Relative Fuzzy Connectedness on Directed Graphs and its Application in a Hybrid Method for Interactive Image Segmentation
Résumé
Image segmentation consists of dividing an image into its compo-
sing regions or objects, for example, to isolate the pixels of a target
object of a given application. In segmentation of medical images,
the object of interest commonly presents transitions at its border
predominantly from bright to dark or dark to bright. Traditio-
nal region-based methods of image segmentation, such as Relative
Fuzzy Connectedness (RFC), do not distinguish well between si-
milar boundaries with opposite orientations. The specification of
the boundary polarity can help to alleviate this problem but
this requires a mathematical formulation on directed graphs.
A discussion on how to incorporate this property in the RFC
framework is presented in this work. A theoretical proof of the
optimality of the new algorithm, called Oriented Relative Fuzzy
Connectedness (ORFC), in terms of an energy function on
directed graphs subject to seed constraints is presented, and
its application in powerful hybrid segmentation methods. The
hybrid method proposed ORFC & Graph Cut preserves the
robustness of ORFC respect to the seed choice, avoiding the
shrinking problem of Graph Cut (GC), and keeps the strong con-
trol of the GC in the contour delination of irregular image
boundaries. The proposed methods are evaluated using medical
images of MRI and CT images of the human brain and thoracic
studies.
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