# Discontinuity-preserving Normal Integration with Auxiliary Edges

arXiv: https://arxiv.org/abs/2404.03138 · HTML: https://mlsanity.com/paper/2404.03138/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 22 references that are in the map.
- First posted on arXiv 4 Apr 2024.

## Builds on (most cited first, 5 of 5)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Function4D: Real-time Human Volumetric Capture from Very Sparse Consumer RGBD Sensors](https://mlsanity.com/paper/2105.01859/) (2021)
- [ECON: Explicit Clothed humans Optimized via Normal integration](https://mlsanity.com/paper/2212.07422/) (2022)
- [Normal Integration: A Survey](https://mlsanity.com/paper/1709.05940/) (2017)
- [Variational Methods for Normal Integration](https://mlsanity.com/paper/1709.05965/) (2017)

## Built on by (most cited first, 4 of 4)

- [Discontinuity-aware Normal Integration for Generic Central Camera Models](https://mlsanity.com/paper/2507.06075/) (2025)
- [Towards Fast and Scalable Normal Integration using Continuous Components](https://mlsanity.com/paper/2510.11508/) (2025)
- [Perspective-aware fusion of incomplete depth maps and surface normals for accurate 3D reconstruction](https://mlsanity.com/paper/2602.07444/) (2026)
- [PixVOD: Pixel-Distributed Direct Visual Odometry and Depth Estimation](https://mlsanity.com/paper/2606.03989/) (2026)

## Abstract (arXiv)

Many surface reconstruction methods incorporate normal integration, which is a process to obtain a depth map from surface gradients. In this process, the input may represent a surface with discontinuities, e.g., due to self-occlusion. To reconstruct an accurate depth map from the input normal map, hidden surface gradients occurring from the jumps must be handled. To model these jumps correctly, we design a novel discretization scheme for the domain of normal integration. Our key idea is to introduce auxiliary edges, which bridge between piecewise-smooth patches in the domain so that the magnitude of hidden jumps can be explicitly expressed. Using the auxiliary edges, we design a novel algorithm to optimize the discontinuity and the depth map from the input normal map. Our method optimizes discontinuities by using a combination of iterative re-weighted least squares and iterative filtering of the jump magnitudes on auxiliary edges to provide strong sparsity regularization. Compared to previous discontinuity-preserving normal integration methods, which model the magnitudes of jumps only implicitly, our method reconstructs subtle discontinuities accurately thanks to our explicit representation of jumps allowing for strong sparsity regularization.