Image Processing Reference
In-Depth Information
all 1024 outer-totalistic two-dimensional CA with 5-cell (von Neumann) neighbor-
hood was done and several useful ID rules were proposed, maximizing the PSNR
for the a given compression rate. In the same work, various block sizes and number
of bit-planes were considered, typical values being
D
=
=
64 to 256
(for very high compression rates). Comparing our compression method to JPEG led
to the conclusion that CA-VQ gives better performance than JPEG for high com-
pression rates (
bpp
32 or 64 and
m
<
0
.
3) such compression rates being also associated with faster
computation.
Herein we present a different approach for choosing the rule of a CA code-
book suitable for compressing a class of images. Unlike in the previous approaches,
the local rule is no more restricted to outer-totalistic and although the same von-
Neumann neighborhood is used, the space of possible rules is now extremely large
(2
32
rules). Moreover, the CA rule can be individually tuned per each bit-plane.
The CA-based dictionary has the following structure: Given
m
and
D
(usually
both are powers of 2) the array size
M
of the 2-dimensional
M
×
M
square CA with
=
√
Dm
. For instance, if
D
periodic boundary condition is determined as
M
=
64
and
m
64. The codebook is composed of
all square
D
blocks of
m
size each cropped from the emergent pattern obtained in
this CA after a certain number
T
of iterations when the initial state is an arbitrary
(but known at Rx) random binary state with equal number of bits in 0 and 1. The
initial state, the rule ID, and the number of iterations
T
may be regarded as a key of
the compression scheme providing a rudimentary form of encryption in addition to
the basic compression functionality.
The CA rule is obtained from a simplified learning process using a certain bit-
plane image (binary image) of arbitrary size. The original bit-plane image is per-
turbed using a uniform distribution i.e. a percentage
=
64, the size of the dictionary CA is
M
=
of its bits are flipped (1
becomes 0 and vice-versa) resulting in an input image for the 5 inputs CA cell (a
sliding 5-cell neighborhood is scanning all
N
pixels of the image as inputs, while
the central cell from the associated image is taken as the desired output. For each
of the 32 possible 5-bit entries (each encoded as an integer
i
in the associated truth
table) two numbers are stored:
n
i
0
indicating the number of times the desired output
was 0 and
n
i
1
the number of times the desired output was 1. For
N
i
occurrences of
the input code
i
it follows that
n
i
0
+
α
n
i
1
=
N
i
. Finally each output for the line
i
of the
truth table is assigned 1 if
n
i
1
>
0, 1 or
0 is picked randomly with a probability 0.5 as the corresponding output in the truth
table. The resulting truth table is then associated with the cell ID, as shown in Fig.
1.14, where
N
i
/
2 and 0 else. For the rare cases with
N
i
=
12 was optimized such that the recovery scheme will minimize
the bit error on the most significant bit-plane. Given a choice for
m
and
D
α
=
0
.
the CA
codebook is generated by running the CA with the previously determined ID for a
certain number of iterations.
The above strategy was motivated by the goal to have a cell ID such that the
resulting CA will converge to a stationary pattern preserving most of the relevant
details in the original bit-plane. A noisy input was found necessary in order to ensure
the diversity of input codes (5-bit words) necessary to construct the associated truth
table.
,
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