计盒维数的算法优化及其在结霜现象中的应用  

Improved Computation Method of Box Dimension and Its Application in Frost Formation

作　　者：刘耀民[1] 刘中良[1] 黄玲艳[1] 

机构地区：[1]北京工业大学环境与能源工程学院传热强化与过程节能教育部重点实验室,北京100124

出　　处：《北京工业大学学报》2012年第11期1724-1730,共7页Journal of Beijing University of Technology

基　　金：国家自然科学基金资助项目(50376001);北京市科学技术委员会北京市科技计划资助项目(Z07020600290793);北京工业大学研究生科技基金资助项目(ykj-2011-4883)

摘　　要：利用MATLAB数字图像处理功能,通过对二值图像网格划分过程中出现的不完整边界网格进行整合处理,优化了二值图像计盒维数计算方法,提高了计算结果的准确性和稳定性.研究中采用的算术阶递增序列网格划分方法,增强了该计算方法对图像尺寸的适应性.同时对分形图像递归深度及分辨率等因素对计算结果的影响进行定量分析,提出具有参考价值的控制条件.最后利用该方法对结霜过程不同时期的霜晶图像进行分形维数计算,并指出分形维数在描述结霜现象中的物理意义.Incomplete boundary boxes will be generated in the edge of an image in most cases, when covering the image with boxes of fixed size. An effective method by which these incomplete boundary boxes can be taken into computation has been proposed to improve the performance of computation method of box dimension, based on the digital image processing function of MATLAB. The improved computation method is well suitable for images of different sizes with the use of arithmetic-step box dividing method. The calculated results derived from this method also showed a better accuracy and stability. In addition, a quantitative discussion was made about the factors that influence the computation results such as recursive series of image and resolution. Meanwhile some useful control conditions were proposed. In the end, the improved method was applied to calculate the fractal dimension of frost crystal images under different frosting time and the physical meaning of fractal dimension in describing the frosting phenomenon was explained.

关 键 词：分形 计盒维数 二值图像 结霜 

分 类 号：TP317.4[自动化与计算机技术—计算机软件与理论]