# Inverse Rendering for Modeling with Line Primitives

arXiv: https://arxiv.org/abs/2609.00625 · HTML: https://mlsanity.com/paper/2609.00625/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 80 references that are in the map.
- First posted on arXiv 1 Sep 2026.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [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)
- [NeuS2: Fast Learning of Neural Implicit Surfaces for Multi-view Reconstruction](https://mlsanity.com/paper/2212.05231/) (2022)
- [Learning to Predict 3D Objects with an Interpolation-based Differentiable Renderer](https://mlsanity.com/paper/1908.01210/) (2019)
- [Flexible Isosurface Extraction for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2308.05371/) (2023)
- [Differentiable Rendering: A Survey](https://mlsanity.com/paper/2006.12057/) (2020)
- [Adaptive Shells for Efficient Neural Radiance Field Rendering](https://mlsanity.com/paper/2311.10091/) (2023)
- [3D Convex Splatting: Radiance Field Rendering with 3D Smooth Convexes](https://mlsanity.com/paper/2411.14974/) (2024)
- [Triangle Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2505.19175/) (2025)
- [Appearance-Driven Automatic 3D Model Simplification](https://mlsanity.com/paper/2104.03989/) (2021)
- [GroomCap: High-Fidelity Prior-Free Hair Capture](https://mlsanity.com/paper/2409.00831/) (2024)
- [3Doodle: Compact Abstraction of Objects with 3D Strokes](https://mlsanity.com/paper/2402.03690/) (2024)
- [SpaceMesh: A Continuous Representation for Learning Manifold Surface Meshes](https://mlsanity.com/paper/2409.20562/) (2024)
- [VectorAdam for Rotation Equivariant Geometry Optimization](https://mlsanity.com/paper/2205.13599/) (2022)
- [Rasterized Edge Gradients: Handling Discontinuities Differentiably](https://mlsanity.com/paper/2405.02508/) (2024)
- [Volumetric Surfaces: Representing Fuzzy Geometries with Layered Meshes](https://mlsanity.com/paper/2409.02482/) (2024)
- [Auto Hair Card Extraction for Smooth Hair with Differentiable Rendering](https://mlsanity.com/paper/2505.18805/) (2025)
- [Radiance Surfaces: Optimizing Surface Representations with a 5D Radiance Field Loss](https://mlsanity.com/paper/2501.18627/) (2025)
- [DiffSoup: Direct Differentiable Rasterization of Triangle Soup for Extreme Radiance Field Simplification](https://mlsanity.com/paper/2603.27151/) (2026)
- [Simplifying Textured Triangle Meshes in the Wild](https://mlsanity.com/paper/2409.15458/) (2024)

## Abstract (arXiv)

Faithfully capturing diverse real-world objects with fuzzy, anisotropic structures, such as hair, fur, fibers, and textiles, for efficient real-time visualization remains challenging. Recent radiance field reconstruction methods capture these structures from multi-view images using translucent volumetric primitives such as 3D Gaussians rather than opaque low-dimensional primitives (e.g., triangles, line segments, and polylines), thereby limiting compatibility with standard depth-tested rasterization, reflection modeling, and physical simulation. We present an inverse rendering method for reconstructing fuzzy geometry using explicit line segments, which are rasterized on a subpixel grid for anti-aliasing to reproduce a semi-transparent appearance. While straightforward to render, optimizing numerous line primitives to match target images poses a significant challenge. We address this by introducing a stochastic differentiable rasterizer for line segments that produces informative gradients with respect to vertex positions, attributes, and discrete connectivity. Experiments on synthetic and real-world datasets show that our method outperforms surface-based approaches in capturing fuzzy boundaries and achieves quality comparable to volumetric representations while relying entirely on explicit geometry. The resulting representation integrates seamlessly with standard graphics pipelines, enabling cross-platform rendering, various shading models, and physical simulation.