Cellular Automata for Image Resizing - Cellular Automata in Image Processing and Geometry - page 33

Fig. 2.3 Some examples of the applied CA transition rules

the low resolution image and the high resolution image, respectively. At the previ-
ous stage, cells indexed by

( , )

2 i 2 j were marked with states that simply apply the

=

following: F 2 i , 2 j f i , j . On the contrary, in order to keep the computational cost

low, pixels with the indices are ex-

pressed as a weighted summation of their adjacent pixel values of the low resolution
image. Thus, for the remapping process of these pixels, the following expressions
are introduced:

( 2 i , 2 j + 1 ) , ( 2 i + 1 , 2 j ) and ( 2 i + 1 , 2 j + 1 )

F 2 i , 2 j + 1 = a 11 × f i , j + a 12 × f i , j (2.5)

F 2 i + 1 , 2 j = b 11 × f i , j + b 12 × f i , j (2.6)

F 2 i + 1 , 2 j + 1 = c 11 × f i , j + c 12 × f i , j + 1 + c 21 × f i + 1 , j + c 22 × f i + 1 , j + 1 (2.7)

Each of the above weights is defined based on the state of the corresponding
cell of the CA grid. Also, the sum of each of the factors a , b and c must be equal
to one. For example, assuming that cell

( , )

2 i 2 j is defined as a non-edge cell and

as an edge cell (Fig. 2.3(a)), weight a 12 must be greater than a 11
to produce a more crisp transition between the non-edge and the edge pixel. In
addition, if both pixels are denoted as non-edge or edge pixels, the weights are
equal in order to produce an expanded homogenous or edged area. Based on the
case that Fig. 2.3(c) presents, the cell Y 2 i , 2 j + 1 is surrounded by the non-edge cell
Y 2 i , 2 j and the edge cell Y 2 i , 2 j + 2 . Thus, the following values are assigned to the a i , j
weights: a 11 =

cell ( 2 i , 2 j + 2 )

25 and a 12 =0.75. On the contrary, the cell Y 2 i + 1 , 2 j + 2 is surrounded
by edge cells, and thus, for the corresponding pixel, the following weights are used:
b 11 =

0 .

b 21 = 0 . 5.

2.4 Experimental Results

To assess the performance of the tested resizing methods including the proposed
method, several tested were performed. Zero-order, bilinear, bicubic [13], the New