Extending Guided Filters Through Effective Utilization of Multi-Channel Guide Images Based on Singular Value Decomposition

Abstract

This paper proposes the SVD-based Guided Filter, designed to address key limitations of the original guided filter and its improved methods, providing better use of multi-channel guide images. First, we analyzed the guided filter framework, reinterpreting it from a patch-based perspective using singular value decomposition (SVD). This revealed that the original guided filter suppresses oscillatory components based on their eigenvalues. Building on this insight, we proposed a new filtering method that selectively suppresses or enhances these components through functions that respond to their eigenvalues. The proposed SVD-based Guided Filter offers improved control over edge preservation and noise reduction compared to the original guided filter and its improved methods, which often struggle to balance these tasks. We validated the proposed method across various image processing applications, including denoising, edge-preserving smoothing, detail enhancement, and edge-enhancing smoothing. The results demonstrated that the SVD-based Guided Filter consistently outperforms the original guided filter and its improved methods by making more effective use of color guide images. While the computational cost is slightly higher than the original guided filter, the method remains efficient and highly effective. Overall, the proposed SVD-based Guided Filter delivers notable improvements, offering a solid foundation for further advancements in guided filtering techniques.