Some properties of digital H-spaces

Abstract

In this paper, we study certain properties of digital H-spaces. We prove that a digital image that has the same digital homotopy type with any digital H-space is also a digital H-space. We show that the digital fundamental group of a digital H-space is abelian. We give examples that are related to a digital homotopy associative H-space and a kappa-contractible digital H-space. Several important applications of digital H-spaces are given in computer vision and image processing. Finally, we deal with the importance of digital H-space in digital topology and image processing. We conclude that any kappa-contractible digital image is a digital H-space.