nD object representation and detection from Single 2D line drawing

Authors:
Hongbo Li;Quan Wang;Lina Zhao;Ying Chen;Lei Huang
Affiliations:
Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P. R. China;Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P. R. China;Department of Mathematics and Computer Science, Science of School, Bejing University of Chemical Technology;Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P. R. China;Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P. R. China
Venue:
IWMM'04/GIAE'04 Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications
Year:
2004

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Abstract

In this paper, we propose the wireframe representation of nD object, which is a single 2D line drawing. A wireframe model of an n D object is composed of a set of edges connecting a set of vertices, a subset of closed r -chains called boundary r -chains which surround the (r +1)D pieces of the object, and a set of filling patterns for the boundary r -chains for 0 r n. The wireframe representation is the perspective projection of the wireframe model of the object from its surrounding space to the image plane. Combining the projective geometric constraints of the wireframe representation with the idea of local construction and deletion, we propose an algorithm for high dimensional object detection from single 2D line drawing, under the most general assumption that neither the dimension of the object nor the dimension of the surrounding space is known, two neighboring faces can be coplanar, and whether or not the object is a manifold is unknown. Our algorithm outperforms any other algorithm in 2D face identification in that it generally does not generate redundant cycles that are not assigned as faces, and can handle 3D solids of over 10,000 faces.