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Figure II. Improved classical hierarchical VQ
A. Volume data Pre-processing
A volumetric data set is typically a set V of samples
( x , y,
z,
v)
,also called voxels, representing the value
v of the some property of the data, at a 3D location
( x , y,
z)
.If the value is simply a 0 or an integer i within
a set I ,with a value of 0 indicating background and the
value of i indicating the presence of an object o
i
,then
the data is referred to as binary data[1]. So, before using
classification scheme, to investigate the characteristic of
the volume data is needed. Historgram Info, a simple but
useful way , to be used by us to get the distribution of the
volume data. Taking the large size of the volume data
into account, we firstly resample the volume data in order
to reduce the algorithm complexity. Fig III shows the
pseudo-code of getting the histogram info.
/*!
raw _data:the volume data reading from the raw file
resx,resy,resy: respectively the volume data size in
x,y,z axis
sample_no: resample numble
historgram[i]:the number of data that equals i of the
resample data*/
getHistorgram(raw_data, resx, resy, resz, sample_no,
histogram[256])
begin
total_sno=sample_no*sample_no*sample_no;
xstep=resx/sample_no;
ystep=resy/sample_no;
zstep=resz/sample_no;
for z=0 to resz
for y=0 to resy
for x=0 to resx
begin
getDataOfSample(x,y,z);
x+=xstep;
y+=ystep;
z+=zstep;
end
for i=0 to total_sno
begin
temp=getDataFromSample(i);
histogram[temp]++;
end
Figure III.
Historgram info of the volume data algorithm
Specifically, the resample number can be user
defined based on different volume size, and then
uniformly sampling is used on the normalization volume
data(0~255), finally get the histogram info of the
resample volume data.
From the histogram info of the resample volume data,
we focus on the raw volume size、user defined resample
volume size、the background size(the total number of data
whose value is 0 ) and the background proportion (equals
background size/ resample size).The experimental results
lists in table I, where background proportion is shorted
for b_proportion.
An important conclusion of the volume data
characteristic obtained from table I is that the useful
size
Volume size
resample size
TABLE I.
CHARACTERISTIC OF THE VOLUME DATA
Volume data
bonsai foot aneurism
16777216 16777216 16777216
262144 262144 262144
background size 207393 1855550 259467
b_proportion 79.11% 70.78% 99%
object information just occupy a little proportion of the
volume data while the background proportion takes more
proportion. It is not unique, [6] presented that the
volumetric data set can be divided into two classes: one
class with the empty blocks and the other class with the
object blocks. These blocks classify into two classes: one
class is empty blocks that the mean value of the block is
0,and the rest blocks is the other class that also called
object blocks, So our Classification scheme show as
following.
⎧ Empty blocks, if Mean( Bi
) = 0
Total Blocks ⎨
⎩ Object blocks, if Mean( Bi
) ≠ 0
Figure IV.the classification strategy of our proposed algorithm
B. Encoding
The compression scheme of our proposed algorithm is
to take different ways to different blocks. Specifically,
only object blocks are decomposed into a three
hierarchical representation manner and should be vector
quantized while the empty blocks are ignored. The
hierarchical strategy is the same as the way used in [3,5].
For compassion convenience, the vector quantization of
the object blocks also take the splitting scheme based on
a principal component analysis[3,5]. One difference
should be pointed is that only the small part of object
blocks are trained in VQ. Thus, we do not only save a
large amount of computation, but also can get better
reconstruction image quantity because of leaving the
whole code words to the blocks that has the meaningful
information of the volume data.
With this compression scheme of our proposed
algorithm, we can get higher compression rate.
Considering a volume of N × M × K data points, each point
holds B bytes, the block size of is n × n×
n and the
down-sample block size of hierarchical representation is
( n /2) × ( n/2)
× n/2
. Suppose the number of object blocks
256