Normal Integration via Inverse Plane Fitting With Minimum Point-to-Plane Distance
Xu Cao, Boxin Shi, Fumio Okura, Yasuyuki Matsushita
Abstract
This paper presents a surface normal integration method that solves an inverse problem of local plane fitting. Surface reconstruction from normal maps is essential in photometric shape reconstruction. To this end, we formulate normal integration in the camera coordinates and jointly solve for 3D point positions and local plane displacements. Unlike existing methods that consider the vertical distances between 3D points, we minimize the sum of squared pointto-plane distances. Our method can deal with both orthographic or perspective normal maps with arbitrary boundaries. Compared to existing normal integration methods, our method avoids the checkerboard artifact and performs more robustly against natural boundaries, sharp features, and outliers. We further provide a geometric analysis of the source of artifacts that appear in previous methods based on our plane fitting formulation. Experimental results on analytically computed, synthetic, and real-world surfaces show that our method yields accurate and stable reconstruction for both orthographic and perspective normal maps 1 .
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Cited by top-tier papers7
- S3-NeRF: Neural Reflectance Field from Shading and Shadow under a Single ViewpointWenqi Yang, Guanying Chen, Chaofeng Chen, Zhenfang Chen et al.NeurIPS 2022 · 48 citations
- Monocular Normal Estimation via Shading Sequence EstimationZongrui Li, Xinhua Ma, Minghui Hu, Yunqing Zhao et al.ICLR 2026 · 3 citations
- FNIN: A Fourier Neural Operator-based Numerical Integration Network for Surface-from-gradientsJiaqi Leng, Yakun Ju, Yuanxu Duan, Jiangnan Zhang et al.AAAI 2025 · 1 citation
- Variational Graph-based Normal IntegrationLixiong Chen, Bohan Yu, Victor Adrian Prisacariu, Imari SatoCVPR 2026
- Discontinuity-Aware Normal Integration for Generic Central Camera ModelsFrancesco Milano, Manuel López-Antequera, Naina Dhingra, Roland Siegwart et al.ICCV 2025
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