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.

翻译：几何畸变导致的图像退化对成像与计算机视觉任务（如目标识别）构成重大挑战。基于深度学习的成像模型通常无法对几何畸变图像提供准确性能。本文提出形变不变神经网络（DINN），这是一个解决几何畸变图像成像任务问题的框架。DINN能够为存在几何畸变但表示相同底层物体或场景的图像输出一致的潜在特征。其核心思想是将一个名为拟共形变换网络（QCTN）的简单组件集成到其他现有深度学习网络中用于成像任务。QCTN是一种深度神经网络，它输出一个拟共形映射，可用于将几何畸变图像转换为更接近自然或良好图像分布状态的改进版本。该网络首先输出Beltrami系数，用于衡量输出形变映射的拟共形程度。通过控制Beltrami系数，可以调控拟共形映射下的局部几何畸变。QCTN轻量且结构简单，可便捷地集成到其他现有深度神经网络中以提升其性能。基于该框架，我们开发了一种能够准确分类畸变图像的图像分类网络。所提框架已应用于大气湍流和水体湍流导致的几何畸变图像恢复。在这些场景下，DINN的性能优于现有的基于GAN的恢复方法，验证了所提框架的有效性。此外，我们将所提框架应用于大气湍流条件下的人脸图像1-1验证任务，并取得了满意的性能，进一步证明了本方法的有效性。