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Parameter Identification of 1D Recurrent Fractal Interpolation Functions with Applications to Imaging and Signal Processing

机译:一维递归分形插值函数的参数识别及其在成像和信号处理中的应用

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摘要

Recurrent fractal interpolation functions are very useful in modelling irregular (non-smooth) data. Two methods that use bounding volumes and one that uses the concept of box-counting dimension are introduced for the identification of the vertical scaling factors of such functions. The first two minimize the area of the symmetric difference between the bounding volumes of the data points and their transformed images, while the latter aims at achieving the same box-counting dimension between the original and the reconstructed data. Comparative results with existing methods in imaging applications are given, indicating that the proposed ones are competitive alternatives for both low and high compression ratios.
机译:循环分形插值函数在对不规则(非平滑)数据进行建模时非常有用。引入了两种使用边界体积的方法,以及一种使用盒计数维度的概念来识别此类函数的垂直比例因子的方法。前两个最小化了数据点与其转换后的图像的边界体积之间的对称差异区域,而后两个目标是在原始数据与重建数据之间实现相同的盒计数尺寸。给出了与现有成像方法的比较结果,表明所提出的方法对于低压缩比和高压缩比都是竞争性的选择。

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