Research On New Methods Of PDEs And VID For The Filtering Of Different Types Of ESPI Fringe Patterns And Their Applications

Electronic speckle pattern interferometry(ESPI)has been well known as an optical non-destructive measurement technology for the capability of providing high precision,full field measurement in a non-contact mode.ESPI has been widely applied in a variety of fields such as vibration measurement,displacement measurement and its derivative measurement,as well as 3D object reconstruction.In ESPI technology,ESPI fringe patterns or ESPI wrapped phase patterns are used as measurement results.Both ESPI fringe patterns and wrapped phase patterns,however,contain a large quantity of speckle noise.Because the filtering of ESPI wrapped phase patterns can be converted to the filtering of ESPI fringe patterns,the effective filtering of ESPI fringe patterns is a key step in the successful application of ESPI technology,and it is of great significance.In this paper,based on partial differential equation(PDE),variational image decomposition(VID),Shearlet transform and fuzzy c-means clustering algorithm,we deeply conduct the study on these problems and propose new PDEs and VID methods for the filtering of different types of ESPI fringe patterns.The primary works are as follows:(1)In order to reduce the number of iterations of the existing OPDEs and improve the computational efficiency,we derived two parabolic-hyperbolic oriented partial differential equations(PH-OPDEs)filtering models based on the variational method.The experimental results show that the PH-OPDEs have significantly better performance in numerical stability and computational efficiency than the existing OPDEs.(2)In order to obtain better filtering results for ESPI fringe patterns with poor quality,we proposed a filtering method for ESPI fringe patterns denoising,which is a combination of SOOPDE and Shearlet transform,named SOOPDE-Shearlet.Although this combination is simple,the experimental results demonstrate the good performance of this method:it can make the low density fringes smooth enough and high density fringes unblurred.(3)For the type of ESPI fringe patterns with low-density fringes,we propose a shape-preserving OPDE for ESPI fringe patterns denoising.The experimental results show that the proposed shape-preserving OPDE is capable of eliminating noise effectively,keeping the integrity of fringes,and more importantly,preserving the shape of fringes and improving the accuracy of subsequent fringe analysis.(4)Based on Shearlet transform,we proposed a new image decomposition model Shearlet-Hilbert-L~2.In this model,the low-density fringes,high-density fringes and noise are respectively described by Shearlet smoothness spaces,adaptive Hilbert space and L~2 space and processed individually.Since Shearlet transform has superior directional sensitivity,the proposed Shearlet-Hilbert-L~2 model achieves commendable filtering results for various types of ESPI fringe patterns,including uniform density fringe patterns,moderately variable density fringe patterns and greatly variable density fringe patterns.(5)Based on fuzzy c-means(FCM)clustering algorithm,the discontinuous region identification method and an adaptive shape-preserving OPDE for discontinuous ESPI fringe patterns denoising are proposed.According to our method,the discontinuous regions are effectively found and with the proposed adaptive shape-preserving OPDE,the noise is well eliminated,the shape and the discontinuity of fringes are well kept.In addition,based on the technology proposed in this paper,a parabolic-hyperbolic adaptive shape-preserving OPDE filtering model is proposed and applied to the discontinuous ESPI fringe patterns obtained from the three-point bending experiment of concrete beams.