Given an nD digital image I based on cubical n-xel, to fully
characterize the degree of internal topological dissimilarity existing in I
when using different adjacency relations (mainly, comparing 2n or 2n −1
adjacency relations) is a relevant issue in current problems of digital
image processing relative to shape detection or identification. In this
paper, we design and implement a new self-dual representation for a
binary 2D image I, called {4, 8}-region adjacency forest of I ({4, 8}-RAF,
for short), that allows a thorough analysis of the differences between the
topology of the 4-regions and that of the 8-regions of I. This model can
be straightforwardly obtained from the classical region adjacency tree
of I and its binary complement image Ic, by a suitable region label
identification. With these two labeled rooted trees, it is possible: (a) to
compute Euler number of the set of foreground (resp. background) pixels
with regard to 4-adjacency or 8-adjacency; (b) to identify new local and
global measures and descriptors of topological dissimilarity not only for
one image but also between two or more images. The parallelization of
the algorithms to extract and manipulate these structures is complete,
thus producing efficient and unsophisticated codes with a theoretical
computing time near the logarithm of the width plus the height of an
image. Some toy examples serve to explain the representation and some
experiments with gray real images shows the influence of the topological
dissimilarity when detecting feature regions, like those returned by the
MSER (maximally stable extremal regions) method.Ministerio de Economía, Industria y Competitividad PID2019-110455GB-I00 (Par-HoT)Junta de Andalucía US-138107
