1 CS4442/9542b Artificial Intelligence II Prof. Olga Veksler Lecture 1 Course Introduction.
Compact Windows for Visual Correspondence via Minimum Ratio Cycle Algorithm Olga Veksler NEC Labs...
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Transcript of Compact Windows for Visual Correspondence via Minimum Ratio Cycle Algorithm Olga Veksler NEC Labs...
Compact Windows for Visual Correspondence via Minimum
Ratio Cycle Algorithm
Olga Veksler
NEC Labs America
Local Approach
• Look at one image patch at at time
• Solve many small problems independently
• Fast, sufficient for some problems
Global Approach
• Look at the whole image • Solve one large problem• Slower, more accurate
Local Approach
• Sufficient for some problems
• Central problem: window shape selection
• Efficiently solved using Minimum Ratio Cycle algorithm for graphs
stereo
left image right image disparity = x1-x2
Visual Correspondence
(x1,y) (x2,y)
motion
first image second image
vertical motion
horizontal motion(x1,y1) (x2,y2)
Local Approach [Levine’73]
left image right image
p
1C
1
2C
2
3C
3
++
+2 2
2 2=Common C
pd = i which gives best iC
Fixed Window Shape Problems
true disparities
fixed small window fixed large window
left image
nee
d d
iffe
ren
t w
ind
ow
sh
apes
• Two inefficient methods proposed previously 1. Local greedy search [Levine CGIP’73, Kanade’PAMI94]
2. Direct search [Intille ECCV94,Geiger IJCV95]
Variable Window: Previous Work
…….
• Need efficient optimization algorithm over sizes and shapes
Minimum Ratio Cycle
• G(V,E) and w(e), t(e): E R 0Ce
et
image pixels
• Find cycle C which minimizes:
WC
Ce
ew
Ce
et=
W
t
From Area to Cycle
blue edge
red edge+
5
-2sum up terms inside
using weights of edges
1
111
11
1
Window Cost
C(W) = =size of W+ … +
2 2
WC
Ce
ew
Ce
et
OK for any graphs
not OK for any graph 0Ce
et
positive negative
Compact Windows
p
simple graph cycles C
one-to-one
correspondencecompact windows W
we construct graph s.t. 0Ce
et
only clockwise cycles
Cycle which is not Simple
C Cin this case:
cycle C
cycle C
Solving MRC
• search for smallest s.t. there is negative cycle on graph with edge weights:
• negative cycle detection takes time due to the special structure of our graphs
find smallest s.t. for some cycle ew
et
ew et-
nnO
ew et -
• there are are compact windows, if the largest allowed window is n by n
• Contains all possible rectangles but much more general than just rectangles
• Find optimal window in in theory, linear ( ) in practice
• Search over in time
nO 2
4nO
3n 2n
perimeterarea
examples of compact windows
(small )
312O 231O
Sample Compact Windows
Speedup
for pixel p, the algorithm extends windows over pixels which are likely to have the same disparity as p
use the optimal window computed for p to approximate for pixels inside that window
Comparison to Fixed Window
Compact windows:16% errorstrue disparities
fixed small window: 33% errors fixed large window: 30% errors
motion
motion
Algorithm Tsukuba Venus Sawtooth Map
Layered 1.58 1.52 0.34 0.37Graph cuts 1.94 1.79 1.30 0.31Belief prop 1.15 1.00 0.98 0.84GC+occl. 1.27 2.79 0.36 1.79
Graph cuts 1.86 1.69 0.42 2.39Multiw. Cut 8.08 0.53 0.61 0.26
Comp. win. 3.36 1.67 1.61 0.33
Results
13 other algorithms, local and global
all
glo
bal
Running time: 8 to 22 seconds
Future Work
• Generalize the window class
• Generalize objective function – mean?– variance?