利用纸张弹性几何知识，修复开本扫描导致的扭曲图像。
Image Reconstruction from an Elastically Distorted Scan
- 基于纸张弯曲的物理模型构建逆问题求解方法。
- 仅需3个可测量参数即可显著提升重建质量。
- 适合图像修复与逆问题研究者参考学习。
本文研究开本扫描（如复印）产生的图像失真问题，这类失真源于书脊刚性导致纸张不均匀弯曲，进而引发非均匀扭曲、模糊和变暗。不同于纯数据驱动方法，我们结合纸张的几何与弹性知识，提出并求解一个最小物理一致性的逆问题以实现图像重建。该方法仅依赖三个可测量的无量纲参数，均来自扫描设备本身，实验表明其性能优于现有数据驱动方法。更广泛地，本工作可作为生成机制知识加速逆问题求解的示范案例，具备教学价值。
原文摘要 · Abstract (English)
We consider the problem of inverting the artifacts associated with scanning a page from an open book, i.e. "xeroxing." The process typically leads to a non-uniform combination of distortion, blurring and darkening owing to the fact that the page is bound to a stiff spine that causes the sheet of paper to be bent inhomogeneously. Complementing purely data-driven approaches, we use knowledge about the geometry and elasticity of the curved sheet to pose and solve a minimal physically consistent inverse problem to reconstruct the image. Our results rely on 3 dimensionless parameters, all of which can be measured for a scanner, and show that we can improve on the data-driven approaches. More broadly, our results might serve as a "textbook" example and a tutorial of how knowledge of generative mechanisms can speed up the solution of inverse problems.
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