Bio-medical Ontologies Maintenance and Change Management

End;
for x1 = 0; 2*side+1 do
for y1 = 0; 2*side+1 do
Gr[x1,y1] = Gr[x1,y1]-m;
End;
End;
End;
Multimedia Medical Databases 115
Proposition 1: The Gabor_filter procedure has a temporal complexity O(n 2 ) where
n is the maximum dimension of the image (n= max{side, xs, ys}).
Proof: The operations from the beginning of the procedure are elementary and
don’t have the complexity more than O(1). The products of the matrices have
complexity O(dim1 *dim2 ), where ‘dim1 ’ and ‘dim2 ’ are the matrix dimensions (no
more than ‘n’, as it has been stated at the beginning of the procedure). The
function calls aren’t recursive, and the functions have a complexity no more than
O(n 2 ). So, the Gabor function has complexity O(side 2 ), due to the FOR loops
which contain only elementary operations of O(1) complexity. The functions
MatrixFFT2D, MatrixFFT2D, MatrixIFFT2D have complexity no more than
O(n 2
), because they contain at most 2 nested FOR loops each having the maximum
dimension ‘n’ and operations of O(1) complexity. The result is that the whole
procedure has the time complexity O(n 2
).
4.3 Co-occurrence Matrices
For comparison, the method based on co-occurrence matrices is implemented.
In the case of color images, one matrix was computed for each of the three
channels (R, G, B). For an image f(x, y), the co-occurrence matrix hdf (i, j) is
defined so that each entry (i, j) is equal to the number of times for that f(x 1 ,y 1 )=i
and f(x 2 ,y 2 )=j, where (x 2 ,y 2 ) = (x 1 ,y 1 ) + (d cos φ, d sin φ) [18].
This leads to three quadratic matrices with a dimension equal to the number of
the color levels presented in an image (256 in our case), for each distance d and
orientation f.
The classification of texture is based on the characteristics extracted from the
co-occurrence matrix: energy, entropy, maximum probability, contrast, inverse
difference moment and correlation [18].
Energy:
Entropy:
∑
∑
a , b ; a ≠ b
P
λ
Φ , d
( a,
b)
a − b
2
PΦ , d Φ d
a,
b
( a,
b)
log 2 P , ( a,
b)
k
(4.5)
(4.6)