Scale Value Decision Method for Discrete Grid Gabor Wavelet Transform

doi:10.11834/jig.200609213

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Scale Value Decision Method for Discrete Grid Gabor Wavelet Transform
Vol. 11, Issue 9, Pages: 1266(2006)
Published：2006
DOI： 10.11834/jig.200609213
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DOI：

Scale Value Decision Method for Discrete Grid Gabor Wavelet Transform[J]. Journal of Image and Graphics, 2006, 11(9): 1266. DOI： 10.11834/jig.200609213.

摘要

在工程分析中应用离散化的小波变换，通常是在尺度方向上按以2为底的幂级数对尺度参数α进行离散化来得到离散栅格下的小波变换，但实际分析时则往往需要加大尺度方向的栅格密度，以获得细致的分析，而现行的增加密度的方法都具有一定的任意性，为了解决实际工程应用中离散栅格小波变换分析尺度增加密度的不确定性问题，根据小波基在空／时-频平面上的能量分布特性，通过理论推导计算验证，提出了小波变换分析尺度参数取值的理论方法以及尺度参数α的离散化理论取值公式α=1．15^nα0，同时以3维形貌测量轮廓术为基础，以Gabor解析小波的尺度参数取值为例展开了讨论计算，并给出了Gabor解析小波尺度参数选取的理论公式。从计算机模拟和实验结果可见，该方法根据中心频率对尺度参数α进行取值，能够较好地解决各尺度小波之间的频谱拉距以及混叠现象所造成测量误差。

Abstract

Discrete grid wavelet transform has wide application in the engineering analysis. The way to decide the value of the scale factor widely used in present is to set the scale fact or aasa=an0(a0=2

n=0

…

N). But for the actual applications

it is too rough for analysis. Therefore

people should reduce the scale factor interval to increase the density of the discrete grids of the wavelet transform. However existing ways to increase the density of the discrete grids have some what of randomicity. Through the research in the wavelet transform profilometry

Weng Jiawen and Zhong Jingang proposed another new approach to the analysis of the values of the scale factor in the light of the energy characteristic of the wavelets. In this paper

they took the Gabor wavelet for example and figured out the length of the frequency border of the Heisenberg box for each“daughter wavelet”. Therefore they got the theory formula of the decision of the scale factor for the Gabor wavelet asa=1.15 na0. The theory and the accuracy check by a simulation and an example of 32D shape measurement are explained and shown in this paper. And the results of the simulation and experiments have shown the advantage of the presented method.