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IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 13, NO. 6, JUNE 2004 853 Constraining Active Contour Evolution
 

Summary: IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 13, NO. 6, JUNE 2004 853
Constraining Active Contour Evolution
via Lie Groups of Transformation
Abdol-Reza Mansouri, Dipti Prasad Mukherjee, Senior Member, IEEE, and Scott T. Acton, Senior Member, IEEE
Abstract--We present a novel approach to constraining the
evolution of active contours used in image analysis. The proposed
approach constrains the final curve obtained at convergence of
curve evolution to be related to the initial curve from which evo-
lution begins through an element of a desired Lie group of plane
transformations. Constraining curve evolution in such a way is
important in numerous tracking applications where the contour
being tracked in a certain frame is known to be related to the
contour in the previous frame through a geometric transformation
such as translation, rotation, or affine transformation, for example.
It is also of importance in segmentation applications where the
region to be segmented is known up to a geometric transformation.
Our approach is based on suitably modifying the Euler-Lagrange
descent equations by using the correspondence between Lie groups
of plane actions and their Lie algebras of infinitesimal generators,
and thereby ensures that curve evolution takes place on an orbit of

  

Source: Acton, Scott - Department of Electrical and Computer Engineering, University of Virginia

 

Collections: Computer Technologies and Information Sciences