Organizations: 1CERI SN, IMT Nord Europe, Villeneuve D’Ascq, 59650 (France) · Univ. Lille, CNRS, Centrale Lille, UMR 9013 - LaMcube - Laboratoire de Mécanique, Multiphysique, Multiéchelle, F-59000 Lille, France · Downs, 59670 Sainte-Marie-Cappel (France) · School of Information Technology, Murdoch University (Australia)
The selection of an appropriate 3D representation is a fundamental design decision that dictates the efficiency, quality, and capabilities of modern computer vision and graphics pipelines for tasks such as 3D reconstruction, novel-view synthesis and rendering, shape and motion analysis, recognition, and generation. While traditional representations (\eg meshes, point clouds, and volumetric grids) remain standard outputs of 3D sensors (\eg LiDAR and 3D scanners) and are widely used in downstream applications (\eg editing and simulation), recent neural and primitive-based representations (\eg 3D Gaussian Splatting) offer compact and differentiable alternatives opening a wide range of opportunities in applications such as games, AR/VR, autonomous driving, robot navigation, and medical imaging, to name a few. The goal of this paper is to survey the main families of 3D representations from discrete explicit formats to continuous implicit fields based either on neural rendering or primitive splatting. For each type of representation, we present the general formulation and its variants, discuss its benefits and limitations, and highlight key applications. We conclude the paper by outlining the open challenges and potential directions for future research. Distinct from recent surveys that broadly cover 3D object and scene reconstruction, this paper provides a focused analysis on the evolution of 3D representations themselves. We specifically emphasize the paradigm shift toward implicit representations, offering a novel perspective on how these emerging formats fundamentally alter 3D/4D workflows.
3D vision has rapidly evolved, driven by increasingly diverse data representations, learning paradigms, and modeling strategies. Yet the field remains fragmented across representations and benchmarks, making it difficult to develop unified perspectives on efficiency, fidelity, and scalability. This work provides a data-centric taxonomy of 3D vision that connects geometric representations, datasets, learning frameworks, and applications within a single conceptual map. We begin by analysing the principal structural representations of 3D data--point clouds, meshes, voxels, and 3D Gaussians--along with their acquisition pipelines. We then examine how dataset design, benchmark construction, and supervision regimes shape recent advances, spanning 2D-supervised 3D learning, implicit neural representations, and 4D world modeling. Through this integrative lens, we clarify the relationships among representations, learning paradigms, and downstream tasks in reconstruction, generation, and video modeling, offering a consolidated view of emerging trends toward balancing efficiency and fidelity and toward multimodal geometric grounding.
Three-dimensional reconstruction from unorganized point clouds remains a challenging problem in computer vision, geometric modeling, and computer-aided design. While neural implicit methods achieve impressive reconstruction accuracy, geometry is typically encoded in latent representations that limit interpretability and reuse within engineering workflows. We present NeuSOGA3D (Neuro-Symbolic Geometric Abstraction in 3D), a hybrid framework that combines learned perceptual priors inherited from NeuSOGA with explicit symbolic geometric reasoning. The method projects point clouds onto principal orthographic planes, constructs symbolic implicit spline representations from the resulting observations, and fuses them through shape-preserving constructive solid geometry operations to generate a coarse visual hull. Additional geometric detail is recovered through cross-sectional decomposition and volumetric reconstruction using Partial Shape-Preserving Splines. Unlike conventional neural implicit approaches, NeuSOGA3D progressively transforms observations into explicit symbolic entities, including control polygons, implicit spline fields, cross-sections, and volumetric lofts. Experiments on all forty categories of the ModelNet40 benchmark demonstrate the ability of the framework to recover structurally meaningful and CAD-compatible geometric representations from diverse point-cloud observations. The results highlight the potential of combining learned perception with symbolic geometric reasoning for explainable geometric intelligence.
3D Gaussian Splatting (3DGS) is a recent approach for scene rendering. Although primarily designed for view synthesis, its potential for scene understanding tasks remains underexplored. In this work, we conduct a comparative evaluation of various geometric deep learning architectures for the classification of 3D scenes represented using Gaussian Splatting. We benchmark point-based and graph-based models across both traditional point cloud datasets and dedicated Gaussian Splatting datasets. Scenes are embedded into latent representations, which are evaluated through end-to-end classification, linear probing, and clustering analysis. Our study provides insight into the suitability of different geometry-aware architectures and input feature configurations for learning effective 3D Gaussian Splat representations. The results highlight consistent differences between architectural families and reveal the impact of Gaussian-specific attributes on the quality of representation.
Julia Farganus, Krzysztof Żurawicki, Arkadiusz Gaweł +2