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

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.