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Level set methods and dynamic implicit surfaces
TLDR
A student or researcher working in mathematics, computer graphics, science, or engineering interested in any dynamic moving front, which might change its topology or develop singularities, will find this book interesting and useful.
The Split Bregman Method for L1-Regularized Problems
TLDR
This paper proposes a “split Bregman” method, which can solve a very broad class of L1-regularized problems, and applies this technique to the Rudin-Osher-Fatemi functional for image denoising and to a compressed sensing problem that arises in magnetic resonance imaging.
Algorithms Based on Hamilton-Jacobi Formulations
TLDR
New numerical algorithms, called PSC algorithms, are devised for following fronts propagating with curvature-dependent speed, which approximate Hamilton-Jacobi equations with parabolic right-hand-sides by using techniques from the hyperbolic conservation laws.
Weighted essentially non-oscillatory schemes
TLDR
A new version of ENO (essentially non-oscillatory) shock-capturing schemes which is called weighted ENO, where, instead of choosing the "smoothest" stencil to pick one interpolating polynomial for the ENO reconstruction, a convex combination of all candidates is used.
A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method)
TLDR
A new numerical method for treating interfaces in Eulerian schemes that maintains a Heaviside profile of the density with no numerical smearing along the lines of earlier work and most Lagrangian schemes is proposed.
Fast Global Minimization of the Active Contour/Snake Model
TLDR
This paper proposes to unify three well-known image variational models, namely the snake model, the Rudin–Osher–Fatemi denoising model and the Mumford–Shah segmentation model, and establishes theorems with proofs to determine a global minimum of the active contour model.
Nonlocal Operators with Applications to Image Processing
TLDR
This topic can be viewed as an extension of spectral graph theory and the diffusion geometry framework to functional analysis and PDE-like evolutions to define new types of flows and functionals for image processing and elsewhere.
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