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Summary: INCLUSION FILTERS: A CLASS OF SELF-DUAL
CONNECTED OPERATORS
Nilanjan Ray, Member, IEEE, and Scott T. Acton, Senior Member, IEEE
Abstract In this paper we define a connected operator that either fills or retains the holes of the
connected sets depending on application-specific criteria that are increasing in the set theoretic
sense. We refer to this class of connected operators as inclusion filter, which is shown to be
increasing, idempotent and self-dual (gray level inversion invariance). We demonstrate self-
duality for 8-adjacency on a discrete Cartesian grid. Inclusion filters are defined first for binary-
valued images, and then the definition is extended to grayscale imagery. It is also shown that
inclusion filters are levelings, a larger class of connected operators. Several important
applications of inclusion filters are demonstrated automatic segmentation of the lung cavities
from magnetic resonance imagery, user interactive shape delineation in content based image
retrieval, registration of intravital microscopic video sequences, and detection and tracking of
cells from these sequences. The numerical performance measures on 100 cell tracking
experiments show that the use of inclusion filter improves the total number of frames
successfully tracked by five times and provides a threefold reduction in the overall position error.
Index terms connected operator, adjacency tree, self-duality, level sets.
Accepted in: IEEE Transactions on Image Processing (EDICS 2-NFLT)
This work has been supported in part by the Whitaker Foundation.
Corresponding Author:
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