  Multiscale shape skeletonization on pixel adjacency graphs is an advanced
intriguing research subject in the field of image processing, computer vision
and data mining. The previous works in this area almost focused on the graph
vertices. We proposed novel structured based graph morphological
transformations based on edges opposite to the current node based
transformations and used them for deploying skeletonization and reconstruction
of infrared thermal images represented by graphs. The advantage of this method
is that many widely used path based approaches become available within this
definition of morphological operations. For instance, we use distance maps and
image foresting transform (IFT) as two main path based methods are utilized for
computing the skeleton of an image. Moreover, In addition, the open question
proposed by Maragos et al (2013) about connectivity of graph skeletonization
method are discussed and shown to be quite difficult to decide in general case.
