Stanley J. Osher
American applied mathematician known for contributions to numerical analysis and partial differential equations, notably level set methods and the Rudin–Osher–Fatemi (ROF) model for image denoising; long-time researcher and professor in applied mathematics.
Books
This list of books are ONLY the books that have been ranked on the lists that are aggregated on this site. This is not a comprehensive list of all books by this author.
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1. Level Set Methods And Dynamic Implicit Surfaces
A compact introduction to the mathematical foundations and numerical techniques for representing and evolving interfaces implicitly as the zero level set of a higher-dimensional function; it presents the governing PDEs (Hamilton–Jacobi type and curvature-driven flows), the viscosity-solution framework, and stable high-resolution discretizations (upwind, ENO/WENO, reinitialization) while demonstrating applications in multiphase fluid dynamics, image processing, shape optimization and related problems, with emphasis on robustness for topological changes and accurate computation of geometric quantities.
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2. Geometric Level Set Methods In Imaging, Vision, And Graphics
In Imaging, Vision, And Graphics
This book presents the mathematical foundations, numerical techniques, and practical applications of geometric level set methods for image processing, computer vision, and computer graphics, showing how evolving interfaces governed by partial differential equations can be used for tasks such as image segmentation, shape modeling, and tracking while naturally handling topology changes; it combines theory (curvature-driven flows, Hamilton–Jacobi formulations), stable discretizations, and computational examples to demonstrate robust, flexible tools for representing and evolving shapes in 2D and 3D.
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