1. Edge and Boundary interpretation Consistent line drawing labeling via backtracking Presented by Guy Shtub

2. Perceiving 3D from 2D ► How can humans and machines reconstruct the 3D nature of a scene from a 2D image representing them? ► Additional knowledge is needed

3. Assumptions ► Trihedral (formed by 3 planes meeting at a point) world. ► General viewpoint ► Edges represent surface and depth continuities

4. Huffman and Clowes catalog 1971 ► Define edge type symbols:

5. ► Define 16 possible edge intersections

6. Constraint Satisfaction Problems (CSPs) ► Consist of a set of variables ► Each variable must be assigned a value from a possible domain ► Backtracking attempts to find a solution be trying all combinations in order to find a solution ► Line labeling is a CSP

7. Naïve Backtracking – 4 queens Example 1 3 2 4 3241

8. Forward Checking (FC) - 4 Queens Example 1 3 2 4 3241

9. Problem Representation ► Edge intersections are variables - N ► 16 catalog possibilities are the domain for each variable - D ► Variable Conflicts Matrix NxN (adjacent intersections) ► For each pair of adjacent intersections a Constraints matrix DxD ► Both Algorithms implemented in Java

10. Algorithm Performance Evaluation ► Constraint Checks (CCs) – machine and implementation independent

11. Results

12. Results – performance

13. Conclusions ► Written Program able to provide consistent line labeling ► As expected FC performs better the Naïve Backtracking ► Future work: comparison to line labeling via relaxation labeling performance ► Questions?

14. References ► M. B. Clowes, "On seeing things," Artificial Intelligence, Vol. 2, No. 1, pp. 79-116, 1971. ► D.A. Huffman, “Impossible objects as nonsense sentences,” Machine Imlligencc 6, pp, 295- 323,1971. ► Depth and Shape Inference (II), Introduction to Computational and Biological Vision, Computer Science Department, BGU, Ohad Ben-Shahar ► P. Prosser: "Hybrid algorithms for the constraint satisfaction problem", Computational Intelligence, Vol. 9, pp. 268-99, 1993.