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Shapes, shocks, and deformations I: The components of two-dimensional shape and the reaction-diffusion space
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
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The partial differential equation u t + uu x = μ xx
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Hyperbolic systems of conservation laws II
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On Affine Plane Curve Evolution
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Controlled Markov Processes and Viscosity Solutions
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Shock Waves and Reaction—Diffusion Equations
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Numerical Methods for Propagating Fronts
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Shock Waves and Reaction—Diffusion Equations
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Mathematical Methods of Classical Mechanics
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The Design of Algorithms for Hypersurfaces Mowing with Curvature-Dependent Speed
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Recognising and Locating Partially Visible Objects: The Local-Feature-Focus Method
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Constructing simple stable descriptions for image partitioning
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Fourier transform magnitudes are unique pattern recognition templates
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Curvature and the evolution of fronts
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Toward a computational theory of shape: An overview
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Inferring surfaces from images
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Symbolic reasoning among 3-D models and 2-D images
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A process-grammar for shape
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Shape instabilities and pattern formation in solidification: A new method for numerical solution of the moving boundary problem
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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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Biological shape and visual science (part I)
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Implementing continuous-scale morphology via curve evolution
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The effect of contour closure on the rapid discrimination of two-dimensional shapes
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Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations
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Image analysis and mathematical morphology
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Morphological transformations of binary images with arbitrary structuring elements
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Inferring causal history from shape
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Codon constraints on closed 2D shapes
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Symmetry-curvature duality
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SCALE-SPACE FILTERING
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Shock Waves and Entropy
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An iterative procedure for the polygonal approximation of plane curves
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An efficient three-dimensional aircraft recognition algorithm using normalized fourier descriptors
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Preattentive processing in vision
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Recognition-by-components: A theory of human image understanding.
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Some informational aspects of visual perception.
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Psychophysical support for a two-dimensional view interpolation theory of object recognition.
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Viscosity solutions of Hamilton-Jacobi equations
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User’s guide to viscosity solutions of second order partial differential equations
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Discontinuous solutions of non-linear differential equations
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Representation and recognition of the spatial organization of three-dimensional shapes
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Instabilities and pattern formation in crystal growth
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Parts of visual form: computational aspects
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Recovery of parametric models from range images: the case for superquadrics with global deformations
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Scale-space and edge detection using anisotropic diffusion
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Recovering shape from contour for constant cross section generalized cylinders
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Evolution equations for continuous-scale morphology
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Mathematical morphology: The Hamilton-Jacobi connection
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The Representation and Matching of Pictorial Structures
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Fourier Preprocessing for Hand Print Character Recognition
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Fourier Descriptors for Plane Closed Curves
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Cell Tracking: A Modeling and Minimization Approach
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The Curvature Primal Sketch
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Scale-Based Description and Recognition of Planar Curves and Two-Dimensional Shapes
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Multiple Resolution Skeletons
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Hierarchical Shape Description Via the Multiresolution Symmetric Axis Transform
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Shape Discrimination Using Fourier Descriptors
inferredcites →https://doi.org/10.1117/12.146627openalex-snapshot
Nonlinear shape approximation via the entropy scale space
inferredcites →https://doi.org/10.1137/0729052openalex-snapshot
Image Selective Smoothing and Edge Detection by Nonlinear Diffusion. II
inferredcites →https://doi.org/10.1137/1.9781611970562openalex-snapshot
Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves
inferredcites →https://doi.org/10.1137/1.9781611971309openalex-snapshot
Optimization and Nonsmooth Analysis
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Computer Processing of Line-Drawing Images
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Strip trees: a hierarchical representation for curves
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Two Stages of Curve Detection Suggest Two Styles of Visual Computation
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Part Segmentation for Object Recognition
inferredcites →https://doi.org/10.1163/156856887x00187openalex-snapshot
Sensitivity to corners in flow patterns
inferredcites →https://doi.org/10.1177/027836498200100304openalex-snapshot
Recognizing and Locating Partially Visible Objects: The Local-Feature-Focus Method
inferredcites →https://doi.org/10.1364/josaa.3.001483openalex-snapshot
Encoding contour shape by curvature extrema
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The zero set of a solution of a parabolic equation.
inferredcites →https://doi.org/10.4310/jdg/1214439902openalex-snapshot
The heat equation shrinking convex plane curves
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Numerical algorithms for propagating interfaces: Hamilton-Jacobi equations and conservation laws
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Differential geometry of curves and surfaces
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Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Zoom-Invariant Vision of Figural Shape
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Convexity Rule for Shape Decomposition Based on Discrete Contour Evolution
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Contour Fragment Grouping and Shared, Simple Occluders
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Ligature Instabilities in the Perceptual Organization of Shape
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Measuring the Performance of Shape Similarity Retrieval Methods
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Geometric Shock-Capturing ENO Schemes for Subpixel Interpolation, Computation and Curve Evolution
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Contrast Enhancement via Image Evolution Flows
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A Hierarchical Markov Modeling Approach for the Segmentation and Tracking of Deformable Shapes
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An Even Faster and More Unifying Algorithm for Comparing Trees via Unbalanced Bipartite Matchings
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Histogram Modification via Differential Equations
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Symmetry-Based Indexing of Image Databases
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Reconciling Distance Functions and Level Sets
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Surface Evolution under Curvature Flows
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Geometric Regularizers for Level Sets
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Mean Curvature Flows, Edge Detection, and Medical Image Segmentation
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Partial Differential Equations for Morphological Operators
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2D Shape Modeling using Skeletal Graphs in a Morse Theoretic Framework
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Optimal Embedding for Shape Indexing in Medical Image Databases
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Structural and Textural Skeletons for Noisy Shapes
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Polygon Decomposition Based on the Straight Line Skeleton
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Towards Feature Fusion - The Synthesis of Contour Sections Distinguishing Contours from Different Classes
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Discovering Shape Categories by Clustering Shock Trees
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Efficiently Computing Weighted Tree Edit Distance Using Relaxation Labeling
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Region Matching with Missing Parts
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Boolean Operations on Free Form Shapes in a Level Set Framework
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/10.1007/978-981-19-0105-8_23openalex-snapshot
Skeletonization and Its Application to Quantitative Structural Imaging
inferred← citeshttps://doi.org/10.1007/bf00379537openalex-snapshot
Conformal curvature flows: From phase transitions to active vision
inferred← citeshttps://doi.org/10.1007/bf01539551openalex-snapshot
Shape from shading: Level set propagation and viscosity solutions
inferred← citeshttps://doi.org/10.1007/bfb0015526openalex-snapshot
Three dimensional object modeling via minimal surfaces
inferred← citeshttps://doi.org/10.1007/bfb0054730openalex-snapshot
Matching hierarchical structures using association graphs
inferred← citeshttps://doi.org/10.1007/bfb0056308openalex-snapshot
Segmentation of carpal bones from 3D CT images using skeletally coupled deformable models
inferred← citeshttps://doi.org/10.1007/bfb0105775openalex-snapshot
A level-set approach for eddy current imaging of defects in a conductive half-space
inferred← citeshttps://doi.org/10.1007/bfb0109672openalex-snapshot
Visual tracking, active vision, and gradient flows
inferred← citeshttps://doi.org/10.1007/s00013-016-1010-3openalex-snapshot
Group invariant solutions to a centro-affine invariant flow
inferred← citeshttps://doi.org/10.1007/s00158-012-0846-9openalex-snapshot
Shape equilibrium constraint: a strategy for stress-constrained structural topology optimization
inferred← citeshttps://doi.org/10.1007/s002110050294openalex-snapshot
Minimal surfaces: a geometric three dimensional segmentation approach
inferred← citeshttps://doi.org/10.1007/s00371-013-0857-6openalex-snapshot
A nonlinear level set model for image deblurring and denoising
inferred← citeshttps://doi.org/10.1007/s003710050118openalex-snapshot
Warp-guided object-space morphing
inferred← citeshttps://doi.org/10.1007/s00466-008-0287-xopenalex-snapshot
Topology optimization of thermoelastic structures using level set method
inferred← citeshttps://doi.org/10.1007/s00500-002-0171-0openalex-snapshot
Towards a singularity-based shape language: ridges, ravines, and skeletons for polygonal surfaces
inferred← citeshttps://doi.org/10.1007/s00500-018-3491-4openalex-snapshot
New level set approach based on Parzen estimation for stroke segmentation in skull CT images
inferred← citeshttps://doi.org/10.1007/s10044-021-01039-yopenalex-snapshot
A novel fully parallel skeletonization algorithm
inferred← citeshttps://doi.org/10.1007/s100440200006openalex-snapshot
Fusion of Region and Boundary/Surface-Based Computer Vision and Pattern Recognition Techniques for 2-D and 3-D MR Cerebral Cortical Segmentation (Part-II): A State-of-the-Art Review
inferred← citeshttps://doi.org/10.1007/s10851-006-7249-8openalex-snapshot
Harmonic Embeddings for Linear Shape Analysis
inferred← citeshttps://doi.org/10.1007/s10851-006-9004-6openalex-snapshot
A New Active Convex Hull Model for Image Regions
inferred← citeshttps://doi.org/10.1007/s10851-011-0291-1openalex-snapshot
A Pruning Algorithm for Stable Voronoi Skeletons
inferred← citeshttps://doi.org/10.1007/s10851-026-01319-4openalex-snapshot
Skeleton Sparsification and Densification Scale-Spaces
inferred← citeshttps://doi.org/10.1007/s11042-015-3196-yopenalex-snapshot
Morphological region-based initial contour algorithm for level set methods in image segmentation
inferred← citeshttps://doi.org/10.1007/s11042-016-4173-9openalex-snapshot
Real-time recognition of medial structures within hand postures through Eigen-space and geometric skeletal shape features
inferred← citeshttps://doi.org/10.1007/s11045-015-0365-0openalex-snapshot
A novel method for image segmentation using reaction–diffusion model
inferred← citeshttps://doi.org/10.1007/s11263-006-6121-zopenalex-snapshot
2D-Shape Analysis Using Conformal Mapping
inferred← citeshttps://doi.org/10.1007/s11263-006-8929-yopenalex-snapshot
Discovering Shape Classes using Tree Edit-Distance and Pairwise Clustering
inferred← citeshttps://doi.org/10.1007/s11263-007-0045-0openalex-snapshot
Statistical Multi-Object Shape Models
inferred← citeshttps://doi.org/10.1007/s11263-007-0054-zopenalex-snapshot
Prior Knowledge, Level Set Representations & Visual Grouping
inferred← citeshttps://doi.org/10.1007/s11263-009-0286-1openalex-snapshot
An Approach to the Parameterization of Structure for Fast Categorization
inferred← citeshttps://doi.org/10.1007/s11263-010-0366-2openalex-snapshot
Highly Accurate Schemes for PDE-Based Morphology with General Convex Structuring Elements
inferred← citeshttps://doi.org/10.1007/s11263-010-0412-0openalex-snapshot
Skeleton Search: Category-Specific Object Recognition and Segmentation Using a Skeletal Shape Model
inferred← citeshttps://doi.org/10.1007/s11263-012-0521-zopenalex-snapshot
Shape-Based Object Detection via Boundary Structure Segmentation
inferred← citeshttps://doi.org/10.1007/s11390-005-0009-1openalex-snapshot
Polygonal Shape Blending with Topological Evolutions
inferred← citeshttps://doi.org/10.1007/s13131-024-2460-2openalex-snapshot
Separation between water and land in synthetic aperture radar images based on improved level set model
inferred← citeshttps://doi.org/10.1016/0042-6989(94)00286-uopenalex-snapshot
Object representation by cores: Identifying and representing primitive spatial regions
inferred← citeshttps://doi.org/10.1016/0042-6989(95)00106-9openalex-snapshot
Linking object boundaries at scale: a common mechanism for size and shape judgments
inferred← citeshttps://doi.org/10.1016/0895-7177(96)00117-3openalex-snapshot
Three snippets of curve evolution theory in computer vision
inferred← citeshttps://doi.org/10.1016/b978-0-08-101291-8.00002-xopenalex-snapshot
Skeletonization and its applications – a review
inferred← citeshttps://doi.org/10.1016/b978-0-08-101291-8.00012-2openalex-snapshot
Characterization of trabecular bone plate–rod micro-architecture using skeletonization and digital topologic and geometric analysis
inferred← citeshttps://doi.org/10.1016/b978-012119792-6/50098-xopenalex-snapshot
PDEs for Morphological Scale Spaces and Eikonal Applications
inferred← citeshttps://doi.org/10.1016/b978-012500451-0/50008-4openalex-snapshot
Nonlinear Partial Differential Equations in Image Processing
inferred← citeshttps://doi.org/10.1016/j.actpsy.2006.02.004openalex-snapshot
Surface geometry influences the shape of illusory contours
inferred← citeshttps://doi.org/10.1016/j.apm.2010.04.003openalex-snapshot
Level set evolution for boundary extraction based on a p-Laplace equation
inferred← citeshttps://doi.org/10.1016/j.apm.2011.10.023openalex-snapshot
Adaptive level set evolution starting with a constant function
inferred← citeshttps://doi.org/10.1016/j.asoc.2016.03.004openalex-snapshot
A survey on image segmentation using metaheuristic-based deformable models: state of the art and critical analysis
inferred← citeshttps://doi.org/10.1016/j.cag.2016.05.009openalex-snapshot
The 2D shape structure dataset: A user annotated open access database
inferred← citeshttps://doi.org/10.1016/j.cag.2024.103947openalex-snapshot
Topological 3D reconstruction of multiple anatomical structures from volumetric medical data
inferred← citeshttps://doi.org/10.1016/j.cognition.2005.03.004openalex-snapshot
Segmentation of object outlines into parts: A large-scale integrative study
inferred← citeshttps://doi.org/10.1016/j.cogpsych.2016.08.002openalex-snapshot
Visual perception of complex shape-transforming processes
inferred← citeshttps://doi.org/10.1016/j.compmedimag.2005.09.002openalex-snapshot
Segmentation of cardiac cine-MR images and myocardial deformation assessment using level set methods
inferred← citeshttps://doi.org/10.1016/j.compmedimag.2013.12.005openalex-snapshot
Biomedical image segmentation using geometric deformable models and metaheuristics
inferred← citeshttps://doi.org/10.1016/j.cviu.2004.03.006openalex-snapshot
A skeletal measure of 2D shape similarity
inferred← citeshttps://doi.org/10.1016/j.cviu.2004.10.007openalex-snapshot
Gray skeletons and segmentation of shapes
inferred← citeshttps://doi.org/10.1016/j.cviu.2004.11.001openalex-snapshot
Force field feature extraction for ear biometrics
inferred← citeshttps://doi.org/10.1016/j.cviu.2005.06.005openalex-snapshot
A new shape descriptor defined on the Radon transform
inferred← citeshttps://doi.org/10.1016/j.cviu.2007.09.013openalex-snapshot
Strategies for shape matching using skeletons
inferred← citeshttps://doi.org/10.1016/j.cviu.2009.04.001openalex-snapshot
Surface reconstruction from point clouds by transforming the medial scaffold
inferred← citeshttps://doi.org/10.1016/j.cviu.2021.103243openalex-snapshot
Near-convex decomposition of 2D shape using visibility range
inferred← citeshttps://doi.org/10.1016/j.dam.2004.09.015openalex-snapshot
Expanding selfsimilar solutions of a crystalline flow with applications to contour figure analysis
inferred← citeshttps://doi.org/10.1016/j.dsp.2020.102852openalex-snapshot
Challenges, taxonomy and techniques of iris localization: A survey
inferred← citeshttps://doi.org/10.1016/j.imavis.2003.11.006openalex-snapshot
Deformable model-guided region split and merge of image regions
inferred← citeshttps://doi.org/10.1016/j.imavis.2005.07.021openalex-snapshot
Region matching with missing parts
inferred← citeshttps://doi.org/10.1016/j.imavis.2008.10.003openalex-snapshot
A game–theoretic approach to partial clique enumeration
inferred← citeshttps://doi.org/10.1016/j.imavis.2010.11.005openalex-snapshot
3D block-based medial axis transform and chessboard distance transform based on dominance
inferred← citeshttps://doi.org/10.1016/j.imavis.2011.09.009openalex-snapshot
Spaces and manifolds of shapes in computer vision: An overview
inferred← citeshttps://doi.org/10.1016/j.imavis.2012.11.002openalex-snapshot
On growth and formlets: Sparse multi-scale coding of planar shape
inferred← citeshttps://doi.org/10.1016/j.isprsjprs.2007.01.002openalex-snapshot
Generalization of 3D building data based on a scale-space approach
inferred← citeshttps://doi.org/10.1016/j.isprsjprs.2007.08.008openalex-snapshot
Object extraction in photogrammetric computer vision
inferred← citeshttps://doi.org/10.1016/j.isprsjprs.2024.10.024openalex-snapshot
3D point cloud regularization method for uniform mesh generation of mining excavations
inferred← citeshttps://doi.org/10.1016/j.jmaa.2008.05.082openalex-snapshot
Symmetry reductions and exact solutions of the affine heat equation
inferred← citeshttps://doi.org/10.1016/j.jphysparis.2003.09.003openalex-snapshot
On the role of medial geometry in human vision
inferred← citeshttps://doi.org/10.1016/j.jphysparis.2003.09.015openalex-snapshot
Computations in the early visual cortex
inferred← citeshttps://doi.org/10.1016/j.jphysparis.2012.08.001openalex-snapshot
Local field potentials and border ownership: A conjecture about computation in visual cortex
inferred← citeshttps://doi.org/10.1016/j.jvcir.2013.01.001openalex-snapshot
Perceptually friendly shape decomposition by resolving segmentation points with minimum cost
inferred← citeshttps://doi.org/10.1016/j.media.2008.02.003openalex-snapshot
A geometric flow for segmenting vasculature in proton-density weighted MRI
inferred← citeshttps://doi.org/10.1016/j.media.2010.01.001openalex-snapshot
Optimal embedding for shape indexing in medical image databases
inferred← citeshttps://doi.org/10.1016/j.media.2021.102020openalex-snapshot
Fitting unbranching skeletal structures to objects
inferred← citeshttps://doi.org/10.1016/j.neucom.2007.11.033openalex-snapshot
Isotree: Tree clustering via metric embedding
inferred← citeshttps://doi.org/10.1016/j.neucom.2015.11.023openalex-snapshot
Deformable models direct supervised guidance: A novel paradigm for automatic image segmentation
inferred← citeshttps://doi.org/10.1016/j.neuroimage.2004.02.004openalex-snapshot
Deformable model with surface registration for hippocampal shape deformity analysis in schizophrenia
inferred← citeshttps://doi.org/10.1016/j.neuroimage.2008.10.051openalex-snapshot
Continuous medial representation of brain structures using the biharmonic PDE
inferred← citeshttps://doi.org/10.1016/j.patcog.2004.12.015openalex-snapshot
Segmentation of external force field for automatic initialization and splitting of snakes
inferred← citeshttps://doi.org/10.1016/j.patcog.2006.08.007openalex-snapshot
The multiresolution gradient vector field skeleton
inferred← citeshttps://doi.org/10.1016/j.patcog.2008.12.029openalex-snapshot
Graph characteristics from the heat kernel trace
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