Hybrid 2D/3D Representation

• Hybrid 2D/3D representation is a framework that unifies 2D cues, such as images and curves, with 3D constructs like meshes and implicit fields to leverage the strengths of both dimensions.
• Methodologies including parallel architectures, hierarchical strategies, and latent hybrid encodings effectively extract, couple, and fuse multimodal signals, ensuring geometric and semantic consistency.
• These representations are applied in robotics, medical imaging, and computer graphics, delivering enhanced reconstruction quality, improved interpretability, and robust performance metrics.

A hybrid 2D/3D representation encodes and combines information spanning both two-dimensional (2D) and three-dimensional (3D) domains within a unified framework. This approach aims to integrate the complementary strengths of 2D and 3D primitives, data structures, or neural features—thereby overcoming the limitations inherent to purely 2D or purely 3D representations. Defined broadly, hybrid 2D/3D representations can encompass explicit geometry, implicit fields, parametric primitives, or learned neural features that participate in both planar (2D) and volumetric (3D) aspects of computer vision, graphics, medical imaging, robotics, or visualization systems.

1. Principles and Taxonomy of Hybrid 2D/3D Representations

Hybrid representations operate by simultaneously managing information across different spatial dimensionalities. These systems are typically motivated by:

• The need to combine the high efficiency, interpretability, or regularity of 2D primitives with the descriptive richness and spatial coherence of 3D structures.
• Application requirements such as sparse-to-dense signal lifting (e.g., 2D images to 3D geometry), geometric priors (e.g., planar or curved primitives plus full volumes), or efficient learning from multimodal data (e.g., incorporating 2D segmented masks/plans as constraints or cues for 3D modeling).

Hybrid frameworks are often instantiated via:

• Parallel architectures: Independent 2D (e.g., mesh, spline, or image) and 3D (e.g., SDF, volume, Gaussian blob) branches that are later fused or coupled via loss functions or constraint propagation (Poursaeed et al., 2020).
• Hierarchical strategies: Multistage pipelines in which 2D cues drive or refine subsequent 3D representations, as in multiview curve aggregation, scene surface proposals, or surrogate mesh extraction synchronized to neural field learning (Usumezbas et al., 2016, Huang et al., 8 Jan 2024, Taktasheva et al., 19 Sep 2025).
• Latent hybrid spaces: Unified neural latent spaces blending 2D planes (e.g., triplanes or spatial embeddings) with coarse 3D grids, enabling efficient representation and variation of shape and structure (Guo et al., 13 Mar 2025, Kim et al., 21 Feb 2024).

A schematic taxonomy is presented in the following table.

Category	2D Component	3D Component	Coupling Mechanism
Planar + Volumetric	2D mesh, curve, or Gaussian	3D mesh, SDF, or Gaussian	Alternating or joint optimization
Feature hybridization	2D CNN/triplane features	3D CNN/grid features	Concatenation, cross-attention
Parametric hybrid	2D explicit primitives	3D implicit/parametric	Union/minimum, consistency loss
Application-driven	2D semantic or annotation	3D geometry or field	Mapping, supervision

2. Methodologies: Constructing and Coupling 2D and 3D Primitives

Contemporary hybrid approaches employ several methodologies to construct and couple 2D with 3D representations:

• Extraction and Aggregation: 2D features—such as image curves or edge fragments—are detected across multiple calibrated views and then triangulated or paired to hypothesize 3D geometry (Usumezbas et al., 2016). Robust multi-view verification and local grouping rules are used to ensure that only spatially consistent and well-supported portions are reconstructed. These steps are often combined with occlusion-handling and redundancy resolution procedures.
• Explicit-Implicit Coupling: Parallel streams generate both explicit surfaces (e.g., meshes via chart atlases) and implicit fields (e.g., occupancy networks or SDFs), with synergy enforced by consistency losses:
  • Surface point consistency: Each explicit 2D chart point must land on the level set of the implicit function.
  • Normal consistency: The normals from explicit mesh differentials and implicit function gradients must align (Poursaeed et al., 2020, Huang et al., 8 Jan 2024).
  • Optimization typically alternates or jointly refines these coupled objectives to improve geometric and photometric accuracy.
• Hybrid Latent Encodings: Multimodal neural architectures fuse 2D triplane features with 3D grids (or vice versa). Example strategies include:
  • Attending from learned grid tokens and triplane tokens to octree-based mesh features (Guo et al., 13 Mar 2025).
  • Cross-attention blocks fusing global (2D/layerwise) and local (3D/volume) cues, such as in hybrid video autoencoders for generation or reconstruction (Kim et al., 21 Feb 2024).
• Semantic or Structural Decomposition: Part-aware hybrid models use superquadrics or other geometric abstractions for interpretable segmentation, combining these with surface-based 2D Gaussians that faithfully render texture and appearance (Gao et al., 20 Aug 2024).

3. Structural Organization and Topological Reasoning

A significant contribution of hybrid representations is the capacity to organize reconstructed entities in a manner that reflects both geometric and topological structure:

• Graph-Structured Outputs: In 3D curve drawing systems, spatial organization is captured by assembling recovered curves into a graph structure, where vertices encode junctions (merges, splits, endpoints) and edges are continuous curve segments. This enables subsequent semantic reasoning, such as distinguishing between surface boundaries and structural scaffolds (Usumezbas et al., 2016).
• Planar and Nonplanar Hybridization: Hybrid approaches targeting scene reconstruction from color images employ planar detection and constraint: flat, textureless regions are identified, and Gaussians representing those regions are constrained to 2D planes. The remaining geometry is modeled as unconstrained 3D Gaussians. Alternating optimization refines the planar fits and fills in volumetric structure, leading to faithful segmentation of planar surfaces while retaining the global scene’s volumetric nature (Taktasheva et al., 19 Sep 2025).
• Part-aware Decomposition: In interpretable scene reconstruction, hybrid blocks comprising coupled 2D Gaussians and superquadrics ensure that each semantic part is well-modeled both in geometry and rendering attributes, directly supporting editing, simulation, or manipulation at a structured component level (Gao et al., 20 Aug 2024).

4. Performance and Evaluation: Geometric, Photometric, and Semantic Metrics

Hybrid approaches have demonstrated advances across several types of evaluation metrics:

• Geometric Metrics: Chamfer Distance (CD), point-to-surface errors, and normal consistency are common for evaluating 3D surface or mesh recovery (Poursaeed et al., 2020, Guo et al., 13 Mar 2025).
• Photometric Fidelity: Peak Signal-to-Noise Ratio (PSNR), Structural Similarity (SSIM), and learned perceptual metrics (LPIPS) are applied to photorealistic rendering and view synthesis tasks (Taktasheva et al., 19 Sep 2025, Huang et al., 8 Jan 2024).
• Semantic/Structural Precision: In part-decomposition, object editing, or downstream manipulation tasks, interpretability and semantic clarity of components is assessed, sometimes by quantifying the coverage or parsimony of parts (Gao et al., 20 Aug 2024).
• Topological Completeness: The ability to recover explicit connectivity and minimize partial, redundant, or fragmented reconstructions is measured via graph-theoretic statistics and compared with prior curve or mesh-based pipelines (Usumezbas et al., 2016).

Hybrid approaches such as 3D Gaussian Flats exhibit state-of-the-art depth estimation accuracy (lower RMSE, MAE, AbsRel) on large-scale indoor benchmarks (ScanNetv2, ScanNet++), while also delivering mesh extractions with fewer artifacts on planar regions relative to baselines specializing in either volume or strict surface fitting (Taktasheva et al., 19 Sep 2025).

5. Applications Across Scientific and Technical Domains

Hybrid 2D/3D representations have enabled or improved solutions in domains including:

• Robotics and Perception: Dense color point cloud upsampling and scene reconstruction, crucial for navigation and manipulation tasks in robotics, leverage hybrid pipelines combining 2D image restoration and 3D Gaussian splatting with geometric point relocation strategies (Guo et al., 3 Sep 2024).
• Medical Imaging: Progressive hybrid MLP-CNN networks and hybrid CNN frameworks are used for high-accuracy 2D-to-3D reconstruction (e.g., oral panoramic X-ray to volume), 3D retinal layer segmentation with continuity constraints, and volumetric segmentation with superior cross-scan coherence (Li et al., 2 Aug 2024, Liu et al., 2022).
• 3D Shape Generation and Design: CAD and generative pipelines exploit hybrid SDFs (deep implicit plus explicit geometric branches), part-aware decompositions, and latent triplane/grid spaces for shape editing, style transfer, and diffusion-based generative modeling (Vasu et al., 2021, Guo et al., 13 Mar 2025, Gao et al., 20 Aug 2024).
• Visual Analytics and Human-Computer Interaction: Hybrid 2D/3D visualizations facilitate spatial reasoning, interactive feedback, and design review, supported by linked representations, animated transitions, and spatial mapping pipelines across desktop, AR, and mixed reality environments (Hong et al., 8 Jan 2024, Chen, 5 Jun 2025, Lu et al., 27 Jun 2025).

6. Challenges, Limitations, and Open Research Directions

• Coupling and Optimization: Alternating block-coordinate optimization is critical when fusing primitives in different dimensionalities. Joint or simultaneous optimization without structural regularization can degrade performance, particularly on planar or semantically significant regions (Taktasheva et al., 19 Sep 2025).
• Segmentation and Primitive Assignment: Initial plane or semantic masks are susceptible to errors from upstream modules (e.g., unsupervised mask prediction). Improving segmentation accuracy and adaptive primitive selection remain ongoing challenges for robust hybridization.
• Computational Overheads: Hybrid systems introduce additional steps (e.g., RANSAC plane fitting, densification/relocation), which increase computational time compared to simpler pipelines. This is especially relevant for high-resolution or large-scale scenes.
• Modeling Limitations: Weak appearance models, such as low-order spherical harmonics, can force excessive geometric complexity to fit view-dependent effects. Integration of more expressive neural shading or appearance decoders is a potential avenue for further improvement.

Current research is exploring:

• Generalization to outdoor and mixed indoor-outdoor environments, where the diversity of surface types grows (Taktasheva et al., 19 Sep 2025).
• Adaptive and learnable primitive assignment for more nuanced scene decomposition.
• Extension of hybrid architectures to multi-modality signals and broader generative paradigms, as well as cross-domain transfer for low-data learning scenarios (Guo et al., 13 Mar 2025, Kim et al., 21 Feb 2024).
• Application to real-time, interactive systems where computational costs and latency are critical (Guo et al., 3 Sep 2024).

7. Significance in the Context of Computational Representation

Hybrid 2D/3D representations mark an important paradigm for modern computational geometry, machine perception, and vision. By explicitly encoding both lower- and higher-dimensional structural elements, they enable systems to simultaneously capture regularities, semantic structure, fine geometric details, and photorealistic evidence—resulting in improved performance across a wide range of tasks. The explicit integration of dense planar fitting, parametric primitives, mesh-surface constraints, or cross-dimensional feature fusion is showing demonstrable impact in both physics-based graphics and learning-based generative models, with evidence of superior accuracy, generalization, and interpretability relative to their monolithic 2D or 3D counterparts.

Hybrid 2D/3D representation thus serves as a foundational concept at the intersection of signal processing, representation learning, and geometric modeling, and is driving advances in reconstruction, synthesis, editing, and analysis across disciplines involving complex spatial data.