Towards Fast and Scalable Normal Integration using Continuous Components

2025-10-13

AI Summary

To address the low global optimization efficiency and poor real-time performance in large-scale surface reconstruction from normal maps, this paper proposes a novel normal integration paradigm based on continuous geometric components: it reformulates conventional pixel-wise optimization as relative scale estimation among connected geometric components, drastically reducing the number of optimization variables. The method comprises (1) a geometry-connectivity-driven heuristic for component segmentation; (2) an optimization term rebalancing strategy to enhance convergence stability; and (3) an iterative component merging mechanism enabling multi-scale optimization. Evaluated on standard benchmarks, our approach achieves state-of-the-art accuracy within seconds—over 10× faster than pixel-wise methods for high-resolution normal maps—while maintaining high reconstruction quality, scalability, and computational efficiency.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Security and Privacy: Large-scale security measurements

Abstract

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.

Problem

• Reconstructing surfaces from normal maps efficiently
• Reducing computational complexity in normal integration
• Enabling scalable processing for large-resolution normal maps

Innovation

• Recasts normal integration as estimating relative scales
• Uses continuous components to reduce optimization variables
• Employs heuristic estimation and iterative component merging