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This paper uses partial differential equation image processing techniques to establish image texture analysis models based on nonlinear anisotropic diffusion equations for image denoising, image segmentation, and image decomposition. This paper proposes a class of denoising models based on the hybrid anisotropic diffusion equation from the characteristics of different noise types. The model exhibits anisotropic diffusion near the image boundary, which can protect the boundary well, and isotropic diffusion inside the image; so, it can remove the noise effectively. We use the immovable point theory to prove the uniqueness of the model solution and further discuss other properties such as asymptotics of the solution. We propose a class of image texture analysis algorithms based on anisotropic diffusion equations and discrete gray level sets. First, a class of nonconvex generalized functions is proposed to remove the noise from the original image to obtain a smooth image while sharpening the edges. Then, an energy generalization function based on the gray level set is proposed, and the existence of the global minimum of this energy generalization function is discussed. Finally, an equivalent form of this energy generalization is given in the discrete case, and an image texture analysis algorithm is designed based on the equivalent form. The algorithm is improved by initial position optimization, dynamic adjustment of parameters, and adaptive selection of thresholds so that the ants can search along the real edges. Experiments show that the improved algorithm for image edge detection can obtain more complete edges and better detection results. The energy generalization function is calculated directly on the discrete gray level set instead of solving the corresponding partial differential equation, which can avoid the selection of the initial level set and the reinitialization of the level set, thus greatly improving the segmentation efficiency. The new algorithm has a high improvement in segmentation efficiency and can efficiently handle large size complex images.

Image Texture Analysis and Edge Detection Algorithm Based on Anisotropic Diffusion Equation