# Towards Fast and Scalable Normal Integration using Continuous Components

arXiv: https://arxiv.org/abs/2510.11508 · HTML: https://mlsanity.com/paper/2510.11508/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 29 references that are in the map.
- First posted on arXiv 13 Oct 2025.

## Builds on (most cited first, 8 of 8)

- [Rethinking Inductive Biases for Surface Normal Estimation](https://mlsanity.com/paper/2403.00712/) (2024)
- [Scalable, Detailed and Mask-Free Universal Photometric Stereo](https://mlsanity.com/paper/2303.15724/) (2023)
- [Normal Integration: A Survey](https://mlsanity.com/paper/1709.05940/) (2017)
- [An Adaptive Screen-Space Meshing Approach for Normal Integration](https://mlsanity.com/paper/2409.16907/) (2024)
- [Variational Methods for Normal Integration](https://mlsanity.com/paper/1709.05965/) (2017)
- [Least squares surface reconstruction on arbitrary domains](https://mlsanity.com/paper/2007.08661/) (2020)
- [Discontinuity-preserving Normal Integration with Auxiliary Edges](https://mlsanity.com/paper/2404.03138/) (2024)
- [Discontinuity-aware Normal Integration for Generic Central Camera Models](https://mlsanity.com/paper/2507.06075/) (2025)

## Abstract (arXiv)

Surface normal integration is a fundamental problem in computer vision, dealing with the objective of reconstructing a surface from its corresponding normal map. Existing approaches require an iterative global optimization to jointly estimate the depth of each pixel, which scales poorly to larger normal maps. In this paper, we address this problem by recasting normal integration as the estimation of relative scales of continuous components. By constraining pixels belonging to the same component to jointly vary their scale, we drastically reduce the number of optimization variables. Our framework includes a heuristic to accurately estimate continuous components from the start, a strategy to rebalance optimization terms, and a technique to iteratively merge components to further reduce the size of the problem. Our method achieves state-of-the-art results on the standard normal integration benchmark in as little as a few seconds and achieves one-order-of-magnitude speedup over pixel-level approaches on large-resolution normal maps.