Image processing and magnetic material have
two similar theoretical structures with each other.
The similarities are very simple.
They are constructed from many elements.
The many elements interact with each other.
As you know, the classical spin systems have a lot of spins
and each spin interacts with the neighboring spins.
The ordered state is determined from interactions and external fields.
On the other hand, images are constructed from a lot of pixels.
Output of each pixel are determined
from the input values of the neighboring pixels.
Output images are determined from a priori information
and given data.
Thus, the conventional image processing theory
and the classical spin system have the similar structure.
In the classical spin system, the phase transition occurs
at a critical temperature.
Below the critical temperature,
the classical spin system has a disordered state,
for example Paramagnetic state.
Above the critical temperature, the classical spin system
has an ordered state, for example Ferromagnetic state.
In statistical mechanics, many researchers investigate
the classical spin systems near the critical temperature.
Near the critical temperature, fluctuation is enhanced.
Statistical mechanics has a lot of techniques
to treat fluctuation near the critical temperature.
On the other hand, it is difficult for conventional filters
to treat fluctuation in data systematically.
In the present project, the statistical mechanical strategies
are employed to treat fluctuation in data in image processing.
