Fast and faithful scale-aware image filters

This paper proposes a fast and accurate computational framework for scale-aware image filters. Our framework is based on accurately approximating $$L^{1}$$ Gaussian convolution with respect to a transformed pixel domain representing geodesic distance on a guidance image manifold in order to recover salient edges in a manner faithful to scale-space theory while removing small image structures. Our framework possesses linear computational complexity with high approximation precision. We examined it numerically in terms of speed, accuracy, and quality compared with conventional methods.