Interpreting and Extending the Guided Filter via Cyclic Coordinate Descent

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
Longquan DaiJinhui Tang

Abstract

The guided filter (GF) is a widely used smoothing tool in computer vision and image processing. However, to the best of our knowledge, few papers investigate the mathematical connection between this filter and the least-squares optimization. In this paper, we first interpret the guided filter as the cyclic coordinate descent (CCD) solver of a least-squares objective function. This discovery implies an extension approach to generalize the guided filter since we can change the least-squares objective function and define new filters as the first pass iteration of the CCD solver of modified objective functions. In addition, referring to the iterative minimizing procedure of the CCD, we can derive new rolling filtering schemes. So, we are reasonable to say that our discovery not only reveals an approach to design new GF-like filters adapting to specific requirements of applications but also offers thorough explanations for two rolling filtering schemes of the guided filter as well as the method to extend them. Experiments prove our new proposed filters and rolling filtering schemes could produce state-of-the-art results.

References

Sep 21, 2004·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Zhou WangEero P Simoncelli
Feb 6, 2008·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Michael Elad
Aug 1, 2012·IEEE Transactions on Pattern Analysis and Machine Intelligence·Asmaa HosniMargrit Gelautz
Aug 28, 2012·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Tianshuang QiuAimin Song
Apr 20, 2013·IEEE Transactions on Pattern Analysis and Machine Intelligence·Kaiming HeXiaoou Tang
Nov 22, 2014·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Zhengguo LiShiqian Wu
Jan 15, 2015·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Laurent CaraffaPierre Charbonnier
Apr 6, 2016·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Longquan DaiXiaopeng Zhang

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