Below are the results of Bayesian Image matting (the alpha matte and the composite image).
Artifact: A light checkered pattern is visible around the lion(toy).
The artifact can be reduced by carefully selecting the value of σ. The results with different values of σ are shown below.
The value of σ (standard deviation) indicates how far away the color, computed from the estimated F, B and α, can be from the foreground/background color.

So σ is used to handle the noise (high frequency patterns) in the image.

σ=0.5

σ=20

σ=30

σ=40

σ=50