Edge and Boundary interpretation

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
8
Forward Checking (FC) - 4 Queens Example
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," ltigtArtificial
  Intelligencelt/igt, 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.