【摘要】 提出一种将双树复小波与分形理论相结合的复合评定方法。即利用双树复小波近似的平移不变性和方向性好等优点,将信号分解成更为细腻的低频和高频信号,同时根据多尺度下信号分形维数的不变性,利用图像灰度值自相关求得高低频信号的分形维数,通过计算高低频信号分形维数之间的差值(即分形维数距)来确定双树复小波的分解尺度。仿真结果表明复合评定法可以较好地提取基准面,且分形维数距确定分解层数的准确性通过均方根S_q值得到了验证;两个实例均说明,复合评定法可以很好地提取具有分形特征的纳米级三维粗糙表面基准或波纹度,为实际工程表面评定提供了可靠的理论基础。更多还原

【Abstract】 Engineering surfaces always have fractal characteristics and now a composite evaluation method is proposed in which the dual tree complex wavelet combined with fractal theory.By using the dual-tree complex wavelets approximate translation invariance and good directions,signal is decomposed into a more delicate low and high frequency signals.Meanwhile,according to the invariance of the signals fractal dimension under multi- scale,the fractal dimension of signals is obtained by the use of the autocorrelation image gray value,and the dual tree complex wavelets decomposition scale is verified by calculating the different fractal dimensions between the high and low frequency signals(the fractal dimension distance).The simulation results show that the datum can be well extracted by the use of the composite evaluation method,and the accuracy of decomposition level which is confirmed by the fractal dimension distance is verified by the use of the root mean square value.Two examples illustrate that reference and waviness of the nano-scale three-dimensional rough surfaces which have fractal characteristic can be well extracted by the use of the composite evaluation method,which provides a reliable theoretical basis for the assessment of the actual engineering surface.更多还原