Huber Fractal Image Coding Based on a Fitting Plane
Huber Fractal Image Coding Based on a Fitting Plane
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基于拟合平面的Huber分形图像编码
DOI：
10.1109/tip.2012.2215619
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发表时间：
2013-01-01
影响因子：
10.6
通讯作者：
Zou, Yuru
中科院分区：
文献类型：
--
作者：
Lu, Jian;Ye, Zhongxing;Zou, Yuru
最近，人们对鲁棒分形图像编码产生了浓厚的兴趣，目的是对异常值的鲁棒性。然而，已知的鲁棒分形编码方法（HFIC和LAD-FIC等）并不是最优的，因为除了计算成本高之外，它们在鲁棒回归模型中使用损坏的域块作为自变量，这可能会对鲁棒估计器计算分形参数（取决于噪声水平）产生不利影响。提出了一种基于Huber拟合平面的分形图像编码方法。该方法分别为域和距离块构建Huber拟合平面（HFPs），确保在鲁棒模型中使用未损坏的自变量。在此基础上，引入了一种新的匹配误差函数来鲁棒地评估最佳比例因子。同时，提出了一种中位数绝对偏差（MAD）分解准则，实现了对椒盐噪声图像的快速自适应四叉树分割。为了减少计算量，采用无搜索方法加快编码速度。实验结果表明，该算法在编码速度和恢复图像质量上都优于传统的鲁棒分形图像编码方法。此外，无搜索方法可以显著减少编码时间，在可接受的图像质量退化情况下实现小于2.0 s的编码。此外，我们还表明，结合MAD分解方案，HFP技术作为一种鲁棒方法可以进一步减少编码时间，同时保持图像质量。
Recently, there has been significant interest in robust fractal image coding for the purpose of robustness against outliers. However, the known robust fractal coding methods (HFIC and LAD-FIC, etc.) are not optimal, since, besides the high computational cost, they use the corrupted domain block as the independent variable in the robust regression model, which may adversely affect the robust estimator to calculate the fractal parameters (depending on the noise level). This paper presents a Huber fitting plane-based fractal image coding (HFPFIC) method. This method builds Huber fitting planes (HFPs) for the domain and range blocks, respectively, ensuring the use of an uncorrupted independent variable in the robust model. On this basis, a new matching error function is introduced to robustly evaluate the best scaling factor. Meanwhile, a median absolute deviation (MAD) about the median decomposition criterion is proposed to achieve fast adaptive quadtree partitioning for the image corrupted by salt & pepper noise. In order to reduce computational cost, the no-search method is applied to speedup the encoding process. Experimental results show that the proposed HFPFIC can yield superior performance over conventional robust fractal image coding methods in encoding speed and the quality of the restored image. Furthermore, the no-search method can significantly reduce encoding time and achieve less than 2.0 s for the HFPFIC with acceptable image quality degradation. In addition, we show that, combined with the MAD decomposition scheme, the HFP technique used as a robust method can further reduce the encoding time while maintaining image quality.