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Computing Gaussian curvature is a fundamental task in image and video processing. However, this task becomes more and more time consuming when the image resolution goes higher and higher. In this paper, we tackle this issue from two aspects. First, we develop a novel discrete computing scheme for Gaussian curvature of discrete images. Our method does not require the image to be smooth. Second, we propose to perform the actual calculation by lookup tables, which significantly reduce the computation time. As a result, our method can compute the Gaussian curvature for 4K videos in real time, without requiring the image to be smooth. Moreover, our method can be implemented on mobile devices. Several experiments confirm the efficiency and effectiveness of our method. Our method can be applied on a large range of image and video processing applications that involve Gaussian curvature.

Computing Gaussian Curvature in Real-Time for 4K Video Processing