CLC-Conference-Proceeding-2018

thresholds, the seeds or centroids or the type of
structuring element to be used. For a review on
these strategies see xxxix and the literature cited
there.
In the development of tools for the
efficient imagenological diagnosis of breast
cancer (mammography images) or cervix cancer
(colposcopy), the segmentation of this type of
images acquires special utility, as injuries can be
marked and related information can be obtained
extracting the corresponding features. These
tools must be able to process a large number of
images in real time, so that the dimension of the
problem to be treated must be taken into account
seriously.
The spectral segmentation based on the
analysis of the eigenvalues of the Normalized
Laplacian, for example, among other equivalent
strategies, in general obtains very good results
but they are expensive processes from the
computational point of view. Because of this,
approaches aimed at reducing the dimension of
the problem have been widely treated in the
literature.
Figure 2 of xl shows a result of the studies
conducted in the segmentation of
mammographies based on the information of the
spectrum of the Normalized Laplacian
Normalized of the adjacency matrix associated to
the graph that contains the information of the
image. In these works the superpixels are
introduced following several strategies as a way
of reducing the dimension of the problem and the
results are compared using several types of
similarity graphs (ε-neighborhood, knn,
knnmutuo). The experiments of these works were
carried out with the images from the INbreast
Database xli .
(a) (b) (c)
Figure 2: In (a) the original image of
INbreast with the marked lesion is shown, in (b)
the segmentation obtained without superpixels
and in (c) with superpixels xlii .
In xliii the equivalence relation between the
NMF, the spectral grouping and K-means is
studied. Once the applications with the spectral
segmentation are carried out, the study will be
extended now to the use of the NMF in its
classical model and to the model that includes
sparsity and orthogonality constraints.
Different ways are considered to initialize
the matrices and to define the internal rank or
dimension of the matrices, among them the
criterion proposed by the group in xliv to obtain a
good sparse approximation of large and dense
matrices. The definition of the internal rank is
directly related to the number of groups or
clusters, so it is very important to use an
appropriate strategy.
The study is also perfomed for
Colposcopy images. The fundamental challenge
in these images is the preprocessing in which
problems such as the elimination of brightness,
uneven lighting and the different appearances
that these images present must be solved.
2.2 Removing the specularity reflection
in Colposcopies
Colposcopy images (Colposcopies) are
taken with a Colposcope that that has a lens with
a light. Colposcopies of cervix have an annoying
effect of brightness in some areas (the wettest)
that affects the proper processing of the image.