The Partial Differential Equations Processing Methods Of Electronic Speckle Pattern Interferometry Fringes And Phase Extraction

The image processing method based on partial differential equations (PDEs) is an important branch of image processing and has become an interest-raising research topic in the past few years, the main idea of which is transforming the image processing to solving partial differential equations. The image is regarded as a continuous signal and the image processing function is treated as a partial differential operator. The operations, such as image filter, contrast enhancement, edge detection and image segmentation, can be realized by solving the PDEs with the original image as initial condition.We discuss the PDEs image processing methods, including five denoising models (i.e. heat conduction equation, Perona-Malik model, selective filter model, divergent diffusion model, selective-divergent diffusion model), two contrast enhancement models (i.e. histogram equalization model, histogram specification model), and the enhancement-denoising model, which can perform filter and contrast enhancement simultaneously. Comparing with the traditional image processing methods, the PDEs image processing methods have two prominent advantages. First, because they progressively improve the image quality until steady state is achieved, the intermediate states are available. This characteristic is useful to choose the best result and avoids some phenomena, such as excessive contrast. Second, it is easy for PDE image processing technique to combine different algorithms. The combination model of enhancement-denoising is able to enhance the contrast and reduce the noise simultaneously.Electronic speckle pattern interferometry (ESPI) is a well-known technique for deformed and nondestructive measurement of optical coarse surface. However, there is strong grain-shape random noise in ESPI fringe patterns. This problem leads to heavy restrain to the fringe on visibility and resolving ability. It is difficult of accurate extraction of phase value from fringe patterns. Therefore, research on effectively filter and improving the visibility to ESPI fringe patterns is of fundamental importance for the development of ESPI. We apply the PDE image processing methods to the ESPI fringe patterns and realize filter and contrast enhancement. Meanwhile, considering the feature of addition fringe pattern, the improved histogram specification is proposed. In addition, to quantitatively evaluate the performance of the different denoising models, two comparative parameters, the image fidelity and the speckle index, are calculated.To test the validity of the PDE denoising and enhancement methods in ESPI, the methods are applied to the closed-fringe pattern obtained by experiment and open-fringe pattern generated by computer simulation. Based on the processed images, mean filter, binarization,...