Curvature-Based Bilateral Filter for Image Smoothing

Abstract

This paper introduces the Quadrilateral filter, an advanced extension of the Bilateral and Trilateral filters aimed at addressing limitations in high-gradient regions of images. While the Bilateral filter effectively preserves edges during smoothing, it struggles with intensity variations, leading to blunted image details. The trilateral filter improves upon this by incorporating local plane geometry approximations but assumes linear pixel intensity distributions, limiting its effectiveness. The proposed Quadrilateral filter utilizes curvature-based geometry approximations to enhance noise reduction, contrast preservation, artifact reduction, and image reconstruction by accounting for nonlinear pixel value distributions. The development of this filter represents the main contribution of the paper while exploring whether the established Bilateral and Trilateral filters’ performance can be further improved through curvature-based local geometry approximations. The findings demonstrate improvements in image quality and detail preservation, with broad implications for applications in image de-noising, tone-mapping, multimedia processing, and beyond.