Method of Creating of Functional Invariants under One-Parameter Geometric Image Transformations

Kinoshenko, Dmitry; Mashtalir, Vladimir; Orlov, Alexander; Yegorova, Elena

doi:10.1007/978-3-540-45243-0_10

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2005

2020

Publication Types

Select...

Article1

Book1

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A problem of great practical interest in applications is the following classification problem: given two functions f 1 , f 2 ∈ F , are they in the same G-orbit? A common approach to this problem, see [1]- [4], is to use invariant functionals. A functional I : F → C is called invariant with respect to the group G ( or G-invariant) if I(g · f ) = I(f ), ∀g ∈ G, ∀f ∈ F.…”

Section: Introductionmentioning

confidence: 99%

2D Geometric Moment Invariants from the Point of View of the Classical Invariant Theory

Bedratyuk

2020

J Math Imaging Vis

View full text Add to dashboard Cite

Invariants allow to classify images up to the action of a group of transformations. In this paper we introduce notions of the algebras of simultaneous polynomial and rational 2D moment invariants and prove that they are isomorphic to the algebras of joint polynomial and rational SO(2)-invariants of binary forms. Also, to simplify the calculating of invariants we pass from an action of Lie group SO(2) to an action of its Lie algebra so 2 . This allow us to reduce the problem to standard problems of the classical invariant theory.

show abstract

Section: Introductionmentioning

confidence: 99%