Thin-plate spline (TPS) is a principal warp that allows for representing elastic, nonlinear transformation with control point motions. With the increase of control points, the warp becomes increasingly flexible but usually encounters a bottleneck caused by undesired issues, e.g., content distortion. In this paper, we explore generic applications of TPS in single-image-based warping tasks, such as rotation correction, rectangling, and portrait correction. To break this bottleneck, we propose the coupled thin-plate spline model (CoupledTPS), which iteratively couples multiple TPS with limited control points into a more flexible and powerful transformation. Concretely, we first design an iterative search to predict new control points according to the current latent condition. Then, we present the warping flow as a bridge for the coupling of different TPS transformations, effectively eliminating interpolation errors caused by multiple warps. Besides, in light of the laborious annotation cost, we develop a semi-supervised learning scheme to improve warping quality by exploiting unlabeled data. It is formulated through dual transformation between the searched control points of unlabeled data and its graphic augmentation, yielding an implicit correction consistency constraint. Finally, we collect massive unlabeled data to exhibit the benefit of our semi-supervised scheme in rotation correction. Extensive experiments demonstrate the superiority and universality of CoupledTPS over the existing state-of-the-art (SoTA) solutions for rotation correction and beyond. The code and data will be available at https://github.com/nie-lang/CoupledTPS.

翻译：薄板样条（TPS）是一种主翘曲变换，能够通过控制点运动表达弹性、非线性变换。随着控制点数量的增加，翘曲变换的灵活性逐步提升，但通常因内容失真等非预期问题而遭遇性能瓶颈。本文探索了TPS在基于单幅图像的翘曲任务（如旋转校正、矩形化、人像校正）中的通用应用。为突破该瓶颈，我们提出耦合薄板样条模型（CoupledTPS），通过迭代方式将有限控制点的多个TPS变换耦合为更灵活、更强大的变换。具体而言，我们首先设计一种迭代搜索方法，根据当前潜在状态预测新控制点；随后引入翘曲流作为不同TPS变换耦合的桥梁，有效消除多次翘曲导致的插值误差。此外，针对标注成本高昂的问题，我们开发了一种半监督学习方案，通过利用无标注数据提升翘曲质量。该方案通过无标注数据搜索得到的控制点与其图形增强之间的对偶变换进行建模，形成隐式校正一致性约束。最后，我们收集大规模无标注数据以展示半监督方案在旋转校正中的优势。大量实验证明，CoupledTPS在旋转校正及其他任务上相较于现有最优方法（SoTA）具有优越性与普适性。代码与数据将开源至https://github.com/nie-lang/CoupledTPS。