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

Autor: Djemel Ziou, Madjid Allili
Rok vydání: 2002
Předmět:
Zdroj: Pattern Recognition. 35:2833-2839
ISSN: 0031-3203
DOI: 10.1016/s0031-3203(01)00238-2
Popis: 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.
Databáze: OpenAIRE