# Perspective Plane Program Induction from a Single Image

arXiv: https://arxiv.org/abs/2006.14708 · HTML: https://mlsanity.com/paper/2006.14708/

## Key facts

- Cited by 9 papers in the map (data through 13 Oct 2026).
- First posted on arXiv 25 Jun 2020.

## Built on by (most cited first, 9 of 9)

- [Decomposing 3D Scenes into Objects via Unsupervised Volume Segmentation](https://mlsanity.com/paper/2104.01148/) (2021)
- [Neuro-Symbolic AI in 2024: A Systematic Review](https://mlsanity.com/paper/2501.05435/) (2025)
- [Structure from Duplicates: Neural Inverse Graphics from a Pile of Objects](https://mlsanity.com/paper/2401.05236/) (2024)
- [Learning Continuous Implicit Representation for Near-Periodic Patterns](https://mlsanity.com/paper/2208.12278/) (2022)
- [Learning to Infer 3D Shape Programs with Differentiable Renderer](https://mlsanity.com/paper/2206.12675/) (2022)
- [Tree-Structured Shading Decomposition](https://mlsanity.com/paper/2309.07122/) (2023)
- [Neural Slot Interpreters: Grounding Object Semantics in Emergent Slot Representations](https://mlsanity.com/paper/2403.07887/) (2024)
- [Conditional Teaching Size](https://mlsanity.com/paper/2107.07038/) (2021)
- [ShapeCodeBench: A Renewable Benchmark for Perception-to-Program Reconstruction of Synthetic Shape Scenes](https://mlsanity.com/paper/2605.11680/) (2026)

## Abstract (arXiv)

We study the inverse graphics problem of inferring a holistic representation for natural images. Given an input image, our goal is to induce a neuro-symbolic, program-like representation that jointly models camera poses, object locations, and global scene structures. Such high-level, holistic scene representations further facilitate low-level image manipulation tasks such as inpainting. We formulate this problem as jointly finding the camera pose and scene structure that best describe the input image. The benefits of such joint inference are two-fold: scene regularity serves as a new cue for perspective correction, and in turn, correct perspective correction leads to a simplified scene structure, similar to how the correct shape leads to the most regular texture in shape from texture. Our proposed framework, Perspective Plane Program Induction (P3I), combines search-based and gradient-based algorithms to efficiently solve the problem. P3I outperforms a set of baselines on a collection of Internet images, across tasks including camera pose estimation, global structure inference, and down-stream image manipulation tasks.