Texture recognition in digital images by computational topology methods. / Urtiev, F.; Knyazeva, I. S.; Malkova, D. B.; Park, I. T.; Karimova, L. M.
In: Sovremennye Problemy Distantsionnogo Zondirovaniya Zemli iz Kosmosa, Vol. 12, No. 1, 2015, p. 131-144.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Texture recognition in digital images by computational topology methods
AU - Urtiev, F.
AU - Knyazeva, I. S.
AU - Malkova, D. B.
AU - Park, I. T.
AU - Karimova, L. M.
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
KW - Image segmentation
KW - Pattern recognition
KW - Persistent Betti numbers
KW - The Cech complex
KW - Topological filtration
UR - http://www.scopus.com/inward/record.url?scp=84949553413&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:84949553413
VL - 12
SP - 131
EP - 144
JO - СОВРЕМЕННЫЕ ПРОБЛЕМЫ ДИСТАНЦИОННОГО ЗОНДИРОВАНИЯ ЗЕМЛИ ИЗ КОСМОСА
JF - СОВРЕМЕННЫЕ ПРОБЛЕМЫ ДИСТАНЦИОННОГО ЗОНДИРОВАНИЯ ЗЕМЛИ ИЗ КОСМОСА
SN - 2070-7401
IS - 1
ER -
ID: 9327405