Topological Framework for Digital Image Analysis with Extended Interior and Closure Operators
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Date
2012-09-25
Authors
Fashandi, Homa
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Abstract
The focus of this research is the extension of topological operators with the addition
of a inclusion measure. This extension is carried out in both crisp and fuzzy topological
spaces. The mathematical properties of the new operators are discussed and compared with
traditional operators. Ignoring small errors due to imperfections and noise in digital images
is the main motivation in introducing the proposed operators. To show the effectiveness of
the new operators, we demonstrate their utility in image database classification and shape
classification. Each image (shape) category is modeled with a topological space and the
interior of the query image is obtained with respect to different topologies. This novel way
of looking at the image categories and classifying a query image shows some promising
results. Moreover, the proposed interior and closure operators with inclusion degree is
utilized in mathematical morphology area. The morphological operators with inclusion
degree outperform traditional morphology in noise removal and edge detection in a noisy
environment
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Keywords
topology, fuzzy topology, inclusion degree, interior operator with inclusion degree, closure operator with inclusion degree, image database classification, mathematical morphology