基于矩阵形态学分形几何图的产生

The Generation of Fractal Geometric Graphs Using Matrix Morphology

提出了一种利用矩阵和形态学相结合产生具有自相似结构分形图案的方法．图像矩阵和结构矩阵定义为其每个元素是具有矩阵下标的单独的图像，图像矩阵和结构矩阵的膨胀包含了大量不同图像元和结构元之间的膨胀，由矩阵理论把它们组合成一个新的图像矩阵．因此采用图像矩阵间的形态运算可以生成比常规形态学方法复杂得多的分形图形．给出了在特定条件下的分形维数的估计公式．

Fractal graphs with self-similar structure can be generated by combining the matrix and the morphology approach. An algorithm for generating a class of self-(mutually-) similar fractal graphs brought about by whirling is proposed. A matrix of graphs or structural elements is defined to be an array where each element is a separate graph with a matrix subscript. The dilation of a matrix of graphs by a matrix of structural elements consists of a number of dilations of various graphic elements with structural elements. The rules of matrix operation will show how the results of these transformations are combined to form a new array. Hence much more complex fractal graphs can be generated with matrix morphology than with traditional morphology approach. A simple formula for the estimation of fractal dimension under specific conditions is given.