Fast Global Image Smoothing via Quasi Weighted Least Squares

Image smoothing is a long-studied research area with tremendous approaches proposed. However, how to perform high-quality image smoothing with less computational cost still remains a challenging problem. In this paper, we try to solve this problem with a newly proposed global optimization based method named quasi weighted least squares. In our method, the 2D image is first re-ordered into a 1D vector via a newly proposed 2D-to-1D transformation. We then properly remove some original 2D neighborhood connections. The remaining neighboring pixels can simply form 1D neighborhood connections in the transformed 1D vector while they still contain the 2D neighborhood information in the original 2D image space. These together result in a quite compact linear system that can be easily and efficiently solved, which makes our method a fast global image smoothing approach. Our method is on par with the fastest approaches in terms of processing speed, however, it is able to yield comparable performance with the state-of-the-art ones in terms of smoothing quality. Our method can also work as a solver to approximate the weighted least squares problem in complex systems, and it can achieve similar results but runs much faster. The efficiency and effectiveness of our method are validated through comprehensive experiments in several tasks. Our code is publicly available at: https://github.com/wliusjtu/Q-WLS.