Cellular Automata for Image Resizing - Cellular Automata in Image Processing and Geometry - page 25

manipulation of these image data types in systems with low technical specifications
is a significant issue in their overall performance. Image interpolation techniques
focus on expanding images originally acquired with low resolution cameras or sen-
sors ( M N pixels) and are found to be

the most commonly adopted methods for image enlargement. Image interpolation
works using known data to estimate values at unknown points, i.e. it works in two
directions, trying to achieve the best approximation of a pixel's color or intensity
based on the values of surrounding pixels.
A usual classification of image interpolation techniques includes adaptive and
non-adaptive algorithms. Non-adaptive algorithms usually apply to all image pixels
with the same manner while adaptive techniques take into account what they are
interpolating (sharp edges vs. smooth texture) and change accordingly the treatment
of the corresponding pixels. The latter algorithms are primarily designed to max-
imize artifact-free detail in enlarged photos, so some cannot be used to distort or
rotate an image. Several commonly non-adaptive used interpolation methods have
been suggested for image resizing, such as the nearest neighbor interpolation [13],
bilinear interpolation [13], bicubic interpolation [18] and spline interpolation [11].
Linear approaches are the most frequently applied for the resizing process due to
their low computational burden. However, those methods produce image artifacts
like blurring on edges since no information related to abrupt changes of light in-
tensity is considered, usually failing to preserve the quality of the edges and con-
sequently produce resized images with blurred edges or annoying zigzag artifacts.
On the contrary, nonlinear methods produce better results. Nevertheless, they have
a larger computational burden and involve blurring, as well. Various generic ap-
proaches have been proposed to improve the subjective quality of the interpolated
images and overcome such deficiencies. In addition, the method in [14] is based on
variation models with smoothing and orientation constraints. The nonlinear Partial
Differential Equation (PDE) problem is simplified into a series of problems with ex-
plicit solutions. Furthermore, the area based interpolation scheme in [1] computes
each interpolated pixel by proportional area coverage of a window filter which is
applied to the input image. A quadratic image interpolation method [23] has been
proposed with adequate visual results but its computational cost remains high. Fi-
nally, a method to estimate the model parameters piecewisely is proposed in [36]
using an autoregressive image model. The method utilizes the covariance matrix of
the high resolution image itself, with missing pixels properly initialized. Neverthe-
less, conventional linear interpolation schemes based on space-invariant models also
fail to preserve the quality of edges and, consequently, result to images with blurred
edges and artifacts.
An alternative type of approaches has been introduced, namely edge-directed in-
terpolation methods, in order to preserve the edges of the low resolution image and
produce more crisp results. Edge-directed interpolation methods apply a variety of
operators according to the edge directions [6]. A fuzzy interpolation approach is pro-
posed in [7] for two dimensional signal resampling however additional processing
for edge identification is required. In addition, a neural network approach has been
proposed in [10] to approximate the computational rules of interpolation algorithms

N pixels) into up-sampled images ( M ×

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