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Computational aspects of the crop field segmentation problem based on anisotropic active contour model
∗
Here, S stands for the area of a standard field in Author contributions
a given region. Conceptualization: All authors
After that we define the function φ 0 ε,τ as a so- Formal analysis: All authors
lution of the problem (51), (52), (53)–(55) with Investigation: All authors
the given collection {l j } M . Let {S j } M be a set
j=1 j=0 Methodology: All authors
of the corresponding segments that we identify by Writing-original draft: All authors
the rules (57)–(59). Then we define the true seg- Writing-review & editing: All authors
ments as follows:
k=1; Availability of data
True_Segment(k):=S_0;
Not applicable.
for j=1:M
if area(S_1)<0.10 S*
combine{True_Segment(k),S_j}; References
else
1. D’Apice C., Kogut PI, Manzo R. On general-
k=k+1;
ized active contour model in the anisotropic BV
True_Segment(k):=S_j; space and its application to satellite remote sens-
end ing of agricultural territory. Netw Heterogen Me-
Number_of_true_Segments:=k; dia. 2025;20(1): 113-142.
2. Mulla DJ. Twenty five years of remote sensing in
Here, the multiplier 0.10 emerges as a part of
precision agriculture: key advances and remaining
the field that can be neglected as a zone of inho-
knowledge gaps. Biosyst Eng. 2013; 114(4):358-
mogeneity.
371.
3. Xue J, Su B. Significant remote sensing vegeta-
tion indices: a review of developments and appli-
6. Conclusion cations. Hindawi J Sens. 2017;2017:1-17. (Article
ID 1353691)
The generalized active contour model, proposed
1
in, to extract agricultural crop fields with a high 4. Hnatushenko VV, Kogut PI, Uvarov M. Varia-
tional approach for rigid co-registration of op-
degree of inhomogeneity from satellite data has
tical/SAR satellite images in agricultural ar-
been implemented. Setting an optimization prob- eas. J Comput Appl Math. 2022;400:15. Id
lem, it was possible to achieve a disjunctive de- 113742.
composition of a given field into a finite number 5. Khanenko P, Kogut PI, Uvarov M. On varia-
of non-empty subsets, each of which could be as- tional problem with nonstandard growth condi-
sociated with a unique value of an agricultural tions for the restoration of clouds corrupted satel-
index. The Euler–Lagrange equation with the lite images. In: CEUR Workshop Proceedings, the
appropriate initial and boundary conditions has 2nd International Workshop on Computational
and Information Technologies for Risk-Informed
been used to express the corresponding optimal-
Systems, CITRisk-2021, September 16-17, 2021,
ity system under certain assumptions. A method
Kherson, Ukraine, Vol. 3101; 2021: 6-25.
for the numerical solution of the Euler–Lagrange
6. Ivanchuk N, Kogut PI, Martyniuk P. On genera-
system has been provided along with a numerical
tion of daily cloud free images at a high resolution
scheme. Using a direct approach to the segmenta-
level. In: M. Zgurovsky, N. Pankratova, eds. Sys-
tion technique and the new adaptive one, numer- tem Analysis and Artificial Intelligence. Studies
ical simulations utilizing real-life satellite images in Computational Intelligence, Vol 1107. Cham:
have been conducted to show the accuracy and Springer; 2023: 203-232.
effectiveness of the proposed model. 7. D’Apice C, Kogut PI, Manzo R. A two-level vari-
ational algorithm in the Sobolev-Orlicz space to
predict daily surface reflectance at LANDSAT
Acknowledgments
high spatial resolution and MODIS temporal fre-
None. quency. J Comput Appl Math. 2023;434:115339.
8. D’Apice C, Kogut PI, Manzo R, Uvarov M. Varia-
tional model with nonstandard growth conditions
Funding for the restoration of satellite optical images using
synthetic aperture radar. Eur J Appl Math. 2023;
None.
34(1):77-105.
9. Hnatushenko VV, Kogut PI, & Uvarov MV. On
Conflict of interest satellite image Segmentation via piecewise con-
stant approximation of selective smoothed target
The authors declare no conflict of interest. mapping. Appl Math Comput. 2021;389:125615.
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