Gaussian error loss function for image smoothing

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Edge-preserving image smoothing plays an important role in the fields of image processing and computational photography, and is widely used for a variety of applications. The edge-preserving filters based on global optimization models have attracted widespread attention due to their nice smoothing quality. According to existing research, the edge-preserving capability is strongly correlated to the penalty function used for gradient regularization. By analyzing the edge-stopping function of existing penalties, we demonstrate that existing image smoothing models are not adequately edge-preserving. In this paper, based on a Gaussian error function (ERF), we propose a Gaussian error loss function (ERLF), which shows stronger edge-preserving capability. We embed the proposed loss function into a global optimization model for edge-preserving image smoothing. In addition, we propose an efficient solution based on additive half-quadratic minimization and Fourier-domain optimization that is capable of processing 720P color images (over 20 fps) in real-time on an NVIDIA RTX 3070 GPU. We have experimented with the proposed filter on a number of low-level vision tasks. Both quantitative and qualitative experimental results show that the proposed filter outperforms existing filters. Therefore, it can be practical for real applications.