## Machine Interpretation of Line DrawingsThis book solves a long-standing problem in computer vision, the interpretation of line drawings and, in doing so answers many of the concerns raised by this problem, particularly with regard to errors in the placement of lines and vertices in the images. Sugihara presents a computational mechanism that functionally mimics human perception in being able to generate three-dimensional descriptions of objects from two-dimensional line drawings. The objects considered are polyhedrons or solid objects bounded by planar faces, and the line drawings are single-view pictures of these objects. Sugihara's mechanism has several potential applications. It can facilitate man-machine communication by extracting object structures automatically from pictures drawn by a designer, which can be particularly useful in the computer-aided design of geometric objects, such as mechanical parts and buildings. It can also be used in the intermediate stage of computer vision systems used to obtain and analyze images in the outside world. The computational mechanism itself is not accompanied by a large database but is composed of several simple procedures based on linear algebra and combinatorial theory. Contents:Introduction. Candidates for Spatial Interpretation. Discrimination between Correct and Incorrect Pictures. Correctness of HiddenPart-Drawn Pictures. Algebraic Structures of Line Drawings. Combinatorial Structures of Line Drawings. Overcoming Superstrictness. Algorithmic Aspects of Generic Reconstructibility. Specification of Unique Shapes. Recovery of Shape from Surface Information. Polyhedrons and Rigidity.Kokichi Sugihara is Professor in the Department of Mathematical Engineering and instrumentation Physics, Faculty of Engineering, the University of Tokyo, Tokyo, Japan. Machine interpretation of Line Drawingsis included in The MIT Press Series in Artificial Intelligence, edited by Patrick Henry Winston and Michael Brady. |

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### Contents

Candidates for Spatial Interpretations | 13 |

Discrimination between Correct and Incorrect Pictures | 40 |

Correctness of HiddenPartDrawn Pictures | 64 |

Copyright | |

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### Common terms and phrases

Assumption augmentable path axis axonometric bipartite graph boundary collinear components condition configurations consider consistent constraint convex coordinate coplanar Corollary corresponding defined degrees of freedom delete denote edges elements equations 5.1 equilibrium vector exactly example face-layer structure gradient space hence hidden-part-drawn line drawing hidden-part-drawn pictures hidden-part-eliminated incidence pairs incidence structure incorrect inequalities interpretation intersection junction labeled line drawing labeled picture left node light intensity line segments linear linear programming linearly independent matrix matroid maximal generically reconstructible method module obtained occluding line octant orthographic projection panels parallel partition perspective projection picture plane planar-panel scene polyhedral scene polyhedron problem PROPERLY-FRONT Proposition reconstructible substructure represents a polyhedral rigid rows satisfies shape shown in Fig side faces side region solution to 5.1 spatial structure specify subset Sugihara tetrahedron Theorem 6.2 three-dimensional truncated pyramid uniquely unknowns values vertex positions VG(P