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

This paper introduces a novel framework for wide-angle correction by distilling the principles of quasi-conformal mapping into an efficient and generalizable deep neural network. Our methodology can be divided into two primary stages. In the first stage, the wide-angle distortion correction problem is treated as a quasi-conformal mapping from the distorted image to the target image. In particular, we minimize the Beltrami smoothness energy with constraints of both line structures and human body regions. The Beltrami coefficient is subsequently estimated using the Proximal Gradient Descent algorithm. This alternating optimization yields the final quasi-conformal mapping and the corresponding corrected image. In the second stage, the Quasi-conformal-mapping Distilled Wide-angle Correction Network (QDWC-Net) is proposed, which is trained on these corrected images to predict the correction flow directly from a distorted input and built upon an encoder-decoder followed by a soft-argmin regression output head and loss functions. Extensive quantitative and qualitative experiments demonstrate the superior effectiveness and efficiency of our distilled approach, which achieves state-of-the-art correction results, especially in mitigating distortion in both portrait and human body regions.