Bio-medical Ontologies Maintenance and Change Management

98 L. Stanescu, D. Dan Burdescu, and M. Brezovan
Rm = wc ∈ ℜ k
: Qc (wc ) = y (3.15)
m
From the partitions definition results that the partitions completely covers ℜ k
and they are not intersected:
U m
k
m = and m ∩ Rn
= θ
R ℜ
R ∀ m ≠ n
(3.16)
In conclusion, the partitions represent a complete partitioning of ℜ k
.
In these circumstances it can be defined the color with the index value m, as a
color unit that corresponds to a partition Rm and which is generated by the color
set of points {vc } m that are assigned to the same code ym for the vector
transformation and quantization [84, 86].
ym = Qc ( Tc vc ) (3.17)
v c
0
1
2
T c
w c
0
1
2
M
Qc Fig. 3.5. The transformation (T c ) and quantization (Q c ) produce the color histogram h c and
the binary color set s c
3.6 Computing Color Features Similarity in Content-Based Visual Retrieval
In this section we present a number of methods used for computing the color
similarity of the images, using color histograms.
As specified above, the histograms indicate the color distribution in an image or
regions. Because the histograms are discrete distributions, they can be represented
as characteristics vectors in an M-dimensional space, where M represents the
number of distinct colors in histogram. This space is defined as the histogram
space, H M .
The histogram space H M is considered to be a metric space and the histograms
h are points in this space, if the following condition is true [18]: for each couple of
histograms hi, hj it can be found a corresponding number v(hi,hj), called the
distance between the points hi and hj, that satisfies the followings:
M
Bc • v(hi,hj) = 0 ( identity)
• v(hi,hj) ≥ 0 ( non-negativity)
• v(hi,hj) = v(hj,hi) ≥ 0 (if hi ≠ hj) (commutability / symmetry )
• v(hi,hq) ≤ v(hi,hj) + v(hj,hq) (triangle non-equality)
h c
s c