Cellular Automata for Image Resizing - Cellular Automata in Image Processing and Geometry - page 31

their application in real-time systems is not prohibitive. In order to produce accurate
edge maps with high frame rates, the Canny edge detector was incorporated. As
mentioned in Subsect. 2.2.2 the proposed edge detector algorithm is considered as
one of the optimal edge detectors found in literature. Taking into account the fact
that the edges occurring in images should not be missed while there should be no
responses for non-edges the Canny detector succeeds to achieve low error rates.
Moreover, it attempts to keep the distance between the selected edge pixels and
the actual edges as closer as possible to minimum. Finally, it seeks for only one
response per edge thus eliminating any multiple responses to an edge. In brief, the
most significant criteria of this selection are as found below:

• Correct detection: Edges are detected with high probability when these exist in

the original images.

• Accurate localization: Marked edges are accurately close to the edges in the

original images.

• Minimal response: A defined edge is detected only once, and where possible,

noise should not create false edges.

2.3.2 CA Resizing

Motivated by the binary nature of the calculated edge maps, a CA is proposed to
define the state of the additional cells that resulted after the resizing process and
eventually the pixels' values. Without the loss of generality, it is assumed that the
high resolution edge map Y i , j of size 2 M

× 2 N directly comes from of size M ×

=

N . Thus, it yields Y 2 i , 2 j X i , j . Figure 2.2 provides a schematic illustration of the

resulted enlarged edge map.
The enlarged edge map is considered to be a 2-D lattice of cells where every
binary pixel is represented by a cell. Thus, the proposed CA grid has the same di-
mensions with the enlarged image. Moreover, in order to update the state of each
cell, Moore neighborhood is adopted; therefore, Equation 2.3 is used with a radius r
equal to 1. In addition, the set of states must be defined. Since the enlarged edge map
includes non-edge cells (stated as “0”), edge cells (stated as “1”) and undefined cells,
we assume that the undefined cells are marked with the state “2”. In conclusion, the
cells of the CA before its evolution can be marked with three states: “0” (non-edge
cell), “1” (edge cell) and “2” (undefined cell). Taking advantage of the CA flexibil-
ity, the transition rules as well as the states of the cells after the evolution are created
in order to preserve the edges. The basic motive is to create states that eventually
will produce more crisp transitions of light intensities from non-edge pixels to edge
pixels during the remapping process. By using such states, the orientation of each
edge is considered.
For example, based on the lattice of Fig. 2.2, let us assume that the cell Y 2 i , 2 j is
marked as a non-edge cell while the cell Y 2 i , 2 j + 2 is an edge cell. The intermediate