New York: Springer, 2010. - 329 p. The present volume collects the lecture notes of courses given at the CIME Summer School in Cetraro in September 2008. The school appeared to be a highly successful event with around 50 participants from all over the world, enjoying both the scientific content of the courses and the atmosphere and opportunities for discussions among participants and with the speakers. Mathematical imaging and inverse problems are two of the fastest growing disciplines in applied and interdisciplinary mathematics, with a strong overlap since many image analysis and reconstruction problems are effectively formulated as inverse problems. A key issue in such problems is to preserve and analyze edges or shapes in the image. Those are taken care by the methods covered in the summer school, which had the particular aim of providing a unified picture to methods of image reconstruction and analysis, on the one hand, and techniques for shape reconstruction and analysis, on the other hand. The key steps connecting those are methods based on level set representations and geometric partial differential equations, which effectively operate on the level sets (respectively, discontinuity set) of an image as well as on a single shape.
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