Databases Reference
In-Depth Information
Range blocks
Domain blocks
F I GU R E 18 . 14
Range blocks and examples of domain blocks.
some function, can we then solve the
inverse
problem? That is, given an image, can we find
the function for which the image is the fixed point? The first practical public answer to this
came from Arnaud Jacquin in his Ph.D. dissertation [
247
] in 1989. The technique we describe
in this section is from Jacquin's 1992 paper [
248
].
Instead of generating a single function directly for which the given image is a fixed point,
we partition the image into blocks
R
k
, called
range
blocks, and obtain a transformation
f
k
for each block. The transformations
f
k
are not fixed-point transformations since they do not
satisfy the equation
f
k
(
R
k
)
=
R
k
(39)
Instead, they are a mapping from a block of pixels
D
k
from some other part of the image.
While each individual mapping
f
k
is not a fixed-point mapping, we will see later that we can
combine all these mappings to generate a fixed-point mapping. The image blocks
D
k
are
called
domain
blocks, and they are chosen to be larger than the range blocks. In [
248
], the
domain blocks are obtained by sliding a
K
×
K
window over the image in steps of
K
/
2or
K
block thus encountered is entered into the domain pool. The set of all domain blocks does
not have to partition the image. In Figure
18.14
we show the range blocks and two possible
domain blocks.
The transformations
f
k
are composed of a
geometric
transformation
g
k
and a
massic
transformation
m
k
. The geometric transformation consists of moving the domain block to the
location of the range block and adjusting the size of the domain block to match the size of the
range block. The massic transformation adjusts the intensity and orientation of the pixels in
the domain block after it has been operated on by the geometric transform. Thus,
K
/
4 pixels. As long as the window remains within the boundaries of the image, each
K
×
R
k
=
f
k
(
D
k
)
=
m
k
(
g
k
(
D
k
))
(40)
