1. KOSYR’2001 Reconstruction of Polyhedron Objects by Structure Graph Integration Krzysztof Skabek Institute of Theoretical and Applied Computer Sciences Polish Academy of Sciences, ul. Bałtycka 5, 44-100 Gliwice, e-mail: krzysiek@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 The scope of the presented method

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 Contour Graph Face Graph 1 2 3 4 1 2 3 4 5 6 7

6. Integration of Structure Graphs I GK i GK i – the contour graph obtained for ith view point GS i GK i GS i – the face graph for ith view created GK i GKM i GKM i – the integrated contour graph after i steps GSM GSM – the integrated face graph after i steps WK i GK i GKM i-1 WK i – set of corresponding vertices in GK i and GKM i-1 WS i GS i GSM i-1 WS i – set of corresponding vertices in GS i and GSM i-1

7. Integration of Structure Graphs II GK i GS i 1. Building GK i and GS i for ith view point GS i GSM i-1 WS i 2. Subgraph matching of GS i and GSM i-1 ; storing the matched vertices in WS i. GK i WS i 3. Finding correspondences between GK i and WS i. T i R i GK i GKM i-1 4. Calculation of the translation vector T i and the rotation matrix R i transformating coordinate system of GK i into the coordinates of GKM i-1 GK i T i R i 5. Calculation of new coordinates for vertices from GK i (using T i and R i ) GKM i-1 & GK i  GKM i GSM i-1 & GS i  GSM i 6. Consolidation of contour graphs: GKM i-1 & GK i  GKM i, GSM i-1 & GS i  GSM i 7. 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 Integrated Contour Graph

10. Stages of Scene Reconstruction I I. II.III.

11. Stages of Scene Reconstruction II IV. V.VI.

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