 2025).
• Sparse spatial coverage: Sampling and grouping mitigate spatial sparsity, while attention and diffusion modules enrich features for image-space mapping (Lin et al., 16 Dec 2024).
• Boundary effects: Weighted kernel neighborhoods (continuous sparse convolution (Jack et al., 2020)) help reduce discontinuities; adaptive strategies may further enhance robustness.
• Interoperability: Unified representations bridge point cloud, frame, and voxel modalities for multi-modal processing.

Plausible implications are broader adoption in vision tasks requiring asynchronous, sparse, and temporally precise input modeling, continued integration of compressed-domain learning for resource-constrained devices, and further refinement of joint spatial-temporal-polarity abstractions.

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Key References:

• Frequency-aware Event Cloud Network (Ren et al., 30 Dec 2024)
• Efficient Human Pose Estimation via 3D Event Point Cloud (Chen et al., 2022)
• Deep Learning-based Event Data Coding: A Joint Spatiotemporal and Polarity Solution (Seleem et al., 5 Feb 2025)
• Rethinking Efficient and Effective Point-based Networks for Event Camera Classification and Regression: EventMamba (Ren et al., 9 May 2024)
• TTPOINT: A Tensorized Point Cloud Network for Lightweight Action Recognition with Event Cameras (Ren et al., 2023)
• Sparse Convolutions on Continuous Domains for Point Cloud and Event Stream Networks (Jack et al., 2020)
• Exploiting Spatiotemporal Properties for Efficient Event-Driven Human Pose Estimation (Zhou et al., 6 Dec 2025)
• Event-based Motion Deblurring via Multi-Temporal Granularity Fusion (Lin et al., 16 Dec 2024)
• Comparing Point Cloud Strategies for Collider Event Classification (Onyisi et al., 2022)
• E2PNet: Event to Point Cloud Registration with Spatio-Temporal Representation Learning (Lin et al., 2023)