Gaussian Fourier Pyramid for Local Laplacian Filter

Multi-scale processing is essential in image processing and computer graphics. Halos are a central issue in multi-scale processing. Several edge-preserving decompositions resolve halos, e.g., local Laplacian filtering (LLF), by extending the Laplacian pyramid to have an edge-preserving property. Its processing is costly; thus, an approximated acceleration of fast LLF was proposed to linearly interpolate multiple Laplacian pyramids. This paper further improves the accuracy by Fourier series expansion, named Fourier LLF. Our results showed that Fourier LLF has a higher accuracy for the same number of pyramids. Moreover, Fourier LLF exhibits parameter-adaptive property for content-adaptive filtering.