Image Processing Algorithms Implementation Using Quantum Cellular Automata - Cellular Automata in Image Processing and Geometry - page 66

Fig. 4.2 The dilation of an object by a structuring element

So, the dilation is the union of the pixels, of a copy of S at every pixel of the binary
object A in the input image. This definition is written as:

S ( A ↕ S = i , j ) (4.2)

( i , j ) ∈ A

Fig. 4.2 presents another object A in an input image, the same structuring element
S which is symmetrical and the dilated image A S where the grey pixels are the

dilated pixels that are considered as part of the output image (in fact they are black).
The design and simulation of morphological erosion and dilation with nanoelec-
tronic circuits will be presented in Sect. 4.5.

↕

4.3 Quantum-dot Cellular Automata

Single electron technology is defined as the capability to control the transport and
the position of a single electron or a small number of electrons in nanometer struc-
tures. Significant research is being done on the field of modelling and simulation of
SET devices and circuits [10, 68, 70], which is accompanied by the development of
an efficient single electron circuit theory [16].
QCA is considered as a single electron technology. The conventional digital tech-
nologies use ranges of voltage or current to represent binary values “0” and “1”. In
contrast, QCA uses the position of electrons in quantum dots to represent the binary
values. The information is stored as configurations of electron pairs in quantum dot
arrays. The unit of information is kept in a QCA cell which is presented in Fig. 4.3.
The QCA cell is the basic building block of QCA devices and it consists of four
quantum dots in a square array coupled by tunnel barriers. The physical mechanisms
for interactions between dots are the Coulomb interactions and quantum-mechanical
tunnelling. Electrons are able to tunnel between the dots, but cannot leave the cell.
If two mobile electrons are placed in the cell, in the ground state and in absence of