Lattice Algebra Approach to Color Image Segmentation
This manuscript describes a new technique for segmenting color images in different color spaces based on geometrical properties of lattice auto-associative memories. Lattice associative memories are artificial neural networks able to store a finite set X of n-dimensional vectors and recall them when a noisy or incomplete input vector is presented. The canonical lattice auto-associative memories include the min memory W (XX) and the max memory M (XX) , both defined as square matrices of size nxn. The column vectors of W (XX) and M (XX) , scaled additively by the components of the minimum and maximum vector bounds of X, are used to determine a set of extreme points whose convex hull encloses X. Specifically, since color images form subsets of a finite geometrical space, the scaled column vectors of each memory will correspond to saturated color pixels. Thus, maximal tetrahedrons do exist that enclose proper subsets of pixels in X and such that other color pixels are considered as linear mixtures of extreme points determined from the scaled versions of W (XX) and M (XX) . We provide illustrative examples to demonstrate the effectiveness of our method including comparisons with alternative segmentation methods from the literature as well as color separation results in four different color spaces.
color image segmentation color spaces lattice auto-associative memories convex sets linear mixing model pixel based segmentation unsupervised clustering