Real-Time Optimizing Weighted Gaussian Curvature for 4K Videos

Weighted Gaussian curvature is an important measurement for surfaces, images and videos. However, since it is a second order quantity, its optimization usually leads to high order geometric flows that cause difficulties for practical applications. In this paper, we propose a novel optimization method for weighted Gaussian curvature. Our method does not require the image (video) to be second-order differentiable, thus, avoiding the high order geometric flows. In addition, we propose a new 4-D look-up table method to accelerate the optimization of weighted Gaussian curvature. Therefore, our algorithm is very efficient and can achieve real-time processing for high resolution videos. For example, our method can process 4K videos with 50 frames per second on a single graphic card (NVIDIA 3090). Several numerical experiments are carried out to confirm the efficiency and effectiveness of the proposed method. Thanks to the high performance, our method can be applied in a large range of applications that involve weighted Gaussian curvature, such as image restoration, registration, enhancement, etc.