Abstract
High spatial resolution satellite images are different
from Gaussian statistics of counts. Therefore, texture
recognition methods based on variances become ineffective.
The aim of this paper is to study possibilities
of completely different, topological approach to problems
of structures classification. Persistent Betti numbers are
signs of texture recognition. They are not associated with
metrics and received directly fromdata in form of so-called
persistence diagram (PD). The different structures built on
PD are used to get convenient numerical statistics. At the
present time, three of such objects are known: topological
landscapes, persistent images and rank functions. They
have been introduced recently and appeared as an attempt
to vectorize PD. Typically, each of the proposed structures
was illustrated by the authors with simple examples.However,
the practical application of these approaches to large
data sets requires to evaluate their efficiency within the
frame of the selected task at the same standard database.
In our case, such a task is to recognize different textures
of the Remote Sensing Data (RSD). We check efficiency of
structure, called persistent images in this work. We calculate
PD for base containing 800 images of high resolution
representing 20 texture classes. We have found out
that average efficiency of separate image recognition in the
classes is 84%, and in 11 classes, it is not less than 90%. By
comparison topological landscapes provide 68% for average
efficiency, and only 3 classes of not less than 90%.
Reached conclusions are of interest for new methods of
texture recognition in RSD.
Face Numbers and Nongeneric Initial Ideals