Proximal Čech Complexes in Approximating Digital Image Object Shapes. Theory and Application

M. Z. Ahmad, James Peters


This article introduces proximal Čech complexes in approximating object shapes in digital images. The theo- retical framework is based on Čech complexes and proximity spaces. Several topological structures are defined for the Čech nerve based covers of a finite region of Euclidean plane. We define k-petals and k-corollas which are the generalizations of spokes and maximal nuclear clusters. We extend the classical notion of a proximity as a binary relation, to arbitrary number of sets. A new shape signature based on the distribution of orders of Čech nerves is defined. A practical application of this framework in approximating object shapes in digital images is given.


Čech complex, Digital image, Nerve, Object shape

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