Circular Image Deturbulence using Quasi-conformal Geometry

2025-04-18

AI Summary

Optical imaging through non-uniform media—such as atmospheric turbulence—induces severe geometric distortions, yet supervised learning methods are hindered by the scarcity of high-fidelity paired ground-truth data. To address this, we propose CQCD, an unsupervised cyclic image de-turbulence framework that achieves geometric fidelity and visual consistency via a forward–inverse mapping loop. Our key contributions are: (1) a novel cyclic reconstruction architecture ensuring mapping consistency; (2) a quasiconformal geometric constraint enforcing strict bijectivity and homeomorphism of the deformation field; and (3) a compact-frame feature encoding module that enhances modeling capability for distortion-sensitive regions. Extensive experiments on both synthetic and real-world datasets demonstrate that CQCD significantly outperforms state-of-the-art methods, achieving superior restoration quality, higher deformation field estimation accuracy, effective artifact suppression, and robust structural preservation.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Machine Learning: Unsupervised & Self-Supervised Learning
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

The presence of inhomogeneous media between optical sensors and objects leads to distorted imaging outputs, significantly complicating downstream image-processing tasks. A key challenge in image restoration is the lack of high-quality, paired-label images required for training supervised models. In this paper, we introduce the Circular Quasi-Conformal Deturbulence (CQCD) framework, an unsupervised approach for removing image distortions through a circular architecture. This design ensures that the restored image remains both geometrically accurate and visually faithful while preventing the accumulation of incorrect estimations.The circular restoration process involves both forward and inverse mapping. To ensure the bijectivity of the estimated non-rigid deformations, computational quasi-conformal geometry theories are leveraged to regularize the mapping, enforcing its homeomorphic properties. This guarantees a well-defined transformation that preserves structural integrity and prevents unwanted artifacts. Furthermore, tight-frame blocks are integrated to encode distortion-sensitive features for precise recovery. To validate the performance of our approach, we conduct evaluations on various synthetic and real-world captured images. Experimental results demonstrate that CQCD not only outperforms existing state-of-the-art deturbulence methods in terms of image restoration quality but also provides highly accurate deformation field estimations.

Problem

• Removing image distortions caused by inhomogeneous media
• Unsupervised restoration without paired-label training data
• Ensuring geometric accuracy and visual fidelity in output

Innovation

• Unsupervised circular architecture for image deturbulence
• Quasi-conformal geometry regularizes deformation mappings
• Tight-frame blocks encode distortion-sensitive features