1. Xiang Liang xlvector@gmail.com
Natural Image Matting
Xiang Liang

2. Introduction
In Image composition, an new image I(x,y) can be blended from a background image B(x,y) and foreground image F(x,y) with its alpha matte : I F B
Our task is get F,B,α from a given image I

3. User Interactive && Trimap
In order to get F,B,α from a given image I, user must specify the foreground, background and unknown area first. Following is a trimap:
White area : foreground
Black area : foreground
Gray area : unknown

4. Estimate F and B Consider an point P in unknown area
we found its nearby background Sb and foreground SF :
Sb(r) = {B(x,y)|{x,y} is background and |BP|<r}
Sf(r) = {F(x,y)|{x,y} is foreground and |BP|<r}
Then, we calculate mean color of points in Sf and denote it with ; calculate mean color of points in Sb and denote it with .
background
foreground
unknown P
Then we estimate foreground and background color in P by :

5. Estimate we estimate by consider two factor: a) We must minimize
C,F,B are vectors because there have are in RGB color space
b) We must minimize
background
foreground
unknown P
point Q is 4-neighbor of point P.

6. Estimate
We consider a) factor because of definition of composition image.
We consider b) factor because we think alpha matte is smooth.
Bayesian matting only consider a) factor and use MAP(maximum a posteriori) to estimate F,B,α.
Poisson matting only consider b) factor and use poisson function to estimate F,B,α.
I combine those two technique and consider both a) and b) factor, then, my task is to minimize :

7. Results:
Image
Trimap
alpha
foreground