Generating cubical complexes from image data and computation of the Euler number

摘要

A number of tasks in image processing and computer vision require the computation of certain topological characteristics of objects in a given image. In this paper, we introduce a new method based on the notion of the algebraic topology complex to compute the Euler number of a given object. First, we attach a cubical complex to the object of interest, then we associate an algebraic structure on which a number of simplifying operations preserving the topology but not necessarily the geometric nature of the complex are possible. This is a unifying dimension independent approach. We show that the Euler number can be obtained directly from the cubical structure or one can perform a collapsing operation that allows to reduce the given image to a lower dimension structure with equivalent topological properties. This reduced structure can be used in a further process, in particular, for the computation of the Euler number.