Gaussian highpass guided image filtering

TL;DR

This paper tackles the limitations of two-parameter local affine models in guided image filtering by introducing a single-parameter Prior Model based on Gaussian highpass/lowpass filtering (PM-GF). The core idea is to express the filter output as a weighted Gaussian highpass component of the guidance image plus a Gaussian-smoothed version of the input, enabling explicit interpretation of the structure transfer via the highpass term. Building on PM-GF, the authors define Gaussian highpass guided image filters (GH-GIFs) and provide formulas for optimal weights through ridge-regularized minimization, yielding a family of improved GIFs with reduced halo artifacts. Extensive experiments across edge-aware smoothing, denoising, detail enhancement, HDR tone mapping, haze removal, and texture smoothing demonstrate that PM-GF–based GIFs consistently outperform their LAM-based counterparts while maintaining linear-time complexity, highlighting practical impact for a wide range of image-processing tasks. The work also suggests potential integration with deep learning for adaptive weight estimation, pointing to future directions in learning-guided PM-GF frameworks.

Abstract

Guided image filtering (GIF) is a popular smoothing technique, in which an additional image is used as a structure guidance for noise removal with edge preservation. The original GIF and some of its subsequent improvements are derived from a two-parameter local affine model (LAM), where the filtering output is a local affine transformation of the guidance image, but the input image is not taken into account in the LAM formulation. In this paper, we first introduce a single-parameter Prior Model based on Gaussian (highpass/lowpass) Filtering (PM-GF), in which the filtering output is the sum of a weighted portion of Gaussian highpass filtering of the guidance image and Gaussian smoothing of the input image. In the PM-GF, the guidance structure determined by Gaussian highpass filtering is obviously transferred to the filtering output, thereby better revealing the structure transfer mechanism of guided filtering. Then we propose several Gaussian highpass GIFs (GH-GIFs) based on the PM-GF by emulating the original GIF and some improvements, i.e., using PM-GF instead of LAM in these GIFs. Experimental results illustrate that the proposed GIFs outperform their counterparts in several image processing applications.

Figures (13)

• Figure 1: (a) $G$ & $I$. (b) $\bar{G}$ and $\bar{I}$. (c) $G- \bar{G}$.
• Figure 2: Comparion of $b_{p'}$ in \ref{['eq.2.1']} and $\beta_{p'}$ in \ref{['eq.3.5-1']} in the self-guided case. (a) $G$ & $I$. (b) $a_{p'}$. (c) $b_{p'}$. (d) $\beta_{p'}$
• Figure 3: The $100th$ horizontal intensity profile of Fig. \ref{['fig:3.3']}(a) and filtered output \ref{['eq.3.4']} (GIF) and \ref{['eq.3.5']} (PM-GF) with $\alpha_p’=a_p’$, given in \ref{['eq.2.3']}.
• Figure 4: Test images. (a) $263 \times 263$. (b) $512 \times 512$. (c) $512 \times 512$. (d) $512 \times 512$.
• Figure 5: Comparison of smoothing results by different filters. (a)-(e) GIF, WGIF, GGIF, SKWGIF, RDWGIF. (f)-(j) GH-GIF, GH-WGIF, GH-GGIF, GH-SKWGIF, GH-RDWGIF.