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In this paper, we first present the general description for partial differential equations (PDEs) based image processing methods, including the basic idea, the main advantages and disadvantages, a few representative PDE models, and the derivation of PDE models. Then we review our contributions on PDE-based anisotropic filtering methods for electronic speckle pattern interferometry, including the second-order, fourth-order, and coupled nonoriented PDE filtering models and the second-order and coupled nonlinear oriented PDE filtering models. We have summarized the features of each model.

This article is concerned with frequency filtering for electronic speckle pattern interferometry wrapped phase patterns. We propose a robust localized Fourier transform filter which is an extension of the root filtering method (RFM). We improve the RFM from a simple technical process and a filter function in the frequency domain. In our method, the proposed filter function is taken as the power spectrum of the convolution of an image and a Gaussian function to the power α. We test the proposed method on two computer-simulated wrapped phase fringe patterns and one experimentally obtained wrapped phase pattern, and compare our models with the widely used, well-known RFM and windowed Fourier filtering (WFF). The experimental results have demonstrated that our localized Fourier transform filter outperforms the RFM and is comparable to WFF. Our method depends on fewer parameters, as compared with WFF, and can achieve a better balance between the computational complexity and the filtered results.