# Rasterized Edge Gradients: Handling Discontinuities Differentiably

arXiv: https://arxiv.org/abs/2405.02508 · HTML: https://mlsanity.com/paper/2405.02508/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 54 references that are in the map.
- First posted on arXiv 3 May 2024.

## Builds on (most cited first, 30 of 35)

- [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)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [Deep High-Resolution Representation Learning for Visual Recognition](https://mlsanity.com/paper/1908.07919/) (2019)
- [Magic3D: High-Resolution Text-to-3D Content Creation](https://mlsanity.com/paper/2211.10440/) (2022)
- [Efficient Geometry-aware 3D Generative Adversarial Networks](https://mlsanity.com/paper/2112.07945/) (2021)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [MVDream: Multi-view Diffusion for 3D Generation](https://mlsanity.com/paper/2308.16512/) (2023)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [Keep it SMPL: Automatic Estimation of 3D Human Pose and Shape from a Single Image](https://mlsanity.com/paper/1607.08128/) (2016)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [Modular Primitives for High-Performance Differentiable Rendering](https://mlsanity.com/paper/2011.03277/) (2020)
- [Neural 3D Mesh Renderer](https://mlsanity.com/paper/1711.07566/) (2017)
- [Soft Rasterizer: A Differentiable Renderer for Image-based 3D Reasoning](https://mlsanity.com/paper/1904.01786/) (2019)
- [SynSin: End-to-end View Synthesis from a Single Image](https://mlsanity.com/paper/1912.08804/) (2019)
- [Dense Depth Priors for Neural Radiance Fields from Sparse Input Views](https://mlsanity.com/paper/2112.03288/) (2021)
- [Learning to Estimate 3D Human Pose and Shape from a Single Color Image](https://mlsanity.com/paper/1805.04092/) (2018)
- [Learning to Predict 3D Objects with an Interpolation-based Differentiable Renderer](https://mlsanity.com/paper/1908.01210/) (2019)
- [Multi-view Supervision for Single-view Reconstruction via Differentiable Ray Consistency](https://mlsanity.com/paper/1704.06254/) (2017)
- [3D Hand Shape and Pose Estimation from a Single RGB Image](https://mlsanity.com/paper/1903.00812/) (2019)
- [Deep Appearance Models for Face Rendering](https://mlsanity.com/paper/1808.00362/) (2018)
- [SDFDiff: Differentiable Rendering of Signed Distance Fields for 3D Shape Optimization](https://mlsanity.com/paper/1912.07109/) (2019)
- [TextMesh: Generation of Realistic 3D Meshes From Text Prompts](https://mlsanity.com/paper/2304.12439/) (2023)
- [Pixel Codec Avatars](https://mlsanity.com/paper/2104.04638/) (2021)
- [Pushing the Envelope for RGB-based Dense 3D Hand Pose Estimation via Neural Rendering](https://mlsanity.com/paper/1904.04196/) (2019)
- [Perspective Transformer Nets: Learning Single-View 3D Object Reconstruction without 3D Supervision](https://mlsanity.com/paper/1612.00814/) (2016)

## Built on by (most cited first, 14 of 14)

- [ATLAS: Decoupling Skeletal and Shape Parameters for Expressive Parametric Human Modeling](https://mlsanity.com/paper/2508.15767/) (2025)
- [3DGH: 3D Head Generation with Composable Hair and Face](https://mlsanity.com/paper/2506.20875/) (2025)
- [LUCAS: Layered Universal Codec Avatars](https://mlsanity.com/paper/2502.19739/) (2025)
- [HairCUP: Hair Compositional Universal Prior for 3D Gaussian Avatars](https://mlsanity.com/paper/2507.19481/) (2025)
- [From Orbit to Ground: Generative City Photogrammetry from Extreme Off-Nadir Satellite Images](https://mlsanity.com/paper/2512.07527/) (2025)
- [BG-Triangle: B'ezier Gaussian Triangle for 3D Vectorization and Rendering](https://mlsanity.com/paper/2503.13961/) (2025)
- [FRESA: Feedforward Reconstruction of Personalized Skinned Avatars from Few Images](https://mlsanity.com/paper/2503.19207/) (2025)
- [DiffSoup: Direct Differentiable Rasterization of Triangle Soup for Extreme Radiance Field Simplification](https://mlsanity.com/paper/2603.27151/) (2026)
- [Mix3R: Mixing Feed-forward Reconstruction and Generative 3D Priors for Joint Multi-view Aligned 3D Reconstruction and Pose Estimation](https://mlsanity.com/paper/2605.03359/) (2026)
- [AssetGen: Deployable 3D Asset Generation at Interactive Speed](https://mlsanity.com/paper/2605.26137/) (2026)
- [FiCA: Feed-forward instant Gaussian Codec Avatars from a Single Portrait Image](https://mlsanity.com/paper/2606.24232/) (2026)
- [Gaussian Pixel Codec Avatars: A Hybrid Representation for Efficient Rendering](https://mlsanity.com/paper/2512.15711/) (2025)
- [Elastic Triangle Splatting](https://mlsanity.com/paper/2608.29106/) (2026)
- [Inverse Rendering for Modeling with Line Primitives](https://mlsanity.com/paper/2609.00625/) (2026)

## Abstract (arXiv)

Computing the gradients of a rendering process is paramount for diverse applications in computer vision and graphics. However, accurate computation of these gradients is challenging due to discontinuities and rendering approximations, particularly for surface-based representations and rasterization-based rendering. We present a novel method for computing gradients at visibility discontinuities for rasterization-based differentiable renderers. Our method elegantly simplifies the traditionally complex problem through a carefully designed approximation strategy, allowing for a straightforward, effective, and performant solution. We introduce a novel concept of micro-edges, which allows us to treat the rasterized images as outcomes of a differentiable, continuous process aligned with the inherently non-differentiable, discrete-pixel rasterization. This technique eliminates the necessity for rendering approximations or other modifications to the forward pass, preserving the integrity of the rendered image, which makes it applicable to rasterized masks, depth, and normals images where filtering is prohibitive. Utilizing micro-edges simplifies gradient interpretation at discontinuities and enables handling of geometry intersections, offering an advantage over the prior art. We showcase our method in dynamic human head scene reconstruction, demonstrating effective handling of camera images and segmentation masks.