Multi-Scale UV-Parameterized Representation

• Multi-scale UV-parameterized representation enables mapping complex 3D data into structured 2D UV domains for efficient processing.
• This technique supports scalable modeling tasks in computer vision, graphics, and 3D reconstruction, utilizing hierarchical feature levels.
• UV mapping strategies allow coarse-to-fine data fusion, hierarchical context propagation, and adaptive workflows with CNN backbones.

A multi-scale UV-parameterized representation refers to a structured encoding where data defined on complex geometric domains—such as 3D surfaces or unstructured point clouds—are mapped onto a regular two-dimensional UV (u,v) coordinate domain, and where information is organized or aggregated at multiple spatial resolutions or hierarchical feature levels. This paradigm is pivotal in computer vision, computer graphics, and 3D reconstruction pipelines, enabling efficient use of 2D convolutional neural network (CNN) backbones, generative models, and offering scalable, resolution-adaptive workflows for tasks such as 3D Gaussian splatting, avatar reconstruction, and scene modeling (Rai et al., 3 Feb 2025, Fan et al., 5 Jan 2026). The following sections describe historical motivation, technical foundations, multi-scale construction mechanisms, integration into generative models, and domain-specific applications.

1. Motivation and Conceptual Foundations

The unstructured nature of point-based geometric representations—such as 3D Gaussian splats—presents severe challenges for scalable modeling, editing, and learning tasks. Naive approaches lack structure for efficient neural modeling and are typically permutation-invariant, complicating the application of grid-based neural architectures.

UV parameterization addresses these issues by establishing a consistent bijective or injective mapping between the geometric domain and a 2D image-like atlas. In classical graphics, this is seen in the unwrapping (parameterization) of mesh surfaces—such as SMPL human templates—onto a 2D coordinate domain for texture mapping (Fan et al., 5 Jan 2026). In unstructured point clouds, such as those from 3D Gaussian Splatting, "spherical UV" mapping allows for transforming each splat's 3D position into structured 2D pixel indices, forming a regular 2D grid where each pixel aggregates the relevant attributes (Rai et al., 3 Feb 2025).

The extension to multi-scale representations—where features are computed, sampled, or aggregated at multiple resolutions—enables coarse-to-fine data fusion, hierarchical context propagation, memory efficiency, and adaptive level-of-detail.

2. UV Mapping Strategies and Spherical Parameterization

UV parameterization fundamentally provides the coordinate transformation between a complex domain and the 2D plane:

• Template-based Mesh UV Atlasing: For mesh surfaces such as SMPL, a predefined UV atlas assigns each 3D mesh vertex a canonical (u,v) ∈ [0,1]^2 (Fan et al., 5 Jan 2026).
• Spherical Mapping for Point Clouds: In the context of unstructured 3D Gaussians, each center position σᵢ=(xᵢ,yᵢ,zᵢ) is mapped to spherical coordinates (ρ,θ,φ):

$$ρ = \sqrt{xᵢ^2 + yᵢ^2 + zᵢ^2},\quad θ = \mathrm{atan2}(yᵢ, xᵢ),\quad φ = \arccos\left(\frac{zᵢ}{ρ}\right)$$

These are quantized into (u, v) pixel indices on an M × N image:

$$u = \left\lfloor \frac{θ + π}{2π} M \right\rfloor,\quad v = \left\lfloor \frac{φ}{π} N \right\rfloor$$

Each UV pixel may aggregate attributes (such as mean position, scale, rotation, color, and opacity), using dynamic selection (highest opacity wins) to handle splat collisions (Rai et al., 3 Feb 2025).

A summary of key UV-parameterization attributes:

Domain	Mapping Method	Range	Application Context
Template mesh	Precomputed atlas	[0,1]^2	Texture/feature mapping
Spherical point clouds	Spherical coords	[0,M-1] × [0,N-1]	3D Gaussian splatting

3. Multi-Scale UV Feature Construction

Multi-scale UV-parameterized representations leverage sets of UV feature maps at varying resolutions, capturing information at different spatial scales:

• Multi-Resolution UV Feature Maps: A hierarchy of L learnable feature maps $\{ F_s \}_{s=1}^L$, where $F_s \in \mathbb{R}^{r_s \times r_s \times C_s}$, each with distinct spatial resolutions $r_s$ and channel widths $C_s$, is established (Fan et al., 5 Jan 2026).
• Feature Sampling: For a given UV coordinate $(u,v)$, bilinear sampling retrieves per-scale features: $f_s = \mathrm{BilinearSample}(F_s; (u,v))$.
• Hierarchical Feature Fusion: At each canonical 3D location (associated to UV coordinates), features across all scales are fused (typically by summation):

$$f_c^i = \sum_{s=1}^L f_s^i,\qquad f_s^i \equiv \mathrm{BilinearSample}(F_s; (u_i,v_i))$$

This process integrates coarse contextual information with fine-grained detail, a critical property for handling occlusions and preserving high-frequency surface characteristics (Fan et al., 5 Jan 2026). Unlike hierarchical CNNs that upsample coarser maps for addition to finer ones, independent UV maps at each scale are maintained and fused post sampling.

• Per-Layer and Per-Pixel Control: For unstructured splats, UV grid resolution (M,N), and layer count (K, allowing for depth or top-K opacity sorting) provide tunable control over capacity and level-of-detail (Rai et al., 3 Feb 2025).

4. Network Architectures for Multi-Scale UV Processing

Multi-branch and multi-stage architectures facilitate the processing and compression of high-dimensional UV representations for compatibility with deep generative models:

• Attribute Decomposition: For spherical-mapped UVGS, 14 input channels (position, rotation, scale, color, opacity) are split into three semantic branches—position, transform (rotation/scale), appearance (color/opacity)—each projected by a dedicated CNN branch (Rai et al., 3 Feb 2025).
• Central Fusion and Compression: Concatenated branch outputs are passed through a central CNN which first expands, then compresses the channel width to a fixed output (e.g., 3 channels, analogous to RGB). This yields the "Super UVGS" representation $S \in \mathbb{R}^{M \times N \times 3}$, suitable for direct processing with standard image foundation models (Rai et al., 3 Feb 2025).
• Coarse-to-Fine MLP Decoding: In mesh-based UV pipelines, multi-scale fused features are concatenated and decoded into geometric and appearance attributes (e.g., 3D Gaussian center adjustments, scale, color) via lightweight multilayer perceptrons (MLPs). This design enables spatially-aware and hierarchical recovery of 3D representations from UV features (Fan et al., 5 Jan 2026).

5. Scalability, Level-of-Detail, and Practical Control

The multi-scale UV parameterization paradigm provides direct and interpretable levers for resolution and complexity control:

• Capacity Scaling: Total splat or feature count per layer in UVGS is M × N; with K depth layers, the total is K × M × N. For instance, 512 × 512 × 4 accommodates ≈1.05M splats (Rai et al., 3 Feb 2025).
• Level-of-Detail Adaptation: Increasing UV resolution enables higher spatial fidelity and supports denser geometry; downsampling reduces memory and computation. Selection of K provides flexibility in occlusion handling and synthesizing view-consistent depth layers. In the avatar domain, scale-variant UV feature maps enable context transfer and occlusion-robustness: coarse maps propagate across missing regions; fine maps restore high-frequency structure (Fan et al., 5 Jan 2026).
• Efficiency: Hierarchical fusion ensures that memory-intensive high-resolution layers need not be active globally; localized upsampling is possible where detail is required.

6. Integration with Generative Models and 3D Reconstruction Pipelines

The regular, image-like structure of UV-parameterized representations allows for the application of generic 2D generative models—VAEs, latent diffusion models, CNNs—without the need for specialized 3D architectures:

• Super UVGS and Latent Diffusion Integration: The 3-channel compressed UV map (Super UVGS) is processed as an ordinary RGB image: it is encoded with pretrained image VAEs, and latent diffusion models are trained or applied with the standard objectives, e.g.

$$\mathcal{L}_{\mathrm{LDM}} = \mathbb{E}_{z_0, \epsilon \sim \mathcal{N}(0,1), t}\, \| \epsilon - \epsilon_\theta(z_t, t) \|^2$$

or, for conditional generative tasks, with text-conditioning. No model modification is required to enforce multi-view or 3D consistency, as this is structurally preserved by the UVGS organization (Rai et al., 3 Feb 2025).

• Avatar Reconstruction Pipelines: In multi-scale UV pipelines for avatars, the process involves mapping 3D surface points to UV space, extracting hierarchical features across scales, decoding to 3D Gaussian attributes, and applying learned skinning or pose transformations. Photometric losses (L₁, SSIM, LPIPS) on rendered images guide optimization, enabling the UV feature maps to encode sufficient information for both visible and occluded regions (Fan et al., 5 Jan 2026).

A generic pipeline for multi-scale UVGS-based 3D generation is as follows (Rai et al., 3 Feb 2025):

1. Fit 3D Gaussians to multi-view images.
2. Spherical/UV mapping to structured map $U \in \mathbb{R}^{M \times N \times 14 K}$.
3. Compression to $S \in \mathbb{R}^{M \times N \times 3}$.
4. VAE encoding to latent z; LDM processing for image synthesis.
5. Decoding through inverse mapping reconstructs high-dimensional $U$ and inverse UV mapping yields 3D Gaussians, which are rendered or edited as 3D scenes.

7. Applications and Significance

Multi-scale UV-parameterized representations are established as foundational for a wide spectrum of high-fidelity 3D content creation tasks:

• 3D Gaussian Splatting: Seamless mapping between unstructured splat clouds and structured, scalable image representations enables efficient 3D modeling, editing, inpainting, and text-driven generation using mature 2D generative methods (Rai et al., 3 Feb 2025).
• Animatable 3D Avatars: Integration of multi-scale UV features provides robust, identity-preserving completion under severe occlusion, leveraging hierarchical context at inference and facilitating consistent animation via pose-space transformations (Fan et al., 5 Jan 2026).
• Adaptive Level-of-Detail and Editing: Multi-scale schemes allow for local detail augmentation or global downscaling as required for task constraints, optimizing both reconstruction accuracy and computational resource usage.
• Pipeline Compatibility: By aligning the 3D modeling process with the architectures and objectives of state-of-the-art 2D image models, the approach bridges otherwise disparate generative ecosystems, accelerating methodological convergence and deployment flexibility.

A plausible implication is that as foundation models in both 2D and 3D domains grow in capacity and scale, the adherence to UV-structured, multi-scale representations will increase, as they offer clear semantic and computational advantages for hybrid tasks in graphics, vision, and generative modeling.

References:

• "UVGS: Reimagining Unstructured 3D Gaussian Splatting using UV Mapping" (Rai et al., 3 Feb 2025)
• "InpaintHuman: Reconstructing Occluded Humans with Multi-Scale UV Mapping and Identity-Preserving Diffusion Inpainting" (Fan et al., 5 Jan 2026)