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Local Laplacian Filters: Edge-aware Image Processing with a Laplacian Pyramid


Local Laplacian Filters, illustration

The Laplacian pyramid is ubiquitous for decomposing images into multiple scales and is widely used for image analysis. However, because it is constructed with spatially invariant Gaussian kernels, the Laplacian pyramid is widely believed to be ill-suited for representing edges, as well as for edge-aware operations such as edge-preserving smoothing and tone mapping. To tackle these tasks, a wealth of alternative techniques and representations have been proposed, for example, anisotropic diffusion, neighborhood filtering, and specialized wavelet bases. While these methods have demonstrated successful results, they come at the price of additional complexity, often accompanied by higher computational cost or the need to postprocess the generated results. In this paper, we show state-of-the-art edge-aware processing using standard Laplacian pyramids. We characterize edges with a simple threshold on pixel values that allow us to differentiate large-scale edges from small-scale details. Building upon this result, we propose a set of image filters to achieve edge-preserving smoothing, detail enhancement, tone mapping, and inverse tone mapping. The advantage of our approach is its simplicity and flexibility, relying only on simple point-wise nonlinearities and small Gaussian convolutions; no optimization or postprocessing is required. As we demonstrate, our method produces consistently high-quality results, without degrading edges or introducing halos.

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1. Introduction

Laplacian pyramids have been used to analyze images at multiple scales for a broad range of applications such as compression,6 texture synthesis,18 and harmonization.32 However, these pyramids are commonly regarded as a poor choice for applications in which image edges play an important role, for example, edge-preserving smoothing or tone mapping. The isotropic, spatially invariant, smooth Gaussian kernels on which the pyramids are built are considered almost antithetical to edge discontinuities, which are precisely located and anisotropic by nature. Further, the decimation of the levels, that is, the successive reduction by factor 2 of the resolution, is often criticized for introducing aliasing artifacts, leading some researchers (e.g., Li et al.21) to recommend its omission. These arguments are often cited as a motivation for more sophisticated schemes such as anisotropic diffusion,1, 29 neighborhood filters,19, 34 edge-preserving optimization,4, 11 and edge-aware wavelets.12


 

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