GVU Technical Report Number:
GIT-GVU-93-27
Title:
Topological Considerations on Gray Level Skeletonization
Authors:
Joaquin Madrid
Russell M. Mersereau
Norberto F. Ezquerra
Abstract:
Analyzing the topological properties of algebraic opening and closing, we
characterized the skeletonization of gray level signals as a homotopic
transformation; i.e. a continuous deformation of the signal into a simple
representation that preserves the connectivity of the signal features.
To perform such a transformation, we interpret the morphological opening
and closing as algorithmic approximations, in which the structural
element imposes the connectivity criteria of the results. Our
implementation is a variation of Serra's residual of openings, and is
valid for any topology on the working space. We show a particular
application and discuss the design of the appropriate structural elements.
Keywords:
Open set, basic neighborhood, connectivity, homotopy, morphological
transformations, complete lattice, skeleton
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