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Axioms and fundamental equations of image processing
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
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On Affine Plane Curve Evolution
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Uniqueness and Existence of Viscosity Solutions of Generalized mean Curvature Flow Equations
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The Measurement of Visual Motion
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A Diffusion Equation with a Nonmonotone Constitutive Function
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Optical flow using spatiotemporal filters
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Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
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On the evolution of curves via a function of curvature. I. The classical case
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Image analysis and mathematical morphology
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The measurement of visual motion
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Nonlinear total variation based noise removal algorithms
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General methods for determining projective invariants in imagery
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ANALYZING ORIENTED PATTERNS
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SCALE-SPACE FILTERING
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Representations based on Zero-crossings in Scale-Space
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Revista Matematica De La Universidad Complutense De Madrid
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Linear and Quasi-linear Equations of Parabolic Type
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User’s guide to viscosity solutions of second order partial differential equations
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On the mathematical foundations of smoothness constraints for the determination of optical flow and for surface reconstruction
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A theory of multiscale, curvature-based shape representation for planar curves
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Pattern spectrum and multiscale shape representation
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Discrete black and white object recognition via morphological functions
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Scale-space and edge detection using anisotropic diffusion
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Partial shape classification using contour matching in distance transformation
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Adaptive smoothing: a general tool for early vision
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Invariant descriptors for 3D object recognition and pose
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Computational Aspects Of Determining Optical Flow
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A Nonlinear Approach To The Motion Correspondence Problem
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Projective invariants of shapes
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Object recognition by affine invariant matching
inferredcites →https://doi.org/10.1109/cvpr.1991.139657openalex-snapshot
Shape representation and recognition from curvature
inferredcites →https://doi.org/10.1109/iccv.1990.139485openalex-snapshot
Computing optical flow from an overconstrained system of linear algebraic equations
inferredcites →https://doi.org/10.1109/iccv.1990.139490openalex-snapshot
Computing spatiotemporal surface flow
inferredcites →https://doi.org/10.1109/iccv.1990.139516openalex-snapshot
An estimation-theoretic framework for image-flow computation
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Edge and Curve Detection for Visual Scene Analysis
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IEEE Transactions on Pattern Analysis and Machine Intelligence
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Snow removal--A noise-stripping process for picture signals
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The Curvature Primal Sketch
inferredcites →https://doi.org/10.1109/tpami.1986.4767748openalex-snapshot
Scaling Theorems for Zero Crossings
inferredcites →https://doi.org/10.1109/tpami.1986.4767750openalex-snapshot
Scale-Based Description and Recognition of Planar Curves and Two-Dimensional Shapes
inferredcites →https://doi.org/10.1117/12.7974127openalex-snapshot
Tutorial On Advances In Morphological Image Processing And Analysis
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Feature-Oriented Image Enhancement Using Shock Filters
inferredcites →https://doi.org/10.1137/0729012openalex-snapshot
Image Selective Smoothing and Edge Detection by Nonlinear Diffusion
inferredcites →https://doi.org/10.1137/0729052openalex-snapshot
Image Selective Smoothing and Edge Detection by Nonlinear Diffusion. II
inferredcites →https://doi.org/10.1137/0732020openalex-snapshot
A Simple Proof of Convergence for an Approximation Scheme for Computing Motions by Mean Curvature
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Motion of hypersurfaces and geometric equations
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Convergence of approximation schemes for fully nonlinear second order equations
inferredcites →https://doi.org/10.3792/pjaa.65.207openalex-snapshot
Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
inferredcites →https://doi.org/10.4310/jdg/1214439902openalex-snapshot
The heat equation shrinking convex plane curves
inferredcites →https://doi.org/10.4310/jdg/1214441371openalex-snapshot
The heat equation shrinks embedded plane curves to round points
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Motion of level sets by mean curvature. I
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Segmentation of image: by variational methods: A constructive approach
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Non-stationary iterated Tikhonov-Morozov method and third-order differential equations for the evaluation of unbounded operators
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Anisotropic Diffusion PDEs for Regularization of Multichannel Images
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Scale‐Space Representations for Gray‐Scale and Color Images
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Sobolev gradient preconditioning for image‐processing PDEs
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Non‐linear coupled CNN models for multiscale image analysis
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Regularizations of forward‐backward parabolic PDEs
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Three‐dimensional adaptive filtering in magnetic resonance angiography
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Computational and qualitative aspects of motion of plane curves with a curvature adjusted tangential velocity
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A direct method for solving an anisotropic mean curvature flow of plane curves with an external force
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Free water elimination and mapping from diffusion MRI
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Finite element analysis and application for a nonlinear diffusion model in image denoising
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On the convergence of discrete schemes for the Perona‐Malik equation
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Herschel-Bulkley diffusion filtering: non-Newtonian fluid mechanics in image processing
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Affine Geometry, Curve Flows, and Invariant Numerical Approximations
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Geometric Heat Equation and Nonlinear Diffusion of Shapes and Images
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Volumetric Segmentation of Medical Images by Three-Dimensional Bubbles
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Nonlinear Multiscale Representations for Image Segmentation
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Model-Based Detection of Tubular Structures in 3D Images
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Implicit and Nonparametric Shape Reconstruction from Unorganized Data Using a Variational Level Set Method
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Contrast Enhancement via Image Evolution Flows
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Level Set Methods: An Overview and Some Recent Results
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Histogram Modification via Differential Equations
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Scale-Space Properties of Nonstationary Iterative Regularization Methods
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Scale-Space from a Level Lines Tree
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Nonlinear Scale-Space Representation with Morphological Levelings
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Variational Numerical Methods for Solving Nonlinear Diffusion Equations Arising in Image Processing
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Algebraic Framework for Linear and Morphological Scale-Spaces
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A Scheme for Coherence-Enhancing Diffusion Filtering with Optimized Rotation Invariance
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An Adaptive Finite Volume Scheme for Solving Nonlinear Diffusion Equations in Image Processing
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Structural Group Analysis of Functional Activation Maps
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Fast Parallel Algorithms for a Broad Class of Nonlinear Variational Diffusion Approaches
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Motion Segmentation and Tracking with Edge Relaxation and Optimization using Fully Parallel Methods in the Cellular Nonlinear Network Architecture
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Affine Invariant Mathematical Morphology Applied to A Generic Shape Recognition Algorithm
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Morphological Scale-Space Operators: An Algebraic Framework
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Mean Curvature Flows, Edge Detection, and Medical Image Segmentation
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Co-Volume Level Set Method in Subjective Surface Based Medical Image Segmentation
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Partial Differential Equations for Morphological Operators
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Shape Recognition Based on an a Contrario Methodology
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A Variational Formulation of PDE’s for Dilations and Levelings
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A Scale-Space Analysis of a Contour Figure Using a Crystalline Flow
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A Four-Pixel Scheme for Singular Differential Equations
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Fast Edge Preserving Picture Recovery by Finite Markov Random Fields
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A Fuzzy Scale-Space Approach to Feature-Based Image Representation and Retrieval
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Deep Structure, Singularities, and Computer Vision
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Random Walks, Constrained Multiple Hypothesis Testing and Image Enhancement
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Curvature-Preserving Regularization of Multi-valued Images Using PDE’s
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Interpolating Orientation Fields: An Axiomatic Approach
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Geometric Filters, Diffusion Flows, and Kernels in Image Processing
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Scale-Based Corner Extraction of a Contour Figure Using a Crystalline Flow
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The Maximum Principle for Beltrami Color Flow
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An Explanation for the Logarithmic Connection between Linear and Morphological Systems
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Comparing Objective and Subjective Quality Results for Compression Pre-processing with Non-linear Diffusion
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Image Decomposition by Radial Basis Functions
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Diffusion Methods for Form Generalisation
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Scale-Spaces, PDE’s, and Scale-Invariance
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A Note on Two Classical Shock Filters and Their Asymptotics
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DEFORMOTION Deforming Motion, Shape Average and the Joint Registration and Segmentation of Images
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Region Matching with Missing Parts
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A Compact and Multiscale Image Model Based on Level Sets
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Morphological Scale Space and Mathematical Morphology
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Scale-Space from a Level Lines Tree
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Numerical Solution Schemes for Continuous-Scale Morphology
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Scale-Space Properties of Regularization Methods
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A Scale-Space Approach to Nonlocal Optical Flow Calculations
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Lattice Boltzmann Models for Nonlinear Diffusion Filtering
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Geometric Multiscale Representation of Numerical Images
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Nonlinear PDEs and Numerical Algorithms for Modeling Levelings and Reconstruction Filters
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A New Time Dependent Model Based on Level Set Motion for Nonlinear Deblurring and Noise Removal
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A Stochastic Scale Space for Multiscale Image Representation
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Shape-adapted smoothing in estimation of 3-D depth cues from affine distortions of local 2-D brightness structure
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Cartan's moving frame method and its application to the geometry and evolution of curves in the euclidean, affine and projective planes
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A review of nonlinear diffusion filtering
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Scale space versus topographic map for natural images
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Linear spatio-temporal scale-space
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Intrinsic scale space for images on surfaces: The geodesic curvature flow
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From high energy physics to low level vision
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Directional anisotropic diffusion applied to segmentation of vessels in 3D images
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Slowed anisotropic diffusion
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On projective plane curve evolution
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Nonlinear diffusion scale-spaces: From the continuous to the discrete setting
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Affine invariant gradient flows
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Geometric Deformable Models
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Geodesics, Distance Maps, and Curve Evolution
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Parallel Co-Volume Subjective Surface Method For 3d Medical Image Segmentation
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Handbook of Mathematical Methods in Imaging
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Differential Methods for Multi-Dimensional Visual Data Analysis
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A Design Problem for Image Processing
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Gradients, Curvature, and Visual Tracking
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Geometrie Flows for Image Processing
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Differential Methods for Multi-dimensional Visual Data Analysis
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Partial Differential Equations in Image Processing
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The Third Order Iterative Method for Solving Nonlinear Parabolic Equations and Its Application to the Biological Tissues Models
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The Convex-Hull-Stripping Median Approximates Affine Curvature Motion
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PDE Evolutions for M-Smoothers: From Common Myths to Robust Numerics
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Sparsification Scale-Spaces
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New Adaptive Morphological Geodesic Active Contour Method for Segmentation of Hemorrhagic Stroke in Computed Tomography Image
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Geodesics, Distance Maps, and Curve Evolution
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Quantisation Scale-Spaces
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Extension of Mathematical Morphology in Riemannian Spaces
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Morphological Counterpart of Ornstein–Uhlenbeck Semigroups and PDEs
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Equivariance-Based Analysis of PDE Evolutions Related to Multivariate Medians
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Generalised Scale-Space Properties for Probabilistic Diffusion Models
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Hamilton-Jacobi Equations and Mathematical Morphology in Pseudo-Riemannian Manifolds
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Wavefronts for Generalized Perona-Malik Equations
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Scale-Space Properties for Discrete Cross-Diffusion Filtering
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Skeletonisation Scale-Spaces
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Diffusion-Shock Filtering on the Space of Positions and Orientations
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Interface Dynamics in Phase Transitions
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Subscale Capturing in Numerical Analysis
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Teichmüller Space, Dynamics, Probability
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Variational Methods in Image Matching and Motion Extraction
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On Evolutionary Integral Models for Image Restoration
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The Morphological Equivalents of Relativistic and Alpha-Scale-Spaces
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PDE-Based Color Morphology Using Matrix Fields
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A Linear Scale-Space Theory for Continuous Nonlocal Evolutions
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When Convex Analysis Meets Mathematical Morphology on Graphs
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Morphological PDE and Dilation/Erosion Semigroups on Length Spaces
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Corner Detection Using the Affine Morphological Scale Space
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Sparse-Data Based 3D Surface Reconstruction for Cartoon and Map
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Image Anisotropic Diffusion Based on Gradient Vector Flow Fields
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Galilean Differential Geometry of Moving Images
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Minimally Stochastic Schemes for Singular Diffusion Equations
inferred← citeshttps://doi.org/10.1007/978-3-540-36841-0_605openalex-snapshot
Automatic Cartilage Detection in MR Image sets using CDSG Snake
inferred← citeshttps://doi.org/10.1007/978-3-540-39966-7_44openalex-snapshot
A Computation of a Crystalline Flow Starting from Non-admissible Polygon Using Expanding Selfsimilar Solutions
inferred← citeshttps://doi.org/10.1007/978-3-540-72823-8_12openalex-snapshot
Discrete Regularization on Weighted Graphs for Image and Mesh Filtering
inferred← citeshttps://doi.org/10.1007/978-3-540-72823-8_36openalex-snapshot
Uniform and Textured Regions Separation in Natural Images Towards MPM Adaptive Denoising
inferred← citeshttps://doi.org/10.1007/978-3-540-72823-8_44openalex-snapshot
Numerical Invariantization for Morphological PDE Schemes
inferred← citeshttps://doi.org/10.1007/978-3-540-72823-8_48openalex-snapshot
A Generic Approach to the Filtering of Matrix Fields with Singular PDEs
inferred← citeshttps://doi.org/10.1007/978-3-540-72823-8_49openalex-snapshot
Combining Curvature Motion and Edge-Preserving Denoising
inferred← citeshttps://doi.org/10.1007/978-3-540-72849-8_65openalex-snapshot
Anisotropic Continuous-Scale Morphology
inferred← citeshttps://doi.org/10.1007/978-3-642-02256-2_21openalex-snapshot
PDE-Driven Adaptive Morphology for Matrix Fields
inferred← citeshttps://doi.org/10.1007/978-3-642-02256-2_63openalex-snapshot
Highly Accurate PDE-Based Morphology for General Structuring Elements
inferred← citeshttps://doi.org/10.1007/978-3-642-03613-2_23openalex-snapshot
A Directional Rouy-Tourin Scheme for Adaptive Matrix-Valued Morphology
inferred← citeshttps://doi.org/10.1007/978-3-642-15816-2_7openalex-snapshot
Multi-Scale and Multi-Orientation Medical Image Analysis
inferred← citeshttps://doi.org/10.1007/978-3-642-17688-3_40openalex-snapshot
Pseudo-morphological Image Diffusion Using the Counter-Harmonic Paradigm
inferred← citeshttps://doi.org/10.1007/978-3-642-19604-1_5openalex-snapshot
Projective Invariant Features Detection and the Registration Group
inferred← citeshttps://doi.org/10.1007/978-3-642-24785-9_20openalex-snapshot
Anisotropic Non-Local Means with Spatially Adaptive Patch Shapes
inferred← citeshttps://doi.org/10.1007/978-3-642-27795-5_35-5openalex-snapshot
Differential Methods for Multidimensional Visual Data Analysis
inferred← citeshttps://doi.org/10.1007/978-3-642-28661-2_2openalex-snapshot
Actionable Information in Vision
inferred← citeshttps://doi.org/10.1007/978-3-642-30232-9_1openalex-snapshot
Supremum/Infimum and Nonlinear Averaging of Positive Definite Symmetric Matrices
inferred← citeshttps://doi.org/10.1007/978-3-642-33221-0_5openalex-snapshot
Discrete Flux-Corrected Transport: Numerical Analysis, Tensor-Valued Extension and Application in Image Processing
inferred← citeshttps://doi.org/10.1007/978-3-642-34141-0_3openalex-snapshot
Segmentation and Skeletonization on Arbitrary Graphs Using Multiscale Morphology and Active Contours
inferred← citeshttps://doi.org/10.1007/978-3-642-34141-0_9openalex-snapshot
A Brief Survey on Semi-Lagrangian Schemes for Image Processing
inferred← citeshttps://doi.org/10.1007/978-3-642-36433-4_2openalex-snapshot
An Introduction to the Theory of Viscosity Solutions for First-Order Hamilton–Jacobi Equations and Applications
inferred← citeshttps://doi.org/10.1007/978-3-642-38267-3_14openalex-snapshot
Anisotropic Third-Order Regularization for Sparse Digital Elevation Models
inferred← citeshttps://doi.org/10.1007/978-3-642-42057-3_108openalex-snapshot
A New Image Denoising and Enhancement Method Combining the Nonsubsampled Contourlet Transform and Improved Total Variation
inferred← citeshttps://doi.org/10.1007/978-3-642-44907-9_4openalex-snapshot
Visual Correspondence, the Lambert-Ambient Shape Space and the Systematic Design of Feature Descriptors
inferred← citeshttps://doi.org/10.1007/978-3-642-54774-4_5openalex-snapshot
A Fast Algorithm for a Mean Curvature Based Image Denoising Model Using Augmented Lagrangian Method
inferred← citeshttps://doi.org/10.1007/978-3-642-55627-2_14openalex-snapshot
On Generalized Mean Curvature Flow in Surface Processing
inferred← citeshttps://doi.org/10.1007/978-3-642-55987-7_2openalex-snapshot
A Geometric Model for Image Analysis in Cytology
inferred← citeshttps://doi.org/10.1007/978-3-642-55987-7_3openalex-snapshot
Level Set Models for Analysis of 2D and 3D Echocardiographic Data
inferred← citeshttps://doi.org/10.1007/978-3-642-55987-7_7openalex-snapshot
Nonlinear Multiscale Analysis Models for Filtering of 3D + Time Biomedical Images
inferred← citeshttps://doi.org/10.1007/978-3-642-59073-3_16openalex-snapshot
Variational Methods in Image Restoration
inferred← citeshttps://doi.org/10.1007/978-3-642-60539-0_3openalex-snapshot
Junction Detection and Filtering
inferred← citeshttps://doi.org/10.1007/978-3-642-80294-2_6openalex-snapshot
Anisotropic Diffusion Based on Mean Curvature Motion: A Computational Study
inferred← citeshttps://doi.org/10.1007/978-3-662-05281-5_8openalex-snapshot
On Anisotropic Geometric Diffusion in 3D Image Processing and Image Sequence Analysis
inferred← citeshttps://doi.org/10.1007/978-3-662-45191-5openalex-snapshot
Shape Reconstruction from Apparent Contours: Theory and Algorithms
inferred← citeshttps://doi.org/10.1007/978-3-663-09823-2_16openalex-snapshot
Differential Invariants and Curvature Flows in Active Vision
inferred← citeshttps://doi.org/10.1007/978-3-7091-6215-6_9openalex-snapshot
Nonlinear Diffusion in Graphics Hardware
inferred← citeshttps://doi.org/10.1007/978-3-7091-6586-7_13openalex-snapshot
Theoretical Foundations of Anisotropic Diffusion in Image Processing
inferred← citeshttps://doi.org/10.1007/978-3-7091-6586-7_9openalex-snapshot
A Variational Approach to the Design of Early Vision Algorithms
inferred← citeshttps://doi.org/10.1007/978-3-7643-7984-1_19openalex-snapshot
Preprocessing for Finite Element Discretizations of Geometric Problems
inferred← citeshttps://doi.org/10.1007/978-81-322-2247-7_44openalex-snapshot
A Non-linear Diffusion Based Partial Differential Equation Model for Noise Reduction in Images
inferred← citeshttps://doi.org/10.1007/978-88-470-2089-4_45openalex-snapshot
Linear co-volume scheme for anisotropic curvature driven motions
inferred← citeshttps://doi.org/10.1007/978-94-010-0510-4_11openalex-snapshot
Recent developments in the theory of front propagation and its applications
inferred← citeshttps://doi.org/10.1007/978-94-010-0510-4_8openalex-snapshot
Image processing with partial differential equations
inferred← citeshttps://doi.org/10.1007/978-94-017-1699-4_11openalex-snapshot
Differential Invariant Signatures and Flows in Computer Vision: A Symmetry Group Approach
inferred← citeshttps://doi.org/10.1007/b10404openalex-snapshot
Geometric Curve Evolution and Image Processing
inferred← citeshttps://doi.org/10.1007/b106657_9openalex-snapshot
Flow Visualization via Partial Differential Equations
inferred← citeshttps://doi.org/10.1007/bf00379537openalex-snapshot
Conformal curvature flows: From phase transitions to active vision
inferred← citeshttps://doi.org/10.1007/bfb0015526openalex-snapshot
Three dimensional object modeling via minimal surfaces
inferred← citeshttps://doi.org/10.1007/bfb0028376openalex-snapshot
Area and length preserving geometric invariant scale-spaces
inferred← citeshttps://doi.org/10.1007/bfb0094298openalex-snapshot
Front propagation: Theory and applications
inferred← citeshttps://doi.org/10.1007/bfb0109672openalex-snapshot
Visual tracking, active vision, and gradient flows
inferred← citeshttps://doi.org/10.1007/pl00005479openalex-snapshot
Semi-implicit finite volume scheme for solving nonlinear diffusion equations in image processing
inferred← citeshttps://doi.org/10.1007/pl00011302openalex-snapshot
Connected components of sets of finite perimeter and applications to image processing
inferred← citeshttps://doi.org/10.1007/pl00013547openalex-snapshot
PDE methods in flow simulation post processing
inferred← citeshttps://doi.org/10.1007/s00028-019-00539-zopenalex-snapshot
Large exponent behavior for power-type nonlinear evolution equations and applications
inferred← citeshttps://doi.org/10.1007/s00030-025-01167-yopenalex-snapshot
Some comparison results for first-order Hamilton-Jacobi equations and second-order fully nonlinear parabolic equations with Ventcell boundary conditions
inferred← citeshttps://doi.org/10.1007/s00032-024-00410-yopenalex-snapshot
Minimizing Movements for the Generalized Power Mean Curvature Flow
inferred← citeshttps://doi.org/10.1007/s00190-012-0587-yopenalex-snapshot
Nonlinear diffusion filtering of data on the Earth’s surface
inferred← citeshttps://doi.org/10.1007/s002050050077openalex-snapshot
A New Approach to Front Propagation Problems: Theory and Applications
inferred← citeshttps://doi.org/10.1007/s00208-006-0047-1openalex-snapshot
Gradient estimates for the Perona–Malik equation
inferred← citeshttps://doi.org/10.1007/s002080050179openalex-snapshot
Maximum and comparison principle for one-dimensional anisotropic diffusion
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