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The basic principle of image processing methods based on partial differential equations (PDE) is introduced, the variational methods used to derive PDE models are described, and the energy functional of widely used PDE denoising models is given. Our recent works of PDE-based image processing on electronic speckle pattern interferometry (ESPI) are reviewed, including performing contrast enhancement and denoising simultaneously for ESPI fringes, proposing new oriented PDE denoising models for dense ESPI fringes and a nearly preprocessing-free method for skeletonization of gray scale ESPI fringes. The main advantages of our methods are given and some suggestions are presented for the development and the research of PDE-based image processing methods on optics test technology.