Biomedical Engineering Reference
In-Depth Information
3.2 GLAM Algorithm for Sparse Model
An image can be modeled as a rectangular constitution S of m
n grids. Fur-
thermore, consider an image s with a neighborhood system N ={N
s
, s
×
∈
S} can be
de
ned. At which, the neighborhood N
s
is built from the basic neighborhood E at
pixel s. The basic neighborhood is thereby a chosen structural element [
13
]. Aura
Measure: [
13
] Given two subsets A, B
S, where |A| is the total number of
elements in A. The aura measure of A with respect to B for neighborhood system
N is given as follows:
ↆ
X
m
ð
A
B
N
Þ¼
a
j
N
s
\
B
j
;
;
S
2
1} be
the gray level set of an image over S with G as the number of different gray levels,
then the GLAM of the image A(N) is as follows:
GLAM: [
13
] let N be the neighborhood system over S and {S
i
,0
≤
i
≤
G
−
a
i
;
j
¼
A
ð
N
Þ¼
ms
i
;
s
j
;
N
∈
whereby S
i
={s
S | x
s
= i} is the gray level set corresponding to the ith level, and
m (S
i
, S
j
, N) is the aura measure of S
i
with respect to S
j
with the neighborhood
system N.
Because of the 16-bit resolution of the original image, the GLAM would be a
matrix with a maximum size of 65,536
65,536. To reduce the size of the matrix
and the necessary time for the retrieval, the ROI has to be quantized before the
GLAM generation. As discussed in the results, the smallest possible number of
allowed gray levels without loss of performance is eight. The result is a matrix with
64 entries which is transformed to a feature vector with 64 entries and normalized
for the feature comparison. Because of the normalization, the GLAM gets inde-
pendent from the size of the ROI. The details of the important variables in the
pseudo code are as follows:
×
Input
—
g = sparse model for ROI,
Output
glam,
gl = minimum in pixels intensity values,
gh = maximum of pixels intensity values,
range = range of pixel values to be considered, i.e., gh
—
−
gl + 1.
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