蒸馏拟共形映射：一种可泛化且高效的广角校正方案
Distilling Quasi-Conformal Mapping: A Generalizable and Efficient Solution for Wide-Angle Correction
把拟共形映射的几何先验（Beltrami 能量 + 线结构/人体区域约束）做成无需标注的教师流程来生成校正光流标签，再用 Mamba 骨干 + soft-argmin 头蒸馏成单次前向的校正网络，可直接迁移到鱼眼/广角镜头畸变校正与光流式几何变换学习。
原文依据 we minimize the Beltrami smoothness energy under constraints of both line structures and human body regions
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论本文提出了一种新的广角校正框架，将拟共形（QC）映射的几何原理蒸馏进一个可泛化且高效的深度神经网络。我们的方法可分为两个主要阶段。在第一阶段，我们构建了一条无需标注的教师流程，把畸变校正问题视为一项拟共形映射任务。具体而言，我们使用线性 Beltrami 求解器与近端梯度下降（LBS-PGD）算法，在线结构与人体区域的双重约束下最小化 Beltrami 平滑能量，从而自动生成高质量的拟共形校正光流标签。在第二阶段，我们提出拟共形映射蒸馏广角校正网络（QDWC-Net），通过蒸馏从这些标签中学习几何变换。QDWC-Net 采用基于 Mamba 的骨干、soft-argmin 头以及低秩先验重建模块，直接从畸变输入预测校正光流。大量定量与定性实验验证了本方法的有效性。值得注意的是，我们蒸馏得到的学生网络相比教师表现出更强的鲁棒性，并实现了高达 32 倍的加速（从 26.33 秒降至 0.81 秒）。总体而言，我们的方法提供了一种最优的解决方案，在多个真实世界数据集上均表现优异，尤其是在缓解人体畸变方面。
英文原文摘要 1412 字符
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.