Graphics Reference
In-Depth Information
However, none of these pyramid-style methods are well suited to the situation
when the source and target colors are not already well matched, as we'll see in the
next section.
3.2
POISSON IMAGE EDITING
An appealing approach to compositing, pioneered by Pérez et al. [
364
], seam-
lessly merges the source region into the target image using an application of the
Poisson equation
. To understand the Poisson compositing technique, we need to
define several concepts from continuous partial differential equations and vector
calculus, which we then translate into the discrete world to apply to digital images.
3.2.1
The Basic Idea
In place of a binary compositing mask
M
, we assume that the source image
S
is
definedover a closed region
. Figure
3.6
illustrates these terms. The target image
T
is assumed to be defined over some
rectangular region in
; the boundary of this region is denoted as
∂
2
.
Formally, the composite image we want to construct,
I
R
(
)
x
,
y
, exactly agrees with
T
. The problem is that if we
directly place the source region on top of
T
and blend across the edge, for example
using the Laplacian pyramid approach, the result can be unacceptable due to color
mismatches, as illustrated in Figure
3.7
.
What canwe do tomake the interior of
(
x
,
y
)
outside of
, and should “look like”
S
(
x
,
y
)
inside
“look like” the source, but avoid the color
mismatch problem? The key idea is to transfer the
edges
of the source image into
,
and then compute colors inside the region that are as harmonious as possible with
the pixels from
T
surrounding
. That is, we want the
gradient
of the desired image,
∇
I
(
x
,
y
)
, inside
tobe as close as possible to
∇
S
(
x
,
y
)
, subject to the constraint that the
result must match the existing values of
T
. This approach is
generally known as
gradient-domain compositing
. In continuous terms, this means
(
x
,
y
)
on the boundary
∂
Ω
Figure 3.6.
Terminology for Poisson image editing.
∂Ω
Source image
