begin with, we extract the feature vectors consisting of mean and
variance of pixel intensity values (as in (2) and (3)) from the
images in the database. We then form initial clusters by applying
K-means clustering algorithm on the extracted features. Subse-
quently, we generate a dictionary for each cluster using the K-SVD
method. By assigning the images that are sparsely represented by
the dictionary, we create a new cluster for each dictionary. These
clusters in turn are used to update the Dictionaries through the
K-SVD algorithm. The updated dictionaries are then used to
update the clusters using the OMP algorithm. This process goes
on iteratively back and forth between dictionary and sparsity
updates, until clusters converge. We match the query image with
the existing dictionaries to identify the dictionary that gives the
sparest representation. The images in the cluster associated with
this dictionary are compared using a similarity measure to retrieve
images similar to the query image. The entire process of proposed
content based medical image retrieval is (shown Fig. 2) elaborated
in more detail through the following steps:
Let fy
j
g
M
j ¼ 1
represent the set of feature vectors of the database
of M images. Suppose N is the number of clusters. We obtain the
initial clusters by solving the following K-means algorithm:
fC
1
; C
2
; …; C
N
g¼ arg min
f
^
C
1
;
^
C
2
;…;
^
C
N
g
X
N
i ¼ 1
X
y
j
A
^
C
i
‖y
j
^
μ
i
‖; ð4Þ
where
^
μ
i
is the mean of points in
^
C
i
.LetC
i
be the matrix containing
cluster members as columns corresponding to the ith cluster. Then
the proposed method may be summarized as follows:
Dictionary update: From the initial clusters C
1
; C
2
; …; C
N
,we
obtain the dictionaries D
1
; D
2
; …; D
N
by using the K-SVD
approach (1) as follows:
ðD
i
; Φ
i
Þ¼arg min
^
D
i
;
^
Φ
i
‖C
i
^
D
i
^
Φ
i
‖
2
F
subject to j
^
γ
i
j
0
r T
0
8i; ð5Þ
satisfying C
i
D
i
Φ
i
; i ¼ 1; 2; …; N:
Cluster assignment: From the Dictionaries so learnt, we update
the clusters in this step, which is done based on the premise
that two images belonging to the same cluster have decom-
position in terms of similar dictionary atoms. Let D be the
concatenation of all dictionaries as ½D
1
; D
2
; …; D
N
. Our pro-
posed method considers obtaining the sparsest representation
of y
j
ðj ¼ 1; 2; ‥; MÞ in an appropriate dictionary D
^
i
from:
α
j
¼ arg min
ω
‖y
j
Dω‖
2
2
subject to ‖ω‖
0
r T
0
;
^
i ¼ arg min
i
‖y
j
Dδ
i
ðα
j
Þ‖
2
2
; j ¼ 1; 2; …; M; ð6Þ
where
δ
i
is a characteristic function that selects the coefficients.
Then y
j
is assigned to C
^
i
which is associated with the
^
ith
dictionary. In (6), the first step finds T
0
number of atoms from D
that sparsely describe y
j
, while the second step identifies the
concentration of atoms from a particular dictionary.
We repeat the cluster assignment and dictionary update steps till
there is no significant change in the clusters C
i
ði ¼ 1; 2; ‥; NÞ. The
above-mentioned clustering methodology may be summarized as
the following optimization problem:
min
fD
i
g;fC
i
g
X
M
j ¼ 1
X
y
j
A C
i
min
α
‖y
j
Dδ
i
ðαÞj
2
2
þγjαj
1
; ð7Þ
where
γ 4 0. Given a query image x
q
, in line with (6),wefind the
cluster that is closest to the query image by identifying the
corresponding dictionary admitting representation to x
q
from
the following optimization problem:
β ¼ arg min
ω
‖x
q
Dω‖
2
2
subject to ‖ω‖
0
r T
0
: ð8Þ
We consider the cluster C
^
i
to be most relevant to the query image
if
^
i satisfies ‖x
q
Dδ
^
l
ðβÞ‖
2
o ‖x
q
Dδ
j
ðβÞ‖
2
8j a
^
i. In the event of
tie, that is,
J x
q
Dδ
^
i
ðβÞ J ¼ J x
q
Dδ
^
l
ðβÞ J o J x
q
Dδ
j
ðβÞ J 8ja
^
l;
^
i; ð9Þ
we search for relevance of x
q
in C
^
i
and C
^
l
.
After determining the most relevant cluster, we identify the
relevant images within the cluster using a similarity metric. To
evaluate similarity between images based on the selected features,
an appropriate similarity/dissimilarity metric needs to be chosen. A
large class of similarity measures are used in the literature [34].In
this paper, we use three type of similarity metrics, namely,
Euclidean distance (ED), Mahalanobis distance (MD) and Cross
correlation (CC). The proposed algorithm is summarized as follows:
Algorithm 1. Summary of the proposed CBMIR algorithm.
Step 1. Extract features from the members of
medical database
Step 2. Apply K-means clustering algorithm on the
extracted features to generate initial clusters
Table 1
Performance measures (%) of the Proposed, Fuzzy C-means and K-means clustering
methods obtained with the first feature extraction method and the Euclidean
distance as similarity measure.
Query Proposed Method-I Fuzzy C-means-I K-means Clustering-
I
Images/Clusters N¼3 N ¼ 4 N¼5 N¼ 3 N¼4 N¼5 N¼3 N¼4 N¼5
1.png 100 90 100 0 0 50 50 0 45
2.png 80 90 100 10 0 40 70 25 10
3.png 70 70 100 100 40 60 60 20 30
4.png 100 100 100 100 50 60 80 100 55
5.png 100 100 80 90 50 50 60 85 45
6.png 100 100 100 80 60 40 80 100 100
7.png 90 100 80 50 100 20 50 0 10
8.png 100 80 100 100 50 0 50 0 60
9.png 70 80 80 80 40 60 70 20 30
10.png 100 100 80 90 50 50 70 80 50
11.png 100 90 100 20 10 50 50 0 50
12.png 90 100 60 90 50 40 70 90 80
13.png 100 80 80 90 40 0 50 0 10
14.png 90 90 90 50 60 20 60 10 50
Precision (%) 92:1 90.7 87.8 67:8 42.8 38.5 62:1 37.8 41.4
Recall (%) 79:6 78.8 74.7 68:2 62 60.7 32:6 35.5 60.2
Table 2
Performance measures (%) of the Proposed, Fuzzy C-means and K-means clustering
methods using second feature extraction method and Euclidean distance as
similarity measure.
Query Proposed Method-
II
Fuzzy C-means-II K-means Clustering-
II
Images/clusters N¼3 N¼4 N ¼ 5 N¼3 N¼4 N¼5 N¼ 3 N¼4 N¼5
1.png 100 100 100 70 60 60 30 30 0
2.png 100 100 90 80 70 60 40 10 20
3.png 90 70 100 80 70 50 57.1 50 50
4.png 100 80 100 90 50 40 50 40 50
5.png 100 100 90 90 70 20 70 40 100
6.png 90 90 80 60 40 80 80 20 70
7.png 100 100 100 50 70 70 100 100 50
8.png 100 100 80 25 0 0 80 40 0
9.png 90 88.8 90 85.7 83.3 87.5 100 90 43
10.png 100 90 90 90 90 80 90 60 32
11.png 100 77.7 60 83.3 50 16.6 100 60 0
12.png 100 100 90 77.7 80 80 80 40 50
13.png 90 90 40 83.3 60 100 0 40 30
14.png 100 100 100 83.3 20 0 0 40 20
Precision (%) 97:14 91.8 86.4 74:8 54 48 62 :6 45 43
Recall (%) 80:1 83.2 76.9 60 58.2 68 48 38 32
M. Srinivas et al. / Neurocomputing 168 (2015) 880–895 883
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