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The singularities of the visual mapping

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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 Singularities of Mappings of Euclidean Spaces. I. Mappings of the Plane Into the Plane
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Stable Mappings and Their Singularities
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Visual perception of rigidity of solid shape
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Geometry of binocular vision and a model for stereopsis
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Das Reafferenzprinzip
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Vorlesungen über Differentialgeometrie
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Handbuch der physiologischen Optik
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Geometry and the Imagination
inferredcites →https://doi.org/10.1016/0304-422x(74)90010-2openalex-snapshot
Stabilité structurelle et morphogenèse
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Mappings of the plane into the plane
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What is a form?
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Mind and Matter
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Qualitative Theory of Second-Order Dynamic Systems
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Optical Velocity Patterns, Velocity-Sensitive Neurons, and Space Perception: A Hypothesis
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The Surrogate Functions of Lines in Visual Perception: Evidence from Antipodal Rock and Cave Artwork Sources
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Outline Picture Perception by the Songe of Papua
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Invariant Properties of the Motion Parallax Field Due to the Movement of Rigid Bodies Relative to an Observer
inferredcites →https://doi.org/10.1145/1476589.1476631openalex-snapshot
Decomposition of a visual scene into three-dimensional bodies
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Reflection and Refraction at a Random Moving Surface I Pattern and Paths of Specular Points
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Local structure of movement parallax of the plane
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The Senses Considered as Perceptual Systems
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Gesetze des Sehens
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The Perception of the Visual World
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On Singularities of Mappings of Euclidean Spaces. I. Mappings of the Plane into the Plane
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Lectures on Classical Differential Geometry.
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The Senses Considered as Perceptual Systems

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Optics, Physiological
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Aspect graphs: An introduction and survey of recent results
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Repetitive Hidden Surface Removal for Polyhedra
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Computing View Graphs of Algebraic Surfaces
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A New 3-D Model Retrieval System Based on Aspect-Transition Descriptor
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Object Recognition in the Geometric Era: A Retrospective
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Efficient Pose Estimation Using View-Based Object Representations
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How Folds Cut a Scene
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Shape Models and Object Recognition
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Repetitive hidden-surface-removal for polyhedral scenes
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Topological reconstruction of a smooth manifold-solid from its occluding contour
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Spherical representations: From EGI to SAI
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Combinatorial geometry for shape representation and indexing
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Structure vs. Appearance and 3D vs. 2D? A Numeric Answer
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The Role of Shape in Visual Recognition
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Shade, Shadow and Shape
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The Empirical Study of Structure from Motion
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3DPO: A Three-Dimensional Part Orientation System
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Panel Summary Looking For Visual Primitives
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Aspect Graph
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Aspect Graph
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Géométrie Algébrique Réelle
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The Structure and Motion of Surfaces
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Aspect graphs of bodies of revolution with algorithms of real algebraic geometry
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Introduction
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Overview
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Apparent Contours for Projections of Smooth Surfaces
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Singularity Equivalence Groups Capturing Interactions
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Preface
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Multi-view Object Categorization and Pose Estimation
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On the Computation of 3D Visibility Skeletons
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Landmarks for Neurogeometry
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Shape from Motion
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Indexing via Color Histograms
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Geometry of Vision
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A Neural Architecture for Emergent Visual Contrast, Brightness, and Space Perception
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CAD-Based Computer Vision: The Automatic Generation of Recognition Strategies
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A Variational Model on Labelled Graphs with Cusps and Crossings
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Hierarchical Visibility in Terrains
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Space, Form and Optical Deformations
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Computing exact aspect graphs of curved objects: Solids of revolution
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A topological stereo matcher
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Surface shape from the deformation of apparent contours
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The schema system
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Viewer-centred and object-centred coding of heads in the macaque temporal cortex
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The internal representation of solid shape with respect to vision
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On the number of views of polyhedral terrains
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Seeing—the mathematical viewpoint
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Le Physique, le Morphologique, le Symbolique
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Efficient pose estimation using view-based object representations
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3D object recognition based on a geometrical topology model and extreme learning machine
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Families of spherical surfaces and harmonic maps
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Topological and Variational Properties of a Model for the Reconstruction of Three-Dimensional Transparent Images with Self-Occlusions
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Local Image Features Resulting from 3-Dimensional Geometric Features, Illumination, and Movement: I
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Topology aware view path design for time-varying volume data
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The geometry of view space of opaque objects bounded by smooth surfaces
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Global surface reconstruction by purposive control of observer motion
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Parts of recognition
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Scene-based and viewer-centered representations for comparing shapes
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Generating aspect graphs for nonconvex polyhedra
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A probabilistic spatial data model
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3-D multiview object representations for model-based object recognition
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Endstopping and curvature
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Object classification for human and ideal observers
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On determining non-isotopic configurations of points on a circle
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On the classification of views of piecewise smooth objects
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Recognition of generic components using logic-program relations of image contours
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Semi-algebraic solids in 3-space: a survey of modelling schemes and implications for view graphs
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A shape representation for computer vision based on differential topology
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Singularités et photographies de surfaces
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Invariant surface characteristics for 3D object recognition in range images
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Computing occluding contours using spherical images
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Parts of recognition**We are grateful to Thomas Banchoff, Aaron Bobick, Mike Brady, Carmen Egido, Jerry Fodor, Jim Hodgson, Jan Koenderink, Jay Lebed, Alex Pentland, John Rubin, Joseph Scheuhammer, and Andrew Witkin for their helpful discussions and. in some cases, for reading earlier drafts. We…
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Models of Static Form Perception
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Visible Information about Structure from Motion
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Pictures and Their Special Status in Perceptual and Cognitive Inquiry
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Geometric Modelling and Spatial Reasoning
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Color Indexing Received January 22, 1991. Revised Jane 6, 1991.
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The perception of 3-D shape from shadows cast onto curved surfaces
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Effect of planar cuts’ orientation on the perceived surface layout and object’s shape
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Three-dimensional shape searching: state-of-the-art review and future trends
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The visual hull of piecewise smooth objects
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Distance perception during self-movement
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An accidental image feature that appears but not disappears
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Boundaries, shading, and border ownership: A cusp at their interaction
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3D object recognition based on pairwise Multi-view Convolutional Neural Networks
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Probabilistic 3D object recognition from 2D invariant view sequence based on similarity
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A survey of visual insight mining: Connecting data and insights via visualization
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Complexity of mental geometry for 3D pose perception
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What defines a view?
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Definition and detection of binocular disparity
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Hot curves for modelling and recognition of smooth curved 3D objects
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The visual potential: One convex polygon
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Retrieval of Shape from Silhouette
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Singularities of Illuminated Surfaces
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Topological Reconstruction of a Smooth Manifold-Solid from Its Occluding Contour
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On Computing Structural Changes in Evolving Surfaces and their Appearance
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A Similarity-Based Aspect-Graph Approach to 3D Object Recognition
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Curve and Surface Duals and the Recognition of Curved 3D Objects from their Silhouettes
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A contour propagation approach to surface filling-in and volume formation.
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Ordinal structure in the visual perception and cognition of smoothly curved surfaces.
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Perception of structure from motion: Is projective correspondence of moving elements a necessary condition?
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Viewpoint-dependent mechanisms in visual object recognition: Reply to Tarr and Bülthoff (1995).
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Perceptual localization of surface position.
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Seeing two sides at once: Effects of viewpoint and object structure on recognizing three-dimensional objects.
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Three-dimensional illusory contours and surfaces
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Illusion and view stability
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Comparing Sky Shape Skeletons for the Analysis of Visual Dynamics along Routes
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What Does the Occluding Contour Tell Us about Solid Shape?
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Characteristic Views and the Visual Inspection of Simple Faceted and Smooth Objects: ‘Tetrahedra and Potatoes’
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The Discriminability of Smooth Stereoscopic Surfaces
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Use of Preferential Inspection to Define the Viewing Sphere and Characteristic Views of an Arbitrary Machined Tool Part
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Guest Editorial: Perceptual Organisation and Object Recognition—POOR is the Acronym, Rich the Notion
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Aspect Graphs for Visual Recognition of Three-Dimensional Objects
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‘Generic-View Principle’ for Three-Dimensional-Motion Perception: Optics and Inverse Optics of a Moving Straight Bar
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A Code-Theoretical Note on Object Handedness
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The Perception and Recognition of Natural Object Shape from Deforming and Static Shadows
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The Role of Junctions in Surface Completion and Contour Matching
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Information Concentration along the Boundary Contours of Naturally Shaped Solid Objects
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The Influence of Illumination Direction on the Pictorial Reliefs of Lambertian Surfaces
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A topological solution to object segmentation and tracking
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The reasonable effectiveness of contours in vision
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CAGD-based computer vision
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Computing the aspect graph for line drawings of polyhedral objects
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Logical/linear operators for image curves
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Toward accurate recovery of shape from shading under diffuse lighting
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Efficiently computing and representing aspect graphs of polyhedral objects
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Geometric modeling and computer vision
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Efficiently Computing And Representing Aspect Graphs Of Polyhedral Objects
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Towards The Automatic Generation Of Recognition Strategies
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HOT curves for modelling and recognition of smooth curved 3D objects
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Fast 2D border ownership assignment
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Probing the 3D Awareness of Visual Foundation Models
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An experimental evaluation of view-based 2D/3D indexing methods
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Representing surface curvature discontinuities on curved surfaces
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Indexing via color histograms
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3D object recognition using shape similiarity-based aspect graph
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Folds and cuts: how shading flows into edges
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3D generic object categorization, localization and pose estimation
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Learning a dense multi-view representation for detection, viewpoint classification and synthesis of object categories
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Multi-view Convolutional Neural Networks for 3D Shape Recognition
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Render for CNN: Viewpoint Estimation in Images Using CNNs Trained with Rendered 3D Model Views
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Object spatial recognition for service robots: Where is the front?
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3D object recognition technique based on muti-resolution aspect graph
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Trajectory tracking among landmarks and binary sensor-beams
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Polyhedral object recognition using view densities
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Shape Memorization and Recognition of 3D Objects Using a Similarity-Based Aspect-Graph Approach
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3D Object Tracking Using Mean-Shift and Similarity-Based Aspect-Graph Modeling
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An Isomap-Eigenanalysis-Regression Pose Estimation Algorithm of Three-Dimentional Object
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Emergent segmentation of monocular visual invariants for space perception
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SkipMard: a multi-attribute peer-to-peer resource discovery approach
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Generating an aspect graph by set operations on sets of viewpoints
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Wavelet Method for CT Colonography Computer-Aided Polyp Detection
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Visual recognition of CAD objects with aspect graphs
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On computing aspect graphs of smooth shapes from volumetric data
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2D-3D registration based on shape matching
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Scene Analysis For Navigation Tasks And Robotics Using A Harmony Theory Network
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Structure-aware viewpoint selection for volume visualization
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Visibility in the presence of occluders with curved boundaries
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Finding the limbs and cusps of generalized cylinders
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Computing the aspect graph for line drawings of polyhedral objects
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Provable strategies for vision-guided exploration in three dimensions
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3-D Human Posture Recognition System Using 2-D Shape Features
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Learning Combinatorial Information from Alignments of Landmarks
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Active multi-view object search on a humanoid head
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Information spaces for mobile robots
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Diversity and emergence in biomedical imaging
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Generating aspect graphs for curved objects
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3-D Object Recognition Using 2-D Views
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