Bio-medical Ontologies Maintenance and Change Management

Multimedia Medical Databases 99
3.6.1 Histogram Intersection
Swain and Ballard were the ones that have investigated the use of histogram intersection
for color image retrieval. Their objective was to find known objects inside
the images, using color histograms. When the size of the object q is smaller than
the size of the image t and the histograms are not normalized, then: |hq| ≤ |ht|.
The histogram intersection hq and ht is given by [84, 85, 86]:
Where:
d
q,
t
M 1
∑ −
min( hq[
m],
ht[
m])
m=
0 = 1−
(3.18)
min(| h |, | h |)
∑ − M 1
m=
0
q
t
| h | = h[
m]
(3.19)
The complexity of the method is O(m × n) where m represents the number of
colors resulted from the quantization process and n represents the number of images
in the database.
3.6.2 Histogram Euclidian Distance
Having two histograms h q and h t , then the Euclidian distance is given by [84,
85, 86]:
,
1
2
∑(| [ ] [ ] |)
0
−
d q t
M
= hq
m − ht
m
m=
(3.20)
The complexity of the method is O(m × n) where m represents the number of
colors resulted from the quantization process and n represents the number of images
in the database.
3.6.3 Quadratic Distance between Histograms
The quadratic distance uses the cross-correlation between histogram elements
based on the perceptual similarity of the colors. The quadratic distance between
the histograms h q and h t is given by [84, 85, 86]:
d
q,
t
=
− M 1 M −1
∑∑
m0
= 0m1
= 0
( h [ m ] − h [ m ] ) a
q
0
t
0
m0m1
( h [ m ] − h [ m ])
q
1
t
1
(3.21)
Where A = [a i,j ], and a i,j represent the similarity between elements having the indexes
i and j. The quadratic metric is a true metric distance when a i,j = a j,i (symmetrical)
and a i,i = 1.