Veenland J F, Grashius J L, van der Meer F, Beckers A L, Gelsema E S
Department of Radiology, Erasmus University, Rotterdam, The Netherlands.
Med Phys. 1996 Apr;23(4):585-94. doi: 10.1118/1.597816.
In the last decade, the fractal dimension has become a popular parameter to characterize image textures. Also in radiographs, various procedures have been used to estimate the fractal dimension. However, certain characteristics of the radiographic process, e.g., noise and blurring, interfere with the straightforward application of these estimation methods. In this study, the influence of quantum noise and image blur on several estimation methods was quantified by simulating the effect of quantum noise and the effect of modulation transfer functions, corresponding with different screen-film combinations, on computer generated fractal images. The results are extrapolated to explain the effect of film-grain noise on fractal dimension estimation. The effect of noise is that, irrespective of the noise source, the fractal dimension is overestimated, especially for lower fractal dimensions. On the other hand, blurring results in an underestimation of the dimensions. The effect of blurring is dependent on the estimation method used; the dimension estimates by the power spectrum method are lowered with a constant value, whereas the underestimation by the methods working in the spatial domain is dependent on the given dimension. The influence of the MTF and noise on fractal dimension estimation seriously limits the comparability of fractal dimensions estimated from radiographs which differ in noise content or MTF. Only when the power spectrum method is used, it is possible to correct for the influence of different MTFs of screen-film combinations. It is concluded that only when using the same object-focus distance, the same exposure conditions, the same digitizer at the same resolution, can fractal dimensions as estimated in radiographs be reliably compared.
在过去十年中，分形维数已成为表征图像纹理的一个常用参数。在射线照片中，也已采用各种方法来估计分形维数。然而，射线照相过程的某些特性，如噪声和模糊，会干扰这些估计方法的直接应用。在本研究中，通过模拟量子噪声的影响以及与不同增感屏 - 胶片组合相对应的调制传递函数对计算机生成的分形图像的影响，定量分析了量子噪声和图像模糊对几种估计方法的影响。研究结果被外推以解释胶片颗粒噪声对分形维数估计的影响。噪声的影响是，无论噪声源如何，分形维数都会被高估，尤其是对于较低的分形维数。另一方面，模糊会导致维数被低估。模糊的影响取决于所使用的估计方法；功率谱法估计的维数会降低一个恒定值，而在空间域中工作的方法所导致的低估则取决于给定的维数。调制传递函数（MTF）和噪声对分形维数估计的影响严重限制了从噪声含量或MTF不同的射线照片估计出的分形维数的可比性。只有当使用功率谱法时，才有可能校正增感屏 - 胶片组合不同MTF的影响。得出的结论是，只有当使用相同的物 - 焦距离、相同的曝光条件、相同分辨率下的相同数字化仪时，射线照片中估计出的分形维数才能可靠地进行比较。
