梨果实与叶片特征关联的分形研究

Fractal study of correlation between fruits and leaves of pear

为了揭示梨果实的大小、形状、果重与叶片的大小及形状特征间的相关性,采用总体抽样方法,复选20个果实与20片叶为试验样本,8个果实与8片叶为检验样本。采集试验样本果实与叶片的图像,并裁剪转化成二值化图像。以梨果实和叶片区域细化后的边界像素数和区域内像素数分别为果实和叶片的周长和面积,结合分形理论中周长与面积的关联模型,得到梨果实的周长与面积的拟合模型y=1.034 2x+0.109 8;叶片周长与面积的拟合模型为y=1.480 7x+1.245 5;叶片周长与果实周长的拟合函数y=0.795 5x+0.778 7;叶片面积与梨果实面积的拟合函数y=0.526 1x+1.433 1;叶片面积与果重的拟合函数y=1.930x+2.718。通过样本检验,各模型拟合精度达90%。

To reveal the correlation between the size, shape and weight of pear fruit and the size, shape of pear leaf, twenty pear fruits as well as their leaves were selected as experimental samples and 8 pear fruits and their leaves as test samples. The images of the experimental fruit and leaf samples were collected and transferred to binary images through cutting process. The numbers of pixels in periphery of the images are representing the perimeter of fruits and leaves and the numbers of pixels within the region are respectively representing the areas of fruits and leaves, combined with the correlation model for perimeter and area in fractal theory, the fitting functions between perimeters and areas for pear fruits which is y=1.034 2x＋0.109 8, and for pear leaves which is y=1.480 7x＋1.245 5 were obtained. In a similar way, the fitting function between leaves＇ perimeters and pears＇ perimeters which is y=0.795 5x＋0.778 7, between leaves＇ areas and pears＇ areas which is y=0.526 1x＋1.433 1, and between leaves＇ areas and pears＇ weights which is y=1.930x＋2.718 were obtained. The fitting precision of these ftmActions reached 90% by testing experiments.