β Scribed by Djemel Ziou; Madjid Allili
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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.
π SIMILAR VOLUMES
The use of Monte Carlo and other statistical procedures that depend on randomization of the observed data has been inhibited by uncertainty about the validity of random numbers generated by a computer. In the empirical test performed here, computergenerated numbers appeared to be just as "random" as
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