Cellular Automata for Image Resizing - Cellular Automata in Image Processing and Geometry - page 34

Edge-Directed Interpolation (NEDI) [20], the edge-oriented [8] and the proposed
method were tested on both color and grayscale images of various resolutions. The
key idea of bilinear interpolation is to perform linear interpolation first in one direc-
tion, and then again in the other direction. The whole interpolation, although each
step is linear in the sampled values and in the position, is considered not linear but
rather quadratic in the sample location. In general, bilinear interpolation can be used
where perfect image transformation with pixel matching is impossible, so that one
can calculate and assign appropriate values to pixels with less computational bur-
den. The nearest neighborhood interpolation selects the value of the nearest point
and does not consider the values of neighboring points at all, yielding a piecewise-
constant interpolant. In bicubic interpolation method [13], interpolated surface is
smoother than corresponding surfaces obtained by bilinear interpolation or nearest
neighbor interpolation and usually applies when speed is not an issue. In contrast
to bilinear interpolation, which only takes 4 pixels (2 × 2) into account, bicubic in-

terpolation considers 16 pixels (4 4) resulted to smoother resampled images with

fewer interpolation artifacts with the handicap of less computational speed com-
pared with bilinear interpolation execution. In NEDI interpolation method, the ba-
sic idea is first to estimate local covariance coefficients from a low resolution image
and then use these covariance estimates to adapt the interpolation at a higher res-
olution based on the geometric duality between the low resolution covariance and
the high-resolution covariance [20]. The edge-directed property of covariance-based
adaptation attributes to its capability of tuning the interpolation coefficients to match
an arbitrarily oriented step edge. A hybrid approach of switching between bilinear
interpolation and covariance-based adaptive interpolation is proposed to reduce the
overall computational complexity. Finally, the basic idea of the edge-oriented algo-
rithm is to partition digital images into homogeneous and edge areas based on the
analysis of the local structure on the images. In addition, in order to have better
performance on interpolating images, specified algorithms are assigned to interpo-
late each classified areas, respectively. In this way, the edge-oriented interpolation
method succeeds to lower the resulting computational complexity when compared
with the aforementioned image interpolation techniques.
To compare all the above resizing methods with the proposed one CA based
method several images were selected based on their appropriateness as found in rel-
evant literature. All original images were initially down sample and then up sampled
by the same algorithm to meet the initial dimensions. The results shown in Figs. 2.4,
2.5, 2.6 and 2.7 are a comparison of all the applied algorithms for gray as well as
color images of the Koala, Cameraman, Lena, Box, Building, Teddy, Statue, Butter-
fly, Port and Garden images, respectively. In order to quantify the effectiveness of
every method, the Peak Signal-to-Noise Ratio ( PSNR ) metric was calculated by the
following formula:

×

√ MSE

PSNR ( db ) = 20 × log 10 ( 255 / ) (2.8)