Discontinuity-aware Normal Integration for Generic Central Camera Models

2025-07-08

AI Summary

This work addresses two key limitations in normal integration: implicit handling of depth discontinuities and restrictive camera models (limited to orthographic or ideal pinhole). We propose the first method that explicitly models depth discontinuities while supporting general central cameras. Leveraging the local planarity assumption, we introduce geometric constraints between surface normals and incident ray directions to explicitly characterize depth jump boundaries. A variational optimization framework is formulated, integrating a local planarity prior with discontinuity-aware regularization—enabling robust reconstruction under arbitrary central projections, including wide-angle and fisheye lenses. Evaluated on standard normal integration benchmarks, our approach achieves state-of-the-art performance, particularly excelling in regions with large-scale depth discontinuities. It significantly improves both accuracy and robustness of 3D shape reconstruction under challenging imaging conditions.

Technology Category

• Computer Vision: 3D Computer Vision
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Recovering a 3D surface from its surface normal map, a problem known as normal integration, is a key component for photometric shape reconstruction techniques such as shape-from-shading and photometric stereo. The vast majority of existing approaches for normal integration handle only implicitly the presence of depth discontinuities and are limited to orthographic or ideal pinhole cameras. In this paper, we propose a novel formulation that allows modeling discontinuities explicitly and handling generic central cameras. Our key idea is based on a local planarity assumption, that we model through constraints between surface normals and ray directions. Compared to existing methods, our approach more accurately approximates the relation between depth and surface normals, achieves state-of-the-art results on the standard normal integration benchmark, and is the first to directly handle generic central camera models.

Problem

• Recovering 3D surfaces from normal maps with discontinuities
• Handling generic central camera models in normal integration
• Improving accuracy of depth-normal relation via local planarity

Innovation

• Explicitly models depth discontinuities
• Handles generic central camera models
• Uses local planarity assumption constraints