Discrete Laplace Operator in the Space with a Fuzzy Partition

DOI

10.2991/asum.k.210827.020How to use a DOI?

Keywords

Discrete Laplace operator, Fuzzy transform, Fuzzy partition, Basic functions, Inner product

Abstract

Differential operators definitely play an important role in image processing tasks. One of the most frequently used operator for this purpose is the Laplace operator, usually defined as the divergence of a gradient of a function. Since images are considered as discrete objects, many applications require discrete version of this operator. But at the same time, these discrete Laplace operators should preserve certain properties known from the continuous case. Based on this fact, we present discrete variant of F-transform-based Laplace operator, satisfying such conditions. Moreover, Laplace operator can be also defined axiaomatically, throughout its certain properties. Therefore, we propose a construction of such operator from the other side, just with notion of the inner product of the current space and its desired properties.

Copyright

© 2021, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Hana Zámečníková
AU  - Irina Perfilieva
PY  - 2021
DA  - 2021/08/30
TI  - Discrete Laplace Operator in the Space with a Fuzzy Partition
BT  - Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)
PB  - Atlantis Press
SP  - 147
EP  - 152
SN  - 2589-6644
UR  - https://doi.org/10.2991/asum.k.210827.020
DO  - 10.2991/asum.k.210827.020
ID  - Zámečníková2021
ER  -