Accelerated Optimization in the PDE Framework Formulations for the Active Contour Case
DOI10.1137/19M1304210zbMath1479.35901arXiv1711.09867OpenAlexW3100594286MaRDI QIDQ5143324
Ganesh Sundaramoorthi, Minas Benyamin, Anthony J. Yezzi
Publication date: 11 January 2021
Published in: SIAM Journal on Imaging Sciences (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1711.09867
manifoldsaccelerationpartial differential equationsgradient descentvariationalNesterovmass transport optimization
Stability in context of PDEs (35B35) Inverse problems for PDEs (35R30) Variational methods for second-order elliptic equations (35J20) Applications of variational problems in infinite-dimensional spaces to the sciences (58E50) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) PDEs in connection with control and optimization (35Q93) PDEs on manifolds (35R01) PDE constrained optimization (numerical aspects) (49M41)
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Cites Work
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- Smooth minimization of non-smooth functions
- Accelerated gradient methods for nonconvex nonlinear and stochastic programming
- Gradient methods for minimizing composite functions
- Geometric applications of the split Bregman method: segmentation and surface reconstruction
- Approximations of shape metrics and application to shape warping and empirical shape statis\-tics
- Accelerating the cubic regularization of Newton's method on convex problems
- Properties of Sobolev-type metrics in the space of curves
- Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
- Geodesic active contours
- Introductory lectures on convex optimization. A basic course.
- Stereoscopic segmentation
- Conformal curvature flows: from phase transitions to active vision
- A first-order primal-dual algorithm for convex problems with applications to imaging
- A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
- Accelerated variational PDEs for efficient solution of regularized inversion problems
- Deep relaxation: partial differential equations for optimizing deep neural networks
- Adaptive restart for accelerated gradient schemes
- Cubic regularization of Newton method and its global performance
- Determining optical flow
- A New Geometric Metric in the Space of Curves, and Applications to Tracking Deforming Objects by Prediction and Filtering
- Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models
- Active contours without edges
- Minimizing Flows for the Monge--Kantorovich Problem
- Geometric Level Set Methods in Imaging, Vision, and Graphics
- A variational perspective on accelerated methods in optimization
- Dynamic Active Contours for Visual Tracking
- Variational, Geometric, and Level Set Methods in Computer Vision