This book explores advanced mathematical techniques for image analysis and reconstruction, focusing on level set and PDE-based methods. The text delves into the core principles of variational and PDE-based approaches, providing insights into their analytical foundations, computational implementation, and practical applications in image processing. It covers key areas such as edge-sharpening, denoising, segmentation, shape analysis, and image matching, highlighting the importance of morphological and geometric structures within images.

The collection of lecture notes from the 2008 Cetraro school presents a comprehensive overview of cutting-edge methods in image analysis. The focus on level set and PDE-based techniques offers a deep dive into the mathematical foundations and computational aspects of modern image reconstruction. The material is structured to provide both theoretical understanding and practical insights for researchers and practitioners in the field. The coverage of diverse applications, from denoising to image matching, underscores the versatility and power of these mathematical tools.