Line Drawing Interpretation

By: Martin Cooper

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Hardcover | 3 November 2008

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268 Pages

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The computer interpretation of line drawings is a classic problem in arti?cial intelligence (AI) which has inspired the development of some fundamental AI tools, including constraint propagation, probabilistic relaxation, the characte- zation of tractable constraint classes and, most recently, the propagationof soft constraintsin?nite-domainoptimizationproblems. Line drawinginterpretation has many distinct applications on the borderline of computer vision and c- puter graphics, including sketch interpretation, the input of 3D object models 1 and the creation of 2 D illustrations in electronic documents. 2 I hope I have made this fascinating topic accessible not only to computer scientistsbutalsotomathematicians,psychologistsandcognitivescientistsand, indeed, to anyone who is intrigued by optical illusions and impossible or - biguous ?gures. This book could not have been written without the support of the CNRS, theFrenchCentreNational deRecherche Scienti?que,who?nancedmyone-year break from teaching at the University of Toulouse III. The UK Engineering and Physical Sciences Research Council also ?nanced several extended visits to the Oxford University Computing Laboratory. Section 9.1 is just a brief summary of the results on tractable constraints that have come out of this very productive joint research programme with David Cohen, Peter Jeavons and Andrei Krokhin. The various soft arc consistency techniques described in Chapter 8 were developed in collaboration with Thomas Schiex and Simon de Givry at INRA, Toulouse. I am also grateful to Ralph Martin and Peter Varley for their comments on the line-labelling constraints presented in Chapter 3.

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You Can Find This Book In

Non-Fiction Computing & I.T.Computer Science Artificial Intelligence Computer Vision Image Processing Psychology Cognition & Cognitive Psychology Graphical & Digital Media Applications Mathematics Mathematical Foundation Mathematical Logic

Databases Data Capture & Analysis

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Published: 10th October 2011

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Preface	p. v
Introduction	p. 1
Impossible Pictures	p. 5
Losing the Third Dimension	p. 7
Two Planar Surfaces	p. 8
Depth Order of Surfaces at a Point	p. 10
Cubic Corners and Improbable Objects	p. 12
Impossible Intersections	p. 14
Impossible Wireframe Projections	p. 17
Labeling Line Drawings of Polyhedra	p. 21
Historical Background	p. 21
Line Drawing Labelling as Optimization	p. 25
Parallel-Lines Constraint	p. 26
A Universal Constraint for Simple Junctions	p. 32
Lines Sharing the Same Two Regions	p. 38
Cyclic-Path Constraint	p. 41
Parallel Junctions on Distinct Faces	p. 44
Encoding of Soft Constraints	p. 50
Non-Manifold Scenes	p. 52
Discussion	p. 52
Discrete Inflation Using Cubic Corners	p. 55
Computer-Enhanced Perception	p. 55
Machine Interpretation of Line Drawings	p. 56
Depth Labels	p. 57
Depth Labels and Impossible Figures	p. 61
Propagation of Depth Labels	p. 65
Orthogonality Constraints on Cubic Corners	p. 67
Experimental Trials	p. 70
Adding Depth Information to Line Drawings	p. 72
Vertices Which Are Not Cubic Corners	p. 73
Discussion	p. 75
Conclusion	p. 76
A Rich Labeling Scheme for Curved Objects	p. 79
Labeling Line Drawings of Curved Objects	p. 79
Regularities in Man-Made Objects	p. 82
Planarity Constraints	p. 84
Constraints from Orthogonal Edges	p. 87
Examples of Drawing Interpretation	p. 91
Complete 3D Reconstruction	p. 94
Discussion	p. 95
Depth Recovery Through Linear Algebra	p. 97
Gradient Space and Gradient Directions	p. 97
Linear Constraints and Curved Objects	p. 100
Formulation of Linear Constraints	p. 102
Deriving Linear Constraints from a Drawing	p. 105
Vanishing Point Constraint	p. 105
Constraints from Collinearity or Intersections	p. 105
T-junction Constraint	p. 106
Convex/Concave Edge Constraints	p. 107
Coplanarity Constraints	p. 112
Hidden-Surface Coplanarity Constraints	p. 114
Orthographic Projection	p. 117
Physical Realizability of Drawings	p. 118
The Computational Problem	p. 119
Conclusion	p. 122
Wireframe Projections	p. 125
Introduction	p. 125
Semantic and Numerical Line Labels	p. 127
Realizability	p. 130
All Wireframes Are Ambiguous	p. 141
Identifying Faces	p. 142
Common-Surface Constraints	p. 146
Coplanarity Constraints	p. 147
Unambiguous Wireframes	p. 150
Residual Ambiguity	p. 153
Constraints Between Distant Lines	p. 155
Tetrahedral Vertices	p. 163
Tangential Edges and Surfaces	p. 169
Rich Labelling Scheme	p. 173
Discussion	p. 178
Conclusion	p. 180
Simplification of Combinatorial Problems	p. 183
Transformations of Combinatorial Problems	p. 183
When Local Reductions Suffice	p. 185
Arc Consistency	p. 187
Neighbourhood Substitution	p. 189
Simplification of Soft Constraint Problems	p. 191
Valuation Structures	p. 192
Valued Constraint Satisfaction	p. 194
Soft Arc Consistency Techniques	p. 195
Optimal Soft Arc Consistency	p. 198
Virtual Arc Consistency	p. 203
VAC Decomposition	p. 209
Soft Neighbourhood Substitution	p. 212
Discussion	p. 214
Tractability of Drawing Interpretation	p. 217
Tractable Constraint Classes	p. 217
Zero/One/All Constraints	p. 217
Max-Closed Constraints	p. 219
Characterization of Tractable Boolean Constraints	p. 220
Characterization of Tractable Boolean Valued Constraints	p. 221
Complexity of Line Drawing Interpretation	p. 224
3D Reconstruction of Ambiguous Pictures	p. 231
Reconstruction of Frontal Geometry	p. 231
Hidden-Part Reconstruction	p. 233
Bibliography	p. 237
Index	p. 251
Table of Contents provided by Ingram. All Rights Reserved.

Line Drawing Interpretation

At a Glance

Hardcover

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Other Editions and Formats

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