Blind image deblurring with Gaussian curvature of the image surface

Abstract This paper presents a blind image deblurring algorithm by utilizing Gaussian curvature (GC) of the image surface. GC is an intrinsic geometric feature and related to the developability of the surface. In recent years, numerous variational models based on GC for image denoising and image reconstruction have been proposed. In this paper, we show that GC regularization is also effective for blind image deblurring when combines it with L 0 -norm of image gradients. By minimizing the combined regularization, our algorithm gradually preserves sharp edges and removes detrimental structures and noises in intermediate latent images. The sharp latent images can then accurately guide the estimation of the blur kernel. However, a complicated optimization problem will occur once the proposed regularization has been involved. As we know, traditional diffusion methods for minimizing the GC regularization not only converges slowly but also requires the differentiability of signals. Moreover, the L 0 -norm of image gradients is non-convex. Consequently, Gaussian curvature filter (GCF) and the half-quadratic splitting strategy are adopted to solve the optimization problem. Extensive experimental results show that the proposed deblurring method achieves state-of-the-art results on benchmark datasets and performs favorably on real-world blurry images.