[Paper Review] Quarter Laplacian Filter for Edge Aware Image Processing

Yuanhao Gong, Wenming Tang+3 more|arXiv (Cornell University)|Jan 20, 2021

Image Enhancement Techniques23 references4 citations

TL;DR

This paper proposes a novel quarter Laplacian filter that preserves edges and corners by using a 2×2 support region, enabling highly local and efficient image smoothing via box filter implementation. It achieves superior edge preservation over classical Laplacian filters in tasks like image smoothing, texture enhancement, and low-light enhancement, with minimal artifacts and high performance for real-time applications.

ABSTRACT

This paper presents a quarter Laplacian filter that can preserve corners and edges during image smoothing. Its support region is $2 imes2$, which is smaller than the $3 imes3$ support region of Laplacian filter. Thus, it is more local. Moreover, this filter can be implemented via the classical box filter, leading to high performance for real time applications. Finally, we show its edge preserving property in several image processing tasks, including image smoothing, texture enhancement, and low-light image enhancement. The proposed filter can be adopted in a wide range of image processing applications.

Motivation & Objective

• To develop a more local and efficient alternative to the classical 3×3 Laplacian filter for edge-preserving image smoothing.
• To address the limitations of deep learning-based filters, such as high memory usage and lack of interpretability, by proposing a lightweight, analytically grounded filter.
• To enable high-performance, real-time image processing by leveraging the computational efficiency of the box filter in a novel anisotropic diffusion framework.
• To improve edge and corner preservation in image smoothing, texture enhancement, and low-light enhancement tasks.

Proposed method

• The method uses four 2×2 quarter windows around each pixel to compute a localized Laplacian operator, replacing the standard 3×3 isotropic kernel.
• The quarter Laplacian filter is formulated as a weighted sum of pixel values within each 2×2 window, derived from the discrete Laplacian operator with a specific kernel.
• The filter is implemented using a cascade of box filters, enabling constant-time computation regardless of filter size, which ensures high performance for real-time applications.
• Edge preservation is achieved by restricting the diffusion process to directional, anisotropic neighborhoods that respect discontinuities in intensity gradients.
• The filter is applied iteratively in a diffusion framework: U^{t+1} = U^t + QuarterLaplacianFilter(U^t), with 10 iterations used as default.
• The method is applied independently per color channel in color images and extended to multi-scale processing in low-light enhancement.

Experimental results

Research questions

• RQ1 Can a 2×2 support region Laplacian filter preserve edges and corners more effectively than the standard 3×3 Laplacian filter?
• RQ2 Can a quarter Laplacian filter be efficiently implemented using only box filters to enable real-time performance?
• RQ3 Does the proposed filter outperform existing edge-preserving methods in image smoothing, texture enhancement, and low-light enhancement tasks?
• RQ4 How does the use of quarter windows instead of half or full windows affect the preservation of image structures and reduction of artifacts?

Key findings

• The quarter Laplacian filter successfully preserves corners and edges during image smoothing, as demonstrated in both qualitative and quantitative comparisons.
• The filter’s 2×2 support region provides higher locality than the standard 3×3 Laplacian, resulting in more precise handling of fine image structures.
• The implementation via box filters enables constant-time computation, making the method highly efficient and suitable for real-time applications.
• In image smoothing tasks, the proposed method produces fewer artifacts compared to Domain Transform, Guided Filter, and Relative Total Variation, especially in regions with sharp transitions.
• In texture enhancement, the method amplifies details with minimal distortion, outperforming state-of-the-art methods in preserving structural integrity.
• In low-light image enhancement, the filter effectively recovers illumination details across scales, producing natural-looking results without introducing halo or noise artifacts.