外文翻譯---通過廣義條紋投影輪廓分析模型來選擇最優(yōu)濾波偏估計

1、附錄附錄 附錄 A 外文翻譯 外文翻譯-原文部分 原文部分Optimal Filtering based Shift Estimation for Fringe Pattern Profilometry by Generalized Analysis ModelAbstract-This paper presents a new algorithm for fringe pattern parofilometry by utilizin

2、g generalized analysis model, called optimal filtering based shift estimation (OFSE) method, which provides much lower complexity compared with traditional methods. Meanwhile, as OFSE is derived based on the generalized

3、analysis model, the reconstruction results will not be influenced by the nonlinearity of fringe pattern projection and acquisition system. The efficiency of the proposed OFSE method is confirmed by simulation results, wh

4、ich show that the accuracy of three-dimensional reconstruction using digital fringe pattern profilemetry technique can be much improved and the computational complexity can be significantly reduced.1.INTRODUCTIONFringe p

5、attern profilometry (FPP) is one of the most popular non-contact approaches to measuring three-dimensional object surfaces. With FPP, a Ronchi grating or sinusoidal grating is projected onto a three-dimensional diffuse s

6、urface, the height distribution of which deforms the projected fringe patterns and modulates them in phase domain. Hence by retrieving the phase difference between the original and deformed fringe patterns, three-dimensi

7、onal profilometry can be achieved. In order to obtain phase maps from original and deformed fringe patterns, research contributed various analysis methods, including Fourier Transform Profilometry (FTP)[1],[2], Phase Sh

8、ifting Profilometry (PSP)[7], Spatial Phase Detection(SPD)[10], Phase Locked Loop(PLL)[11] and other analysis methods[12],[13].In recent years, because of the simplicity and controllability, digital projectors have been

9、widely used to yield fringe patterns for implementing FPP [14]-[17]. However, when generating fringe patterns by using digital projectors, nonlinear distortions are unavoidably introduced and result in visible measuremen

10、t errors [16],[17], which has been theoretically analyzed by Hu et al.[17].In order to eliminate the reconstruction errors caused by nonlinear distortions, Guo et al.[16] proposed a gamma correction based method to recov

11、er the distorted fringes. However, with this method, the precondition is that the projection system strictly matches the gamma distortion model. Moreover, as gamma coefficient varies with projection systems, the correcti

12、on coefficient has to be estimated for different systems or whenever the system condition changes.Hu et al. introduced a generalized analysis model, which revealed the essential relationship between the projected and the

13、 deformed fringe patterns. This model does not depend on the nonlinear characteristics of projection systems[17]. Based on the mathematical model, Gradient-based Shift Estimation(GSE) algorithm[17] and inverse function a

14、nalysis(IFA) method[18] have been presented to reconstruct accurate profiles from nonlinearly distorted fringe patterns.However, with IFA algorithm, the performance of IFA highly depends on the degree of the fundamental

15、component analysis, which is sensitive to nonlinear distortions and highly depends on the performance of filters and the characteristics of the profile.In order to solve this problem and accurately reconstruct three-dime

16、nsional surfaces from nonlinearly distorted fringe patterns, Hu et al. presented a generalized analysis model to explain the principle of FPP technique [17],[18]:(1) ( ) ( ( )) d x s x u x ? ?(2) 00( ) ( ) ( )l u x h x d

17、 u x ? ?Where represents the shift between the fringe patterns captured on the reference plane ( ) u xand the surface of the object, which varies with coordinates .Eq.(1) reveals that the deformed xsignal is a shifted

18、 version of , and the shift function can be used to determine ( ) d x ( ) s x ( ) u xthe object height distribution by Eq.(2). Therefore, the key to reconstructing three dimensional surface is to retrieve the shift fun

19、ction from and .In addition, because of its ( ) u x ( ) s x ( ) d xsimplicity and generality, in following sections of this paper, the generalized model will be used for our algorithm derivation.3、OPTIMAL FILTERING BAS

20、ED SHIFT ESTIMATION(OFSE) ALGORITHMAs theoretically analyzed in [17], nonlinear distortions of the projected and captured fringe pattern will unavoidably introduce measurement errors into the height distribution hp(x) ca

21、lculated by FTP or PSP algorithm. On the other hand, although FTP and PSP can not make an accurate reconstruction when nonlinear distortion exists, either of them is still capable of roughly measuring a profile of an obj

22、ect. Therefore, can be still employed as a pre- estimation of ( ) hp xthe theoretical value of the height distribution .Corresponding to ,denoting ( ) h x ( ) hp x ( ) p u xthe pre-estimated shift signal can be calc

23、ulated by simply inverting Eq.(2).obviously, compared to the theoretical shift distribution ,is not accurate either. Thus, we can regard the ( ) u x ( ) p u xerrors as a sort of noise and further eliminate it by a well

24、-designed digital filter. Hence, the shift estimation problem can be converted into a new problem of designing a filter to make its output be a precise estimation of the theoretical value of the shift distribution, Certa

25、inly, the design of the optimal filter should be based on generalized model given by Eq.(1) and (2).Additionally, as the number of the filter parameter is usually much fewer than number of sample points of the shift dist

26、ribution ,the parameter space will be significantly reduced, so that less computational ( ) u xcomplexity and faster convergence can be achieved.A.notation and representationGenerally, after the pre-estimated signal ha