# Printing the Underdetermined: Materializing Multi-solutionness in Figurative Paintings

arXiv: https://arxiv.org/abs/2609.19782 · HTML: https://mlsanity.com/paper/2609.19782/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 39 references that are in the map.
- First posted on arXiv 17 Sep 2026.

## Builds on (most cited first, 16 of 16)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [Zero-1-to-3: Zero-shot One Image to 3D Object](https://mlsanity.com/paper/2303.11328/) (2023)
- [Magic3D: High-Resolution Text-to-3D Content Creation](https://mlsanity.com/paper/2211.10440/) (2022)
- [ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation](https://mlsanity.com/paper/2305.16213/) (2023)
- [WorldSimBench: Towards Video Generation Models as World Simulators](https://mlsanity.com/paper/2410.18072/) (2024)
- [CLAY: A Controllable Large-scale Generative Model for Creating High-quality 3D Assets](https://mlsanity.com/paper/2406.13897/) (2024)
- [TripoSR: Fast 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/2403.02151/) (2024)
- [WorldPlay: Towards Long-Term Geometric Consistency for Real-Time Interactive World Modeling](https://mlsanity.com/paper/2512.14614/) (2025)
- [ActiveNeRF: Learning where to See with Uncertainty Estimation](https://mlsanity.com/paper/2209.08546/) (2022)
- [Hunyuan3D 1.0: A Unified Framework for Text-to-3D and Image-to-3D Generation](https://mlsanity.com/paper/2411.02293/) (2024)
- [MatAnyone: Stable Video Matting with Consistent Memory Propagation](https://mlsanity.com/paper/2501.14677/) (2025)
- [ProbNeRF: Uncertainty-Aware Inference of 3D Shapes from 2D Images](https://mlsanity.com/paper/2210.17415/) (2022)
- [DreamPrinting: Volumetric Printing Primitives for High-Fidelity 3D Printing](https://mlsanity.com/paper/2503.00887/) (2025)

## Abstract (arXiv)

Figurative paintings are often approached as if they depict a single recoverable 3D scene: viewers infer depth and occlusion, and reconstruction pipelines attempt to converge to one stable model. We instead foreground multi-solutionness, the non-uniqueness of 3D configurations compatible with a single painted image, and propose a workflow that keeps this non-uniqueness visible and material. Multi-solutionness arises from two sources: unobserved content, where backsides and occluded volumes admit multiple plausible completions, and observed cues, where perspective, shading, and occlusion still underconstrain geometry. When additional views are synthesized by a video generative model without explicit 3D constraints, small frame-level drifts become inevitable rather than exceptional. Our pipeline samples multiple camera-orbit multi-view video sequences from one painting, reconstructs each sequence with 3D Gaussian Splatting into a point-based Gaussian scene representation where density halos and ghosting expose unresolved degrees of freedom, and fabricates these representations as physical artifacts using DreamPrinting. By treating multiple compatible interpretations as explicit outputs rather than residual error, we provide a computational framework for spatial readings of figurative painting that can be inspected, compared, and discussed in both digital and physical form.