Transport equation and image interpolation with SBD velocity fields

DOI10.1016/j.matpur.2010.10.010zbMath1229.49053OpenAlexW2033934845MaRDI QIDQ536201

Tuomo Valkonen

Publication date: 16 May 2011

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2010.10.010

zbMATH Keywords

transport equationdiscontinuitiesimage interpolationbounded deformation

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Existence theories for optimal control problems involving partial differential equations (49J20) Absolutely continuous real functions of several variables, functions of bounded variation (26B30)

Related Items (4)

Limiting Aspects of Nonconvex ${TV}^{\phi}$ Models ⋮ Strong polyhedral approximation of simple jump sets ⋮ Predictive online optimisation with applications to optical flow ⋮ The Jump Set under Geometric Regularization. Part 1: Basic Technique and First-Order Denoising

Cites Work

• Transport equation and Cauchy problem for BV vector fields
• A nonlocal approximation of free discontinuity problems in SBV and SBD
• Traces and fine properties of a \(BD\) class of vector fields and applications
• Ordinary differential equations, transport theory and Sobolev spaces
• Compactness and lower semicontinuity properties in \(SBD(\Omega)\)
• Fine properties of functions with bounded deformation
• An approximation result for special functions with bounded deformation
• Medical image registration and interpolation by optical flow with maximal rigidity
• Variational Analysis
• ANALYSIS OF OPTICAL FLOW MODELS IN THE FRAMEWORK OF THE CALCULUS OF VARIATIONS
• A density result in SBV with respect to non-isotropic energies
• A Mathematical Study of the Relaxed Optical Flow Problem in the Space $BV (\Omega)$
• Optimal Control Formulation for Determining Optical Flow
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