随着成像技术的发展，高分辨率图像越来越普及。在高分辨率图像处理中，高斯曲率估计和优化是多个图像处理问题的关键之一。传统的高斯曲率计算方法和优化方法要求被处理图像至少二次光滑可导。这就导致图像处理的结果在图像边缘处过度光滑，也就是视觉上的模糊。本项目拟提出一种新的高斯曲率估计方法和一种新的高斯曲率优化算法，能够完全避免这一问题。针对高斯曲率估计，我们利用了离散图像的空间离散性和灰度值离散性，以及计算机图形学中成熟的离散曲率计算方法。针对高斯曲率的优化问题，我们提出了基于深度学习的优化方法，能够避免高斯曲率优化中的光滑性要求。我们的估计和优化方法都不要求输入图像二次光滑，因此不会模糊图像的边缘，可以得到非常清晰的图像。我们的高斯曲率估计和优化方法预计能够在移动设备上实时处理高分辨率图像。我们进一步会在自然图像恢复和生物医学图像重建两个领域验证本项目成果的有效性。

With imaging technology development, high resolution images are getting more and more popular. Estimation and optimization of Gaussian curvature for such images is a fundamental task for many image processing problems. Traditional methods require the input image to be at least second order differentiable. Therefore, the resulting image is too smooth at large edges, leading to blurring effect. In this project, we plan to develope new estimation and optimization methods that do not have such limitation. For the Gaussian curvature estimation, we use the space and intensity discrete property of digital images and the computation scheme from computer graphics. For Gaussian curvature optimization, we use the deep learning method. And the resulting image can have sharp edges and is very clear. Our methods can be performed on mobile device and achieve real-time performance. We will also valid our methods on natural image restoration and biomedical image reconstruction.