CLC-Conference-Proceeding-2018

The stop function finds the zero or a value below
a threshold ε prefixed, for example:
In the iterations it is observed that there is no
improvement in the minimization of the cost
function, for example,
.
There is only a small change in the update of
factors and .
The maximum number of iterations is exceeded.
About another stopping criteria can be read in
Appendix 5.A of xxxvi .
2. Three selected applications of the NMF
NMF have been used as a solution model
in different areas, for example, signal and image
processing, as clustering methods, in text mining
and many others. In this section some of the
applications in which the Images Group of the
University of Havana is currently working are
presented.
2.1 Image segmetation: Mamographies
and Colposcopies
The segmentation of images viewed from
the perspective of the clustering algorithms can
be considered as a semi-supervised technique.
This task of image processing has been
addressed in the literature with various strategies
and is one of the first steps in the processing of
images after the improvement of contrast,
elimination of noise or some other necessary
preprocessing depending on the appearance of
the images to be treated.
In this paper 2D images are considered
and the adjacency matrix associated with the
similarity graph, where the information of the
pixels and their neighbors can been represented.
.
Depending on the application, information of
similarity or dissimilarity can be represented.
In xxxvii different graphs are studied with
information of similarity between pixels (εneighborhood,
knn, knnmutuo and complete).
The introduction of
superpixels
constructed under certain considerations is also
studied so that they represent the best possible
local information and the dimension of the
problem is reduced. The fundamental idea of
segmentation is to achieve a new representation
of the image so that it can be interpreted better.
We will consider that in our images we
do not have overlapping objects so that the
segmentation can be seen as obtaining a partition
in disjoint subsets whose union constitutes the
complete image. Seen that way we take the
definition from xxxviii :
Definition 1: Let be an image on a 2-D,
domain. Segmentation is defined as the
process of finding
a visual meaning to partitioning the domain
: an object of the
image
.
The term segmentation covers a wide
range of processes through which the division of
the image into different disjoint regions is
obtained based on a certain homogeneity of
these.
Segmentation has been treated using
threshold-based methods, graph-based methods
(hierarchical segmentation), methods based on
the recognition of edges or shapes, methods of
growth of regions, those based on grouping
algorithms and mathematical morphology. The
success of many of them lies in the a priori
information of the image, the definition of the