Hessian-based weighted guided image filtering

Guided image filtering (GIF) is a popular edge-preserving smoothing technique, and the regularization parameter selection plays an important role in the performance of GIF. In this paper, we propose a new guided image filter based on Hessian matrix which consists of the second-order derivatives of an image. More specifically, a new structural measurement index is introduced by using the eigenvalues of the Hessian matrix first, which can distinguish the texture and flat regions of the image. Then the regularization parameter is adjusted based on this Hessian-based second-order structure measurement index, that is, a large regularization parameter is selected to improve the smoothness of the flat regions, while a small regularization parameter is set for the texture regions to preserve the image structure such as edges and corners. To further improve the quality of the filtered images, we also introduce a weighted averaging technique to the linear filter coefficients based on local variance. Experimental results show that the proposed Hessian-based weighted guided image filtering method outperforms the state-of-the-art approaches in image processing applications such as edge-preserving denoising, detail enhancement, dehazing, HDR compression, artifact removal, and scale representation.