13-11-2012, 02:27 PM
Image Reduction Using Means on Discrete Product Lattices
ABSTRACT
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 the 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.