Graphics Reference
In-Depth Information
We begin by introducing matting terminology and the basic mathematical prob-
lem (Section 2.1 ). We then give a brief introduction to the theory and practice
of blue-screen, green-screen, and difference matting, all commonly used in the
effects industry today (Section 2.2 ). The remaining sections introduce different
approaches to the natural image matting problem where a special background
isn't required. In particular, we discuss the major innovations of Bayesian matting
(Section 2.3 ), closed-form matting (Section 2.4 ), Markov Random Fields for matting
(Section 2.5 ), random-walk matting (Section 2.6 ), and Poisson matting (Section 2.7 ).
While high-quality mattes need to have soft edges, we discuss how image seg-
mentation algorithms that produce a hard edge can be “softened” to give a matte
(Section 2.8 ). Finally, we discuss the key issue of matting for video sequences, a very
difficult problem (Section 2.9 ).
2.1
MATTING TERMINOLOGY
Throughout this topic, we assume that a color image I is represented by a 3D discrete
array of pixels, where I
(
x , y
)
is a 3-vector of (red, green, blue) values, usually in the
range
. The matting problem is to separate a given color image I into a fore-
ground image F and a background image B . Our fundamental assumption is that
the three images are related by the matting (or compositing ) equation :
[
0, 1
]
I
(
x , y
) = α(
x , y
)
F
(
x , y
) + (
1
α(
x , y
))
B
(
x , y
)
(2.1)
where
α(
x , y
)
is a number in
[
0, 1
]
. That is, the color at
(
x , y
)
in I is a mix between the
colors at the same position in F and B , where
α(
x , y
)
specifies the relative proportion
of foreground versus background. If
α(
x , y
)
is close to 0, the pixel gets almost all of its
color from the background, while if
is close to 1, the pixel gets almost all of its
color from the foreground. Figure 2.1 illustrates the idea. We frequently abbreviate
Equation ( 2.1 )to
α(
x , y
)
I
= α
F
+ (
1
α)
B
(2.2)
with the understanding that all the variables depend on the pixel location
(
x , y
)
. Since
α
, we can think of it like a grayscale image, which is often called
a matte , alpha matte ,or alpha channel . Therefore, in the matting problem, we are
given the image I and want to obtain the images F , B , and
is a function of
(
x , y
)
α
.
should always be either 0 (that is, the pixel is entirely
background) or 1 (that is, the pixel is entirely foreground). However, this isn't the case
for real images, especially around the edges of foreground objects. The main reason
is that the color of a pixel in a digital image comes from the total light intensity falling
on a finite area of a sensor; that is, each pixel contains contributions frommany real-
world optical rays. In lower resolution images, it's likely that some scene elements
project to regions smaller than a pixel on the image sensor. Therefore, the sensor area
receives some light rays from the foreground object and some from the background.
Even high resolution digital images (i.e., ones in which a pixel corresponds to a very
small sensor area) contain fractional combinations of foreground and background
in regions like wisps of hair. Fractional values of
At first, itmay seem like
α(
x , y
)
α
are also generated by motion
of the camera or foreground object, focal blur induced by the camera aperture, or
 
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