Bayesian Probabilistic reasoning and learning Part 2 Huang Jin State Key Lab of CAD&CG Zhejiang...
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Transcript of Bayesian Probabilistic reasoning and learning Part 2 Huang Jin State Key Lab of CAD&CG Zhejiang...
![Page 1: Bayesian Probabilistic reasoning and learning Part 2 Huang Jin State Key Lab of CAD&CG Zhejiang University.](https://reader031.fdocuments.in/reader031/viewer/2022032723/56649cfa5503460f949cbe69/html5/thumbnails/1.jpg)
Bayesian Probabilistic reasoning and learning
Part 2Huang Jin
State Key Lab of CAD&CGZhejiang University
![Page 2: Bayesian Probabilistic reasoning and learning Part 2 Huang Jin State Key Lab of CAD&CG Zhejiang University.](https://reader031.fdocuments.in/reader031/viewer/2022032723/56649cfa5503460f949cbe69/html5/thumbnails/2.jpg)
Problem
![Page 3: Bayesian Probabilistic reasoning and learning Part 2 Huang Jin State Key Lab of CAD&CG Zhejiang University.](https://reader031.fdocuments.in/reader031/viewer/2022032723/56649cfa5503460f949cbe69/html5/thumbnails/3.jpg)
Alpha Channel
• Instead of 0-1 mask.• What is F, B, and C?• What is alpha?• How to blend F, B into C by alpha?• How to get alpha from F, B, C?
• f: a projection, R3->R
![Page 4: Bayesian Probabilistic reasoning and learning Part 2 Huang Jin State Key Lab of CAD&CG Zhejiang University.](https://reader031.fdocuments.in/reader031/viewer/2022032723/56649cfa5503460f949cbe69/html5/thumbnails/4.jpg)
Known and Unknown
• Known: C• Unknown: F, B• MAP
– find the most likely estimates for F, B, and alpha, given the observation C.
• Why not
![Page 5: Bayesian Probabilistic reasoning and learning Part 2 Huang Jin State Key Lab of CAD&CG Zhejiang University.](https://reader031.fdocuments.in/reader031/viewer/2022032723/56649cfa5503460f949cbe69/html5/thumbnails/5.jpg)
Some Deduce
P(c) is constant
![Page 6: Bayesian Probabilistic reasoning and learning Part 2 Huang Jin State Key Lab of CAD&CG Zhejiang University.](https://reader031.fdocuments.in/reader031/viewer/2022032723/56649cfa5503460f949cbe69/html5/thumbnails/6.jpg)
L(C|F, B, alpha)
Giving F, B, alpha, what’s the probability of C?
![Page 7: Bayesian Probabilistic reasoning and learning Part 2 Huang Jin State Key Lab of CAD&CG Zhejiang University.](https://reader031.fdocuments.in/reader031/viewer/2022032723/56649cfa5503460f949cbe69/html5/thumbnails/7.jpg)
Gaussian Distribution
•Parameters: Mean and variance
•Multivariate Gaussian Distribution
P(x)=
![Page 8: Bayesian Probabilistic reasoning and learning Part 2 Huang Jin State Key Lab of CAD&CG Zhejiang University.](https://reader031.fdocuments.in/reader031/viewer/2022032723/56649cfa5503460f949cbe69/html5/thumbnails/8.jpg)
How to estimate F and B?
• From neighbor
• Weight the pixel’s contribution
• Multivariate: R, G, B
![Page 9: Bayesian Probabilistic reasoning and learning Part 2 Huang Jin State Key Lab of CAD&CG Zhejiang University.](https://reader031.fdocuments.in/reader031/viewer/2022032723/56649cfa5503460f949cbe69/html5/thumbnails/9.jpg)
L(F) and L(B)
distance related weight
![Page 10: Bayesian Probabilistic reasoning and learning Part 2 Huang Jin State Key Lab of CAD&CG Zhejiang University.](https://reader031.fdocuments.in/reader031/viewer/2022032723/56649cfa5503460f949cbe69/html5/thumbnails/10.jpg)
Put them togetherf(F, B, alpha)=
![Page 11: Bayesian Probabilistic reasoning and learning Part 2 Huang Jin State Key Lab of CAD&CG Zhejiang University.](https://reader031.fdocuments.in/reader031/viewer/2022032723/56649cfa5503460f949cbe69/html5/thumbnails/11.jpg)
Iteration
• Why not
• Not a quadratic equation.• we break the problem into two quadratic sub-
problems.• The second one:
![Page 12: Bayesian Probabilistic reasoning and learning Part 2 Huang Jin State Key Lab of CAD&CG Zhejiang University.](https://reader031.fdocuments.in/reader031/viewer/2022032723/56649cfa5503460f949cbe69/html5/thumbnails/12.jpg)
Additional Results
![Page 13: Bayesian Probabilistic reasoning and learning Part 2 Huang Jin State Key Lab of CAD&CG Zhejiang University.](https://reader031.fdocuments.in/reader031/viewer/2022032723/56649cfa5503460f949cbe69/html5/thumbnails/13.jpg)
Where is Bayesian?
• We need alpha:• We guess it under Gaussian Distribution :
![Page 14: Bayesian Probabilistic reasoning and learning Part 2 Huang Jin State Key Lab of CAD&CG Zhejiang University.](https://reader031.fdocuments.in/reader031/viewer/2022032723/56649cfa5503460f949cbe69/html5/thumbnails/14.jpg)
谢谢