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