  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.
