Reconstruction of Polyhedra by a Mechanical Theorem Proving Method (Special Issue on Image Processing and Understanding)

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概要

• 論文の詳細を見る

• In this paper we propose a new application of Wu's mechanical theorem proving method to reconstruct polyhedra in 3-D space from their projection image. First we set up three groups of equations. The first group is of the geometric relations expressing that vertices are on a plane segment, on a line segment, and forming angle in 3-D space. The second is of those relations on image plane. And the rest is of the relations between the vertices in 3-D space and their correspondence on image plane. Next, we classify all the groups of equations into two sets, a set of hypotheses and a conjecture. We apply this method to seven cases of models. Then, we apply Wu's method to prove that the hypotheses follow the conjecture and obtain pseudodivided remainders of the conjectures, which represent relations of angles or lengths between 3-D space and their projected image. By this method we obtained new geometrical relations for seven cases of models. We also show that, in the region in image plane where corresponding spatial measures cannot reconstructed, leading coefficients of hypotheses polynomials approach to zero. If the vertex of an image angle is in such regions, we cannot calculate its spatial angle by direct manipulation of the hypothesis polynomials and the conjecture polynomial. But we show that by stabilty analysis of the pseudodivided remainder the spatial angles can be calculated even in those regions.

• 社団法人電子情報通信学会の論文
• 1993-04-25

著者

• DEGUCHI Koichiro

  Faculty of Engineering, University of Tokyo

• Morishita Iwao

  Faculty Of Engineering The University Of Tokyo

• Koh Kyun

  Faculty of Engineering, the University of Tokyo

• Deguchi Koichiro

  Faculty Of Engineering The University Of Tokyo

• Koh Kyun

  Faculty Of Engineering The University Of Tokyo

関連論文

• A Unified Linear Camera Calibration Method Using Two Parallel Calibration Planes
• Reconstruction of Polyhedra by a Mechanical Theorem Proving Method (Special Issue on Image Processing and Understanding)
• 3-D Shape Reconstruction from Endoscope Image Sequences by The Factorization Method

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