(IEEE, 2012) Beliakov, Gleb; Bustince Sola, Humberto; Paternain Dallo, Daniel; Automática y Computación; Automatika eta Konputazioa
We investigate the problem of averaging values on
lattices, and in particular on discrete product lattices. This
problem arises in image processing when several color values
given in RGB, HSL, or another coding scheme, need to be
combined. We show how the arithmetic mean and the median
can be constructed by minimizing appropriate penalties, and we
discuss which of them coincide with the Cartesian product of
the standard mean and median. We apply these functions in
image processing. We present three algorithms for color image
reduction based on minimizing penalty functions on discrete
product lattices.
