Reconstruction of Polyhedron Objects by Structure Graph Integration

1
Reconstruction of Polyhedron Objects by
Structure Graph Integration

• Krzysztof Skabek
• Institute of Theoretical and Applied Computer
  Sciences
• Polish Academy of Sciences,
• ul. Baltycka 5, 44-100 Gliwice,
• e-mail krzysiek_at_iitis.gliwice.pl

2
Contents

• 1. Stages of 3D Scene Reconstruction
• 2. Graph Representation of 3D Scene
• 3. Structure Graph Integration
• 4. The Example of Scene Reconstruction
• 5. Conclusions

3
Stages of 3D Scene Reconstruction
4
Graph Representation of 3D Scene

• Contour Graph
• Face Graph

• set of vertices in the scene
• set of connections among vertices
• 3D coordinates (x,y,z) of vertices

• set of faces in the scene
• set of connections among faces
• parameters of faces
• parameters of face connections

5
Construction of Structure Graphs
4
7
4
Contour Graph
6
1
3
1
3
5
2
2
Face Graph
6
Integration of Structure Graphs I

• GKi the contour graph obtained for ith view
  point
• GSi the face graph for ith view created GKi
• GKMi the integrated contour graph after i steps
• GSM the integrated face graph after i steps
• WKi set of corresponding vertices in GKi and
  GKMi-1
• WSi set of corresponding vertices in GSi and
  GSMi-1

7
Integration of Structure Graphs II

• Building GKi and GSi for ith view point
• Subgraph matching of GSi and GSMi-1 storing the
  matched vertices in WSi.
• Finding correspondences between GKi and WSi.
• Calculation of the translation vector Ti and the
  rotation matrix Ri transformating coordinate
  system of GKi into the coordinates of GKMi-1
• Calculation of new coordinates for vertices from
  GKi (using Ti and Ri)
• Consolidation of contour graphsGKMi-1 GKi ?
  GKMi, GSMi-1 GSi ? GSMi
• Checking the completeness of reconstruction

8
Completeness of the Representation

• The total rotation angle in all iterations
  exceeds 360º
• Passing a given number of iterations without
  encountering new scene objects

9
The Example of Scene Reconstruction
Input Graph
IntegratedContour Graph
10
Stages of Scene Reconstruction I
II.
III.
I.
11
Stages of Scene Reconstruction II
V.
VI.
IV.
12
Conclusions

• Graph matching makes possible to reconstruct
  unknown polyhedra even if viewpoints are not
  exactly located in the scene
• Heuristics significantly increase the average
  time of graph matching algorithms
• The estimation of a viewpoint position is useful
  to verify the obtained scene models

13
The End