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This book provides an overview of the applications of partial differential equations (PDEs) to image processing, analysis, and computer vision domains, focusing mainly on the most important contributions of the author in these closely related fields. It addresses almost all the PDE-based image processing and analysis areas, and the connections between partial differential equations, computer vision, and artificial intelligence: PDE-based image filtering, inpainting, compression, segmentation, content-based recognition, indexing and retrieval, and video object detection and tracking, energy-based (variational) and nonlinear diffusion-based models of second and fourth order, nonlinear PDE-based scale-spaces in combination to convolutional neural networks and high-level descriptors to perform edge and feature extraction.