Mathematical models for registration and applications to medical imaging

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Image registration is a crucial topic in image processing with applications in medical imaging and multimedia. It involves finding an appropriate transformation between two data sets, necessitating a mathematical model to define "appropriate transformations" and correlation. Depending on the application, various deformations such as Euler, rigid, plastic, and elastic are considered. Similarity measures range from simple pixel value distances to more complex metrics like mutual information or entropy distances. This volume aims to showcase relevant and emerging applications of image registration, highlighting new mathematical technologies in the field. Many current applications utilize variational principles that require advanced analyses, including calculus of variations and partial differential equations. Due to the complexity of registration problems, efficient numerical solutions are essential. Concepts such as multi-level solvers for partial differential equations and non-convex optimization are significant in this context. Experts contribute discussions on mathematical and numerical challenges in registration, emphasizing its importance in both medical imaging and industrial applications from the perspectives of medical professionals and manufacturers.