Distilling Quasi-Conformal Mapping: A Generalizable and Efficient Solution for Wide-Angle Correction

摘要

This paper introduces a novel framework for wide-angle correction by distilling the geometric principles of quasi-conformal (QC) mapping into a generalizable and efficient deep neural network. Our methodology can be divided into two primary stages. In the first stage, we develop an annotation-free teacher pipeline that treats the distortion correction problem as a QC mapping task. Specifically, we minimize the Beltrami smoothness energy under constraints of both line structures and human body regions using a Linear Beltrami Solver and Proximal Gradient Descent (LBS-PGD) algorithm, thereby automatically generating high-quality QC correction flow labels. In the second stage, we propose the Quasi-conformal-mapping Distilled Wide-angle Correction Network (QDWC-Net) to learn the geometric transformation from these labels via distillation. Utilizing a Mamba-based backbone, a soft-argmin head, and a low-rank prior reconstruction module, QDWC-Net predicts the correction flow directly from a distorted input. Extensive quantitative and qualitative experiments verify the effectiveness of our approach. Notably, our distilled student network exhibits enhanced robustness compared to the teacher and achieves a massive 32x speedup (from 26.33s to 0.81s). Overall, our method provides a state-of-the-art solution that excels across multiple real-world datasets, especially in mitigating human body distortion.