Bayesian Probabilistic reasoning and learning
Part 2Huang Jin
State Key Lab of CAD&CGZhejiang University
Problem
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
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
Some Deduce
P(c) is constant
L(C|F, B, alpha)
Giving F, B, alpha, what’s the probability of C?
Gaussian Distribution
•Parameters: Mean and variance
•Multivariate Gaussian Distribution
P(x)=
How to estimate F and B?
• From neighbor
• Weight the pixel’s contribution
• Multivariate: R, G, B
L(F) and L(B)
distance related weight
Put them togetherf(F, B, alpha)=
Iteration
• Why not
• Not a quadratic equation.• we break the problem into two quadratic sub-
problems.• The second one:
Additional Results
Where is Bayesian?
• We need alpha:• We guess it under Gaussian Distribution :
谢谢