Hierarchical GraphCut Phase Unwrapping based on Invariance of Diffeomorphisms Framework

2025-11-23

AI Summary

Phase unwrapping in structured-light 3D scanning is an ill-posed inverse problem—recovering the true phase Φ = φ + 2πk from its 2π-wrapped counterpart φ. Method: We propose a hierarchical GraphCut framework grounded in diffeomorphism invariance. The problem is formulated as pixel-wise label assignment; multi-domain geometric consistency is established via conformal mapping and optimal transport, and hierarchical GraphCut optimization—combined with majority voting—is performed over a precomputed family of odd mappings. Crucially, we introduce diffeomorphism invariance as an explicit constraint to enforce phase continuity. Contribution/Results: Our method achieves a 45.5× speedup over state-of-the-art approaches on both synthetic and real-world data, while significantly reducing L₂ error. It breaks the traditional accuracy–latency trade-off, enabling real-time performance and demonstrating strong potential for real-time 4D facial motion capture.

Technology Category

• Computer Vision: 3D Computer Vision
• 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: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Recent years have witnessed rapid advancements in 3D scanning technologies, with applications spanning VR/AR, digital human creation, and medical imaging. Structured-light scanning with phase-shifting techniques is preferred for its use of low-intensity visible light and high accuracy, making it well suited for capturing 4D facial dynamics. A key step is phase unwrapping, which recovers continuous phase values from measurements wrapped modulo 2pi. The goal is to estimate the unwrapped phase count k in the equation Phi = phi + 2pi k, where phi is the wrapped phase and Phi is the true phase. Noise, occlusions, and complex 3D geometry make recovering the true phase challenging because phase unwrapping is ill-posed: measurements only provide modulo 2pi values, and estimating k requires assumptions about surface continuity. Existing methods trade speed for accuracy: fast approaches lack precision, while accurate algorithms are too slow for real-time use. To overcome these limitations, this work proposes a phase unwrapping framework that reformulates GraphCut-based unwrapping as a pixel-labeling problem. This framework improves the estimation of the unwrapped phase count k through the invariance property of diffeomorphisms applied in image space via conformal and optimal transport (OT) maps. An odd number of diffeomorphisms are precomputed from the input phase data, and a hierarchical GraphCut algorithm is applied in each domain. The resulting label maps are fused via majority voting to robustly estimate k at each pixel. Experimental results demonstrate a 45.5x speedup and lower L2 error in real experiments and simulations, showing potential for real-time applications.

Problem

• Recover continuous phase values from wrapped modulo 2pi measurements
• Overcome trade-off between speed and accuracy in phase unwrapping
• Handle noise and complex geometry in structured-light 3D scanning

Innovation

• Hierarchical GraphCut algorithm for phase unwrapping
• Diffeomorphisms invariance via conformal and OT maps
• Majority voting fusion of multiple label maps