牛肉大理石花纹计盒维和信息维的测定

    Determination of the box-counting fractal dimension and information fractal dimension of beef marbling

    • 摘要: 对牛肉大理石花纹几何特征进行定量描述,是牛肉大理石花纹等级自动判定系统的关键技术。通过对牛肉大理石花纹图像分形特征的分析及分形维数的测定,试图以分形维对牛肉大理石花纹的分布特征进行定量描述。作者以中国及美国牛肉分级系统中的大理石花纹标准图版为研究对象,通过图像预处理,将其转化为二值数字图像,然后根据变粗视化程度的像素点覆盖法,编写出计盒维和信息维的测定程序,计算出上述每一幅图像在不同标尺下的非空盒个数及信息量,再根据标尺与非空盒个数及信息量的关系,分析图像的分形特征;通过回归分析的方法,测定出图像的计盒维数和信息维数。试验结果显示,在一定的标度范围内,牛肉大理石花纹标准图像具有分形性,并且显示出多重分形特征;图像的计盒维数和信息维数均呈现出随着牛肉大理石花纹等级的增加而增大的变化趋势。

       

      Abstract: The box-counting fractal dimension(BFD) and information fractal dimension(IFD) of beef marbling were estimated in order to find out a new parameter for the quantitative description of the distribution of marbling fat. To begin with, the image processing operations were conducted for the pre-processing of beef marbling standard images from China and USDA. Then the authors developed programs based on the principle of changing megascopic degree and applied them to plot the ln[N(r)]~ln(r) and ln[I(r)]~ln(r) respectively, with the number of un-empty box N(r) and information amount I(r) of marbling measured by counting various scale length r using a divider. The relationships between ln[N(r)] and ln(r) as well as ln[I(r)] and ln(r) maintained linearity over a range [1, 116] pixels. Therefore, the BFD and IFD of the above images were obtained from the gradients by regression analysis. The experimental results showed that the BFD values varied according to the score of beef marbling. Further analyses that both the BFD and IFD tend to increase with the increase of beef marbling grade, which implies that the BFD and IFD can be regarded as one of quantitative parameters indicating the beef marbling scores.

       

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