# Semi-Supervised Coupled Thin-Plate Spline Model for Rotation Correction and Beyond

arXiv: https://arxiv.org/abs/2401.13432 · HTML: https://mlsanity.com/paper/2401.13432/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 51 references that are in the map.
- First posted on arXiv 24 Jan 2024.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [Thin-Plate Spline Motion Model for Image Animation](https://mlsanity.com/paper/2203.14367/) (2022)
- [Unsupervised Deep Image Stitching: Reconstructing Stitched Features to Images](https://mlsanity.com/paper/2106.12859/) (2021)
- [Surface Normal Estimation of Tilted Images via Spatial Rectifier](https://mlsanity.com/paper/2007.09264/) (2020)
- [Parallax-Tolerant Unsupervised Deep Image Stitching](https://mlsanity.com/paper/2302.08207/) (2023)
- [UprightNet: Geometry-Aware Camera Orientation Estimation from Single Images](https://mlsanity.com/paper/1908.07070/) (2019)
- [Revisiting Document Image Dewarping by Grid Regularization](https://mlsanity.com/paper/2203.16850/) (2022)
- [Fourier Document Restoration for Robust Document Dewarping and Recognition](https://mlsanity.com/paper/2203.09910/) (2022)
- [Deep Rectangling for Image Stitching: A Learning Baseline](https://mlsanity.com/paper/2203.03831/) (2022)
- [Practical Wide-Angle Portraits Correction with Deep Structured Models](https://mlsanity.com/paper/2104.12464/) (2021)
- [Semi-Supervised Wide-Angle Portraits Correction by Multi-Scale Transformer](https://mlsanity.com/paper/2109.08024/) (2021)
- [Deep Rotation Correction without Angle Prior](https://mlsanity.com/paper/2207.03054/) (2022)
- [RecRecNet: Rectangling Rectified Wide-Angle Images by Thin-Plate Spline Model and DoF-based Curriculum Learning](https://mlsanity.com/paper/2301.01661/) (2023)
- [Correcting Face Distortion in Wide-Angle Videos](https://mlsanity.com/paper/2111.09950/) (2021)

## Built on by (most cited first, 5 of 5)

- [Learning Efficient Meshflow and Optical Flow from Event Cameras](https://mlsanity.com/paper/2510.04111/) (2025)
- [StabStitch++: Unsupervised Online Video Stitching with Spatiotemporal Bidirectional Warps](https://mlsanity.com/paper/2505.05001/) (2025)
- [Beyond Wide-Angle Images: Structure-to-Detail Video Portrait Correction via Unsupervised Spatiotemporal Adaptation](https://mlsanity.com/paper/2504.00401/) (2025)
- [StableMotion: One-Step Motion Estimation with Diffusion Prior](https://mlsanity.com/paper/2505.06668/) (2025)
- [Rectification Reimagined: A Unified Mamba Model for Image Correction and Rectangling with Prompts](https://mlsanity.com/paper/2512.18718/) (2025)

## Abstract (arXiv)

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 are available at https://github.com/nie-lang/CoupledTPS.