# Differentiable Convex Polyhedra Optimization from Multi-view Images

arXiv: https://arxiv.org/abs/2407.15686 · HTML: https://mlsanity.com/paper/2407.15686/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 54 references that are in the map.
- First posted on arXiv 22 Jul 2024.

## Builds on (most cited first, 30 of 36)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Point-E: A System for Generating 3D Point Clouds from Complex Prompts](https://mlsanity.com/paper/2212.08751/) (2022)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [Point-NeRF: Point-based Neural Radiance Fields](https://mlsanity.com/paper/2201.08845/) (2022)
- [MonoSDF: Exploring Monocular Geometric Cues for Neural Implicit Surface Reconstruction](https://mlsanity.com/paper/2206.00665/) (2022)
- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [Modular Primitives for High-Performance Differentiable Rendering](https://mlsanity.com/paper/2011.03277/) (2020)
- [Soft Rasterizer: A Differentiable Renderer for Image-based 3D Reasoning](https://mlsanity.com/paper/1904.01786/) (2019)
- [Extracting Triangular 3D Models, Materials, and Lighting From Images](https://mlsanity.com/paper/2111.12503/) (2021)
- [Learning Deconvolution Network for Semantic Segmentation](https://mlsanity.com/paper/1505.04366/) (2015)
- [Volumetric and Multi-View CNNs for Object Classification on 3D Data](https://mlsanity.com/paper/1604.03265/) (2016)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [Learning Shape Abstractions by Assembling Volumetric Primitives](https://mlsanity.com/paper/1612.00404/) (2016)
- [CvxNet: Learnable Convex Decomposition](https://mlsanity.com/paper/1909.05736/) (2019)
- [SDFDiff: Differentiable Rendering of Signed Distance Fields for 3D Shape Optimization](https://mlsanity.com/paper/1912.07109/) (2019)
- [Flexible Isosurface Extraction for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2308.05371/) (2023)
- [Superquadrics Revisited: Learning 3D Shape Parsing beyond Cuboids](https://mlsanity.com/paper/1904.09970/) (2019)
- [Pixel2Mesh++: Multi-View 3D Mesh Generation via Deformation](https://mlsanity.com/paper/1908.01491/) (2019)
- [DualSDF: Semantic Shape Manipulation using a Two-Level Representation](https://mlsanity.com/paper/2004.02869/) (2020)
- [UCSG-Net -- Unsupervised Discovering of Constructive Solid Geometry Tree](https://mlsanity.com/paper/2006.09102/) (2020)
- [Object-Compositional Neural Implicit Surfaces](https://mlsanity.com/paper/2207.09686/) (2022)

## Built on by (most cited first, 1 of 1)

- [3D Convex Splatting: Radiance Field Rendering with 3D Smooth Convexes](https://mlsanity.com/paper/2411.14974/) (2024)

## Abstract (arXiv)

This paper presents a novel approach for the differentiable rendering of convex polyhedra, addressing the limitations of recent methods that rely on implicit field supervision. Our technique introduces a strategy that combines non-differentiable computation of hyperplane intersection through duality transform with differentiable optimization for vertex positioning with three-plane intersection, enabling gradient-based optimization without the need for 3D implicit fields. This allows for efficient shape representation across a range of applications, from shape parsing to compact mesh reconstruction. This work not only overcomes the challenges of previous approaches but also sets a new standard for representing shapes with convex polyhedra.