G. Urcid and J.C. Valdiviezo-N. (Mexico)
Color image segmentation, convex sets, lattice associative mem ories, linear mixing model, minimax algebra, RGB color space.
This manuscript introduces a new technique for autonomous
segmentation of color images in Red-Green-Blue (RGB) space
that makes use of lattice auto-associative memories (LAAMs).
LAAMs are artiﬁcial neural networks able to store a ﬁnite set X
of pattern vectors and retrieve them almost correctly when a noisy
or incomplete input is presented. Two dual lattice auto-associative
memories have been established, the min memory W XX and the
max memory MXX whose column vectors, scaled appropriately,
are used to determine a tetrahedron enclosing a subset of X.
Speciﬁcally, the column vectors of each memory will correspond
to the most saturated color pixels. Thus, from the perspective of
convex set geometry, the scaled column vectors of a LAAM are
extreme points of a convex subset of X (tetrahedron), and any
other pixel can be considered a linear mixture of these points.
Unsupervised segmentation of a color image is then realized by
unmixing pixels using the non-negative least square method. We
provide illustrative examples to demonstrate the effectiveness of
our method as well as segmentation results for some RGB color