# Deformation-Invariant Neural Network and Its Applications in Distorted Image Restoration and Analysis

arXiv: https://arxiv.org/abs/2310.02641 · HTML: https://mlsanity.com/paper/2310.02641/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 39 references that are in the map.
- First posted on arXiv 4 Oct 2023.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Deformable ConvNets v2: More Deformable, Better Results](https://mlsanity.com/paper/1811.11168/) (2018)
- [Understanding the Effective Receptive Field in Deep Convolutional Neural Networks](https://mlsanity.com/paper/1701.04128/) (2017)
- [Deep Layer Aggregation](https://mlsanity.com/paper/1707.06484/) (2017)
- [DeblurGAN: Blind Motion Deblurring Using Conditional Adversarial Networks](https://mlsanity.com/paper/1711.07064/) (2017)
- [DeblurGAN-v2: Deblurring (Orders-of-Magnitude) Faster and Better](https://mlsanity.com/paper/1908.03826/) (2019)
- [Single Frame Atmospheric Turbulence Mitigation: A Benchmark Study and A New Physics-Inspired Transformer Model](https://mlsanity.com/paper/2207.10040/) (2022)
- [Active Convolution: Learning the Shape of Convolution for Image Classification](https://mlsanity.com/paper/1703.09076/) (2017)
- [Physics-Driven Turbulence Image Restoration with Stochastic Refinement](https://mlsanity.com/paper/2307.10603/) (2023)
- [Atmospheric Turbulence Removal with Complex-Valued Convolutional Neural Network](https://mlsanity.com/paper/2204.06989/) (2022)
- [Restoration of Atmospheric Turbulence-distorted Images via RPCA and Quasiconformal Maps](https://mlsanity.com/paper/1704.03140/) (2017)
- [ATFaceGAN: Single Face Image Restoration and Recognition from Atmospheric Turbulence](https://mlsanity.com/paper/1910.03119/) (2019)
- [Landmark and Intensity Based Registration with Large Deformations via Quasi-conformal Maps](https://mlsanity.com/paper/1310.1710/) (2013)
- [Topology-Preserving 3D Image Segmentation Based On Hyperelastic Regularization](https://mlsanity.com/paper/2103.16768/) (2021)
- [Fast Disk Conformal Parameterization of Simply-connected Open Surfaces](https://mlsanity.com/paper/1408.6974/) (2014)
- [Spherical Conformal Parameterization of Genus-0 Point Clouds for Meshing](https://mlsanity.com/paper/1508.07569/) (2015)
- [Free-boundary conformal parameterization of point clouds](https://mlsanity.com/paper/2010.15399/) (2020)
- [A Deep Learning Framework for Diffeomorphic Mapping Problems via Quasi-conformal Geometry applied to Imaging](https://mlsanity.com/paper/2110.10580/) (2021)

## Built on by (most cited first, 8 of 8)

- [Shape Prior Segmentation Guided by Harmonic Beltrami Signature](https://mlsanity.com/paper/2407.04360/) (2024)
- [Enhancing Image Restoration through Learning Context-Rich and Detail-Accurate Features](https://mlsanity.com/paper/2504.10558/) (2025)
- [Quasi-Conformal Convolution : A Learnable Convolution for Deep Learning on Simply Connected Open Surfaces](https://mlsanity.com/paper/2502.01356/) (2025)
- [Circular Quasiconformal Deturbulence: Geometry-Based Restoration from Multiple Turbulent Frames](https://mlsanity.com/paper/2504.13432/) (2025)
- [Coupled Reconstruction of 2D Blood Flow and Vessel Geometry from Noisy Images via Physics-Informed Neural Networks and Quasi-Conformal Mapping](https://mlsanity.com/paper/2508.11216/) (2025)
- [NAPPure: Adversarial Purification for Robust Image Classification under Non-Additive Perturbations](https://mlsanity.com/paper/2510.14025/) (2025)
- [Harmonic Beltrami Signature Network: a Shape Prior Module in Deep Learning Framework](https://mlsanity.com/paper/2603.02907/) (2026)
- [Learning Task-Aware Sampling with Shared Saliency through Density-Equalizing Mappings](https://mlsanity.com/paper/2606.12869/) (2026)

## Abstract (arXiv)

Images degraded by geometric distortions pose a significant challenge to imaging and computer vision tasks such as object recognition. Deep learning-based imaging models usually fail to give accurate performance for geometrically distorted images. In this paper, we propose the deformation-invariant neural network (DINN), a framework to address the problem of imaging tasks for geometrically distorted images. The DINN outputs consistent latent features for images that are geometrically distorted but represent the same underlying object or scene. The idea of DINN is to incorporate a simple component, called the quasiconformal transformer network (QCTN), into other existing deep networks for imaging tasks. The QCTN is a deep neural network that outputs a quasiconformal map, which can be used to transform a geometrically distorted image into an improved version that is closer to the distribution of natural or good images. It first outputs a Beltrami coefficient, which measures the quasiconformality of the output deformation map. By controlling the Beltrami coefficient, the local geometric distortion under the quasiconformal mapping can be controlled. The QCTN is lightweight and simple, which can be readily integrated into other existing deep neural networks to enhance their performance. Leveraging our framework, we have developed an image classification network that achieves accurate classification of distorted images. Our proposed framework has been applied to restore geometrically distorted images by atmospheric turbulence and water turbulence. DINN outperforms existing GAN-based restoration methods under these scenarios, demonstrating the effectiveness of the proposed framework. Additionally, we apply our proposed framework to the 1-1 verification of human face images under atmospheric turbulence and achieve satisfactory performance, further demonstrating the efficacy of our approach.