Optimizing Gaussian curvature on images is an important task for image processing. But there is no efficient end-to-end optimization method. Therefore, in this paper, we propose a novel unsupervised network for Gaussian curvature optimization on images, which we named GC-Net. First, we introduce a novel computation scheme for Gaussian curvature on images. The scheme can be presented by several convolutions. Second, we design a cascaded convolution network that is composed by multiple residual convolution blocks. To train this network, we use a loss function which contains image similarity part and Gaussian curvature regularization part. Finally, the proposed network is trained and validated on 20k patches from natural images, showing its effectiveness and efficiency. The GC-Net shows the state of the art performance in minimizing Gaussian curvature. In addition, we conduct rationality experiments to verify the GC-Net architecture design. Moreover, GC-Net is adopted in two well-known image processing tasks, Gaussian curvature optimization and edge-preserving smoothing. Several numerical experiments confirm its efficiency. The proposed GC-Net can be applied in a large range of applications where Gaussian curvature is involved.

优化图像的高斯曲率是图像处理的一项重要任务。但是没有有效的端到端优化方法。因此，在本文中，我们提出了一种用于图像高斯曲率优化的新型无监督网络，我们将其命名为 GC-Net。首先，我们介绍了一种新的图像高斯曲率计算方案。该方案可以通过几个卷积来呈现。其次，我们设计了一个由多个残差卷积块组成的级联卷积网络。为了训练这个网络，我们使用包含图像相似性部分和高斯曲率正则化部分的损失函数。最后，所提出的网络在来自自然图像的 20k 块上进行了训练和验证，显示了其有效性和效率。GC-Net 在最小化高斯曲率方面展示了最先进的性能。此外，我们进行了合理性实验来验证 GC-Net 架构设计。此外，GC-Net 被用于两个著名的图像处理任务，高斯曲率优化和边缘保持平滑。几个数值实验证实了它的效率。所提出的 GC-Net 可以应用于涉及高斯曲率的大量应用中。