Interpreting and Extending The Guided Filter Via Cyclic Coordinate Descent

TL;DR

This paper reveals that the Guided Filter can be viewed as a Cyclic Coordinate Descent solver for a least squares problem, enabling the development of new filters and extensions with state-of-the-art performance.

Contribution

It introduces a novel interpretation of the Guided Filter as a CCD solver, allowing for the creation of new filters and extensions based on modified objective functions.

Findings

New filters outperform existing methods.

Extensions achieve state-of-the-art results.

Provides theoretical explanations for existing GF schemes.

Abstract

In this paper, we will disclose that the Guided Filter (GF) can be interpreted as the Cyclic Coordinate Descent (CCD) solver of a Least Square (LS) objective function. This discovery implies a possible way to extend GF because we can alter the objective function of GF and define new filters as the first pass iteration of the CCD solver of modified objective functions. Moreover, referring to the iterative minimizing procedure of CCD, we can derive new rolling filtering schemes. Hence, under the guidance of this discovery, we not only propose new GF-like filters adapting to the specific requirements of applications but also offer thoroughly explanations for two rolling filtering schemes of GF as well as the way to extend them. Experiments show that our new filters and extensions produce state-of-the-art results.