Mean-Field Theory and Its Applications In Computer Vision4 1.
-
Upload
jaden-gonzales -
Category
Documents
-
view
217 -
download
0
Transcript of Mean-Field Theory and Its Applications In Computer Vision4 1.
![Page 1: Mean-Field Theory and Its Applications In Computer Vision4 1.](https://reader035.fdocuments.us/reader035/viewer/2022062318/5515eb17550346dd6f8b5169/html5/thumbnails/1.jpg)
Mean-Field Theory and Its Applications In Computer Vision4
1
![Page 2: Mean-Field Theory and Its Applications In Computer Vision4 1.](https://reader035.fdocuments.us/reader035/viewer/2022062318/5515eb17550346dd6f8b5169/html5/thumbnails/2.jpg)
Motivation
2
Helps in incorporating region/segment consistency in the model
Pairwise CRF
Higher order CRF
![Page 3: Mean-Field Theory and Its Applications In Computer Vision4 1.](https://reader035.fdocuments.us/reader035/viewer/2022062318/5515eb17550346dd6f8b5169/html5/thumbnails/3.jpg)
Motivation
3
Higher order terms can help in incorporating detectors into our model
Image
Without detector
With detector
![Page 4: Mean-Field Theory and Its Applications In Computer Vision4 1.](https://reader035.fdocuments.us/reader035/viewer/2022062318/5515eb17550346dd6f8b5169/html5/thumbnails/4.jpg)
Marginal update
4
General form of meanfield update
Expectation of the cost given variable vi takes a label
![Page 5: Mean-Field Theory and Its Applications In Computer Vision4 1.](https://reader035.fdocuments.us/reader035/viewer/2022062318/5515eb17550346dd6f8b5169/html5/thumbnails/5.jpg)
Marginal Update
5
General form of meanfield update
Expectation of the clique given variable vi takes a label
• Summation over the possible states of the clique
![Page 6: Mean-Field Theory and Its Applications In Computer Vision4 1.](https://reader035.fdocuments.us/reader035/viewer/2022062318/5515eb17550346dd6f8b5169/html5/thumbnails/6.jpg)
Marginal Update in Meanfield
6
Some possible states
Total number of possible states: 36
labels
![Page 7: Mean-Field Theory and Its Applications In Computer Vision4 1.](https://reader035.fdocuments.us/reader035/viewer/2022062318/5515eb17550346dd6f8b5169/html5/thumbnails/7.jpg)
Marginal Update in Meanfield
7
Exponential # of possible states for clique of size |c| and labels L: |L|C
Expectation evaluation (summation) becomes infeasible
![Page 8: Mean-Field Theory and Its Applications In Computer Vision4 1.](https://reader035.fdocuments.us/reader035/viewer/2022062318/5515eb17550346dd6f8b5169/html5/thumbnails/8.jpg)
Marginal Update in Meanfield
8
• Use restricted form of cost
• Pattern based potential
![Page 9: Mean-Field Theory and Its Applications In Computer Vision4 1.](https://reader035.fdocuments.us/reader035/viewer/2022062318/5515eb17550346dd6f8b5169/html5/thumbnails/9.jpg)
Marginal Update in Meanfield
9
Restrict the number of states to certain number of patterns
Simple patterns
Segment takes a label from label set of 4 patterns Or none
![Page 10: Mean-Field Theory and Its Applications In Computer Vision4 1.](https://reader035.fdocuments.us/reader035/viewer/2022062318/5515eb17550346dd6f8b5169/html5/thumbnails/10.jpg)
Marginal Update in Meanfield
10
Expectation calculation is quite efficient
![Page 11: Mean-Field Theory and Its Applications In Computer Vision4 1.](https://reader035.fdocuments.us/reader035/viewer/2022062318/5515eb17550346dd6f8b5169/html5/thumbnails/11.jpg)
Pattern based cost
11
Segment takes one of the forms
![Page 12: Mean-Field Theory and Its Applications In Computer Vision4 1.](https://reader035.fdocuments.us/reader035/viewer/2022062318/5515eb17550346dd6f8b5169/html5/thumbnails/12.jpg)
Pattern based cost
12
Segment does not take one of the forms
![Page 13: Mean-Field Theory and Its Applications In Computer Vision4 1.](https://reader035.fdocuments.us/reader035/viewer/2022062318/5515eb17550346dd6f8b5169/html5/thumbnails/13.jpg)
Pattern based cost
13
• Simple patterns
Simple patterns
• Pattern based higher order terms
![Page 14: Mean-Field Theory and Its Applications In Computer Vision4 1.](https://reader035.fdocuments.us/reader035/viewer/2022062318/5515eb17550346dd6f8b5169/html5/thumbnails/14.jpg)
PN Potts based patterns
14
• PN Potts based patterns
Potts patterns
![Page 15: Mean-Field Theory and Its Applications In Computer Vision4 1.](https://reader035.fdocuments.us/reader035/viewer/2022062318/5515eb17550346dd6f8b5169/html5/thumbnails/15.jpg)
Potts cost
15
• Potts cost
Potts patterns
![Page 16: Mean-Field Theory and Its Applications In Computer Vision4 1.](https://reader035.fdocuments.us/reader035/viewer/2022062318/5515eb17550346dd6f8b5169/html5/thumbnails/16.jpg)
Marginal Update in Meanfield
16
General form of meanfield update
Expectation of the cost given variable vi takes a label
![Page 17: Mean-Field Theory and Its Applications In Computer Vision4 1.](https://reader035.fdocuments.us/reader035/viewer/2022062318/5515eb17550346dd6f8b5169/html5/thumbnails/17.jpg)
Expectation update
17
Probability of segment taking that label
Potts patterns
![Page 18: Mean-Field Theory and Its Applications In Computer Vision4 1.](https://reader035.fdocuments.us/reader035/viewer/2022062318/5515eb17550346dd6f8b5169/html5/thumbnails/18.jpg)
Expectation update
18
Probability of segment not taking that label
Potts patterns
![Page 19: Mean-Field Theory and Its Applications In Computer Vision4 1.](https://reader035.fdocuments.us/reader035/viewer/2022062318/5515eb17550346dd6f8b5169/html5/thumbnails/19.jpg)
Expectation update
19
Expectation update
Potts patterns
![Page 20: Mean-Field Theory and Its Applications In Computer Vision4 1.](https://reader035.fdocuments.us/reader035/viewer/2022062318/5515eb17550346dd6f8b5169/html5/thumbnails/20.jpg)
Complexity
20
• Expectation Updation:
• Time complexity• O(NL)
• Preserves the complexity of original filter based method
![Page 21: Mean-Field Theory and Its Applications In Computer Vision4 1.](https://reader035.fdocuments.us/reader035/viewer/2022062318/5515eb17550346dd6f8b5169/html5/thumbnails/21.jpg)
PascalVOC-10 dataset
21
• Inclusion of PN potts term:
Algorithm Time (s) Overall Av. Recall Av. I/U
AHCRF+Cooc 36 81.43 38.01 30.09
Dense CRF 0.67 71.63 34.53 28.4
Dense + PN Potts
4.35 79.87 40.71 30.18
• Slight improvement in I/U score compared to more complex model which includes Pn Potts + cooccurrence terms• Almost 8-9 times faster than the alpha-expansion based method