Regularity selection for effective 3D object reconstruction from a single line drawing
Pattern Recognition Letters
A survey on geometrical reconstruction as a core technology to sketch-based modeling
Computers and Graphics
Discrete Applied Mathematics
Polyhedral scene analysis combining parametric propagation with calotte analysis
IWMM'04/GIAE'04 Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications
nD polyhedral scene reconstruction from single 2D line drawing by local propagation
ADG'04 Proceedings of the 5th international conference on Automated Deduction in Geometry
On the evolution of geometrical reconstruction as a core technology to sketch-based modeling
SBM'04 Proceedings of the First Eurographics conference on Sketch-Based Interfaces and Modeling
A hybrid intelligent system for 3D reconstruction from a single line drawing
International Journal of Computer Applications in Technology
Journal of Mathematical Imaging and Vision
Design of solids for antigravity motion illusion
Computational Geometry: Theory and Applications
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Mathematical structures of line drawings of polyhedrons are studied and practical as well as theoretical solutions are obtained for several fundamental problems aroused in scene analysis and in man-machine communication. First, a necessary and sufficient condition for a line drawing to correctly represent a polyhedron is obtained in terms of linear algebra. Next, combinatorial structures are investigated and practical solutions are obtained to such problems as how to discriminate between correct and incorrect line drawings and how to correct vertex-position errors in incorrect line drawings. Lastly, distribution of the degree of freedom of a line drawing is elucidated and a method is proposed for interactive reconstruction of a polyhedron from a line drawing. The results obtained here enable us to make manmachine communication more ``flexible'' in the sense that a machine can reconstruct three-dimensional objects from hand-drawn pictures even if the pictures are not perfect.