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: [email protected]
KOSYR’2001
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
Stages of 3D Scene Reconstruction
Complete
structure graph
YES
Stereo head
Acquisition of raster
stereo images
Raster stereo
images
Segmentation,
Depth map calculation
Stereo images
+ rear depth map
NO
Is
the representation
complete?
Integration of
actual structure graphs
into complete structure graphs
Face graph
+ rule description
Region extraction,
Analysis of scene
faces and their connections
Contour graf
for the actual view
Ekstraction of edges
and vertices
The scope of the presented method
Graph Representation of 3D Scene
Contour Graph: GC  VC , EC , C ,C 
VC
- set of vertices in the scene
EC  VC VC
- set of connections among vertices
C : VC  LVC , LVC - 3D coordinates (x,y,z) of vertices
C : VC  LE
GF  VF , EF , F ,F 
C
Face Graph:
VF
EF  VF VF
F : VF  LVF , LVF
F : VF  LE , LE
F
F
set of faces in the scene
- set of connections among faces
- parameters of faces
- parameters of face connections
-
Construction of Structure Graphs
4
7
4
Contour Graph
6
1
1
3
3
5
2
2
0 .0
Face Graph
3
0 .0
3
4
4
0 .0
0 .0
4
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
Integration of Structure Graphs II
1.
2.
3.
4.
5.
6.
7.
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 graphs:
GKMi-1 & GKi  GKMi, GSMi-1 & GSi  GSMi
Checking the completeness of reconstruction
Completeness of the Representation

The total rotation angle in all iterations exceeds 360º

Passing a given number of iterations without
encountering new scene objects
The Example of Scene Reconstruction
Input Graph
Integrated
Contour Graph
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
The End