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Dynamic Programming (DP), Shortest Paths (SP)

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processed nodes (distance to A is known) - active nodes (front) ... Chamfer matching: L1 distance on distance transform. Not robust at all. Hausdorff distance ... – PowerPoint PPT presentation

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Title: Dynamic Programming (DP), Shortest Paths (SP)


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
Lecture theme
5
Dijkstra algorithm
6
Shortest paths segmentation
7
Shortest paths segmentation
Example find the shortest closed contour in a
given domain of a graph
Repeat for all points on the black line. Then
choose the optimal contour.
8
DP (SP) for stereo
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
12
Energy minimization by SP
sites
states
1
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
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