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NPNet: A Non-Parametric Network with Adaptive Gaussian-Fourier Positional Encoding for 3D Classification and Segmentation

Mohammad Saeid, Amir Salarpour, Pedram MohajerAnsari, Mert D. Pesé

TL;DR

NPNet addresses 3D point-cloud classification and segmentation with a fully non-parametric pipeline that eschews learned weights in favor of deterministic operators and a memory-bank inference. Its core is an adaptive Gaussian–Fourier positional encoding that adjusts bandwidth and Gaussian–cosine mixing from input geometry, supplemented by a fixed-frequency Fourier channel for segmentation to provide global context. Across ModelNet40, ModelNet-R, ScanObjectNN, and ShapeNetPart, NPNet achieves state-of-the-art performance among non-parametric methods and strong few-shot results, while offering low memory footprint and fast inference. The work demonstrates that training-free deployment is viable for 3D perception and lays groundwork for lightweight hybrids that integrate minimal learnable components when needed.

Abstract

We present NPNet, a fully non-parametric approach for 3D point-cloud classification and part segmentation. NPNet contains no learned weights; instead, it builds point features using deterministic operators such as farthest point sampling, k-nearest neighbors, and pooling. Our key idea is an adaptive Gaussian-Fourier positional encoding whose bandwidth and Gaussian-cosine mixing are chosen from the input geometry, helping the method remain stable across different scales and sampling densities. For segmentation, we additionally incorporate fixed-frequency Fourier features to provide global context alongside the adaptive encoding. Across ModelNet40/ModelNet-R, ScanObjectNN, and ShapeNetPart, NPNet achieves strong performance among non-parametric baselines, and it is particularly effective in few-shot settings on ModelNet40. NPNet also offers favorable memory use and inference time compared to prior non-parametric methods

NPNet: A Non-Parametric Network with Adaptive Gaussian-Fourier Positional Encoding for 3D Classification and Segmentation

TL;DR

NPNet addresses 3D point-cloud classification and segmentation with a fully non-parametric pipeline that eschews learned weights in favor of deterministic operators and a memory-bank inference. Its core is an adaptive Gaussian–Fourier positional encoding that adjusts bandwidth and Gaussian–cosine mixing from input geometry, supplemented by a fixed-frequency Fourier channel for segmentation to provide global context. Across ModelNet40, ModelNet-R, ScanObjectNN, and ShapeNetPart, NPNet achieves state-of-the-art performance among non-parametric methods and strong few-shot results, while offering low memory footprint and fast inference. The work demonstrates that training-free deployment is viable for 3D perception and lays groundwork for lightweight hybrids that integrate minimal learnable components when needed.

Abstract

We present NPNet, a fully non-parametric approach for 3D point-cloud classification and part segmentation. NPNet contains no learned weights; instead, it builds point features using deterministic operators such as farthest point sampling, k-nearest neighbors, and pooling. Our key idea is an adaptive Gaussian-Fourier positional encoding whose bandwidth and Gaussian-cosine mixing are chosen from the input geometry, helping the method remain stable across different scales and sampling densities. For segmentation, we additionally incorporate fixed-frequency Fourier features to provide global context alongside the adaptive encoding. Across ModelNet40/ModelNet-R, ScanObjectNN, and ShapeNetPart, NPNet achieves strong performance among non-parametric baselines, and it is particularly effective in few-shot settings on ModelNet40. NPNet also offers favorable memory use and inference time compared to prior non-parametric methods
Paper Structure (24 sections, 7 equations, 9 figures, 6 tables)

This paper contains 24 sections, 7 equations, 9 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Overview of NPNet
  5. Adaptive Gaussian--Fourier Positional Encoding
  6. Adaptive channel.
  7. Fourier channel (segmentation).
  8. Hybrid code and neighborhood modulation.
  9. NPNet Classification Architecture
  10. NPNet Segmentation Architecture
  11. Non-Parametric Training and Inference
  12. Classification.
  13. Segmentation.
  14. Experiments
  15. Datasets and Evaluation Metrics
  16. ...and 9 more sections

Figures (9)

  • Figure 1: Radar comparison on ModelNet40 and ShapeNetPart. Metrics are normalized to $[0,1]$ per dataset (higher is better). GPU memory, GFLOPs, and inference time are inverted so larger values indicate better efficiency.
  • Figure 2: Adaptive Gaussian--Fourier positional encoding. The encoding adapts bandwidth $\sigma$ and mixing coefficient $\lambda$ from input geometry; an additional fixed-frequency Fourier branch provides global context for segmentation.
  • Figure 3: Stage block used in NPNet. FPS selects centroids, $k$-NN groups local neighborhoods, positional encoding modulates features, and mean/max pooling produces a stage descriptor; concatenating stages forms a multi-scale representation.
  • Figure 4: NPNet architecture for classification and part segmentation. The model contains no trainable weights; inference is performed by similarity matching to stored shape descriptors (classification) or part prototypes (segmentation).
  • Figure 5: Effect of disabling adaptivity on ModelNet40. Accuracy when (a) $\sigma$ is fixed and (b) the Gaussian--cosine mixing ratio is fixed in the positional encoding.
  • ...and 4 more figures