1. Dynamic Programming (DP), Shortest Paths (SP)
CS664 Lecture 22
Thursday 11/11/04
Some slides care of Yuri Boykov, Dan Huttenlocher

2. Level sets
[Donald Tanguay]

3. Level sets and curve evolution

4. Shortest path problem A Z
Lecture theme

5. Dijkstra algorithm - processed nodes (distance to A is known)B
- processed nodes (distance to A is known)
- active nodes (front)
- active node with the smallest distance value

6. Shortest paths segmentation
Graph edges are “cheap” in places with high intensity gradients
Example: 4 1 3 2

7. Shortest paths segmentation
Example:
find the shortest
closed contour in a given domain of a graph
Shortest paths
approach
Compute the shortest path p ->p for a point p. p
Repeat for all points on the black line. Then choose the optimal contour.

8. DP (SP) for stereo Disparities of pixels in the scan line
photoconsistency
regularization

9. Discrete snakes Represent the snake as a set of points
Curve as spline, e.g. (particle method)
Local update problem can be solved exactly (compute global min)
Do this repeatedly
Problems with collisions, change of topology

10. Discrete snake energy Best location of the last vertex vn
depends only the location of vn-1

11. Discrete snakes example
control points
Fold data term into smoothness term
First-order interactions

12. Energy minimization by SP
sites
states 1 A B 2 … m

13. Distance transform (DT)
Note: can be generalized beyond 1P
(DT of arbitrary f)

14. Computing distance transforms
Depends on the distance measure (L1 or L2 distance)
Linear time algorithms based on dynamic programming
Fast in practice
Can think of this as smoothing in feature space

15. Distance transform applications
Primarily used in recognition
Represent the model as a set of points
Edges, or maybe corners
Compare model to image
Under some transformation of the model
Chamfer matching: L1 distance on distance transform
Not robust at all

16. Hausdorff distance Defined between two sets of points
h(A,B)= if every point in A lies within  of the nearest point in B
 is the smallest value for which this holds