In this paper we discuss the recognition of textures of digital images with the help of methods of computation topology. The main idea is to use the logic of attributes based on a topological filtration. Pixels sorted by photometric measure are scanned by ascending levels of gray. Each local minimum generates a connected component. It disappears if a similar in magnitude maximum appears in its local neighborhood. When the level increases, the clusters generated by the primary components merge. The process ends when it turns one global cluster. The number of connected components is measured by the topological invariant - Betti-zero. The life span of the components or its persistence is measured by the difference of the two levels. The first one marks appearance of the component, the second - a merging with neighboring clusters. Merging of the individual components is accompanied by the appearance of holes within the complex clusters. The amount of Holes is measured by Betti-1 number and the persistence by the difference between the levels of cancellation and the appearance of the Hole. We show how the distribution of persistent Betti numbers can be used for texture recognition in digital images.