We assess the benefit of including an image inpainting filter before passing damaged images into a classification neural network. We employ an appropriately modified Cahn–Hilliard equation as an image inpainting filter which is solved numerically with a finite-volume scheme exhibiting reduced computational cost and the properties of energy stability and boundedness. The benchmark dataset employed is Modified National Institute of Standards and Technology (MNIST) dataset, which consists of binary images of handwritten digits and is a standard dataset to validate image-processing methodologies. We train a neural network based on dense layers with MNIST, and subsequently we contaminate the test set with damages of different types and intensities. We then compare the prediction accuracy of the neural network with and without applying the Cahn–Hilliard filter to the damaged images test. Our results quantify the significant improvement of damaged-image prediction by applying the Cahn–Hilliard filter, which for specific damages can increase up to 50% and is advantageous for low to moderate damage.

我们评估了在将损坏的图像传递到分类神经网络之前包含图像修复过滤器的好处。我们采用适当修改的 Cahn-Hilliard 方程作为图像修复滤波器，通过有限体积方案进行数值求解，显示出降低的计算成本以及能量稳定性和有界性的特性。采用的基准数据集是修改后的国家标准与技术研究所 (MNIST) 数据集，它由手写数字的二进制图像组成，是验证图像处理方法的标准数据集。我们使用 MNIST 训练基于密集层的神经网络，随后我们用不同类型和强度的损坏来污染测试集。然后，我们比较在损坏图像测试中应用和不应用 Cahn-Hilliard 滤波器的神经网络的预测精度。我们的结果量化了通过应用 Cahn-Hilliard 滤波器对损坏图像预测的显着改进，对于特定损坏可以提高高达 50%，并且对于低到中度损坏是有利的。