Anisotropic variation formulas for imaging applications

Thomas Asaki; Heather A. Moon; Thomas Asaki; Heather A. Moon

doi:10.3934/math.2019.3.576

AIMS Mathematics

2019, Volume 4, Issue 3: 576-592. doi: 10.3934/math.2019.3.576

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Research article

Anisotropic variation formulas for imaging applications

Thomas Asaki ^{1
,
,},
Heather A. Moon ²

1.
Department of Mathematics and Statistics, Washington State University, P.O. Box 3113, Pullman, WA 99164, USA
2.
Division of Natural Sciences and Mathematics, Lewis-Clark State College, 500 8th Avenue, Lewiston, ID 83501, USA

Received: 16 April 2019 Accepted: 15 May 2019 Published: 30 May 2019
MSC : 49Mxx, 68U05, 65D18, 65D25

The discrete anisotropic variation, sometimes referred to as the anisotropic gradient, and its integral are important in a variety of image processing applications and set boundary measure computations. We provide a method for computing the weight factors for general anisotropic variation approximations of functions on ${\mathbb{R}^2}$. The method is developed in the framework of regular arrays, but applicability extends to arbitrary finite discrete sampling strategies. The mathematical model and computations use concepts from vector calculus and introductory linear algebra so the discussion is accessible for upper-division undergraduate students.
- anisotropic gradient,
- image analysis
Citation: Thomas Asaki, Heather A. Moon. Anisotropic variation formulas for imaging applications[J]. AIMS Mathematics, 2019, 4(3): 576-592. doi: 10.3934/math.2019.3.576

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Abstract

The discrete anisotropic variation, sometimes referred to as the anisotropic gradient, and its integral are important in a variety of image processing applications and set boundary measure computations. We provide a method for computing the weight factors for general anisotropic variation approximations of functions on ${\mathbb{R}^2}$. The method is developed in the framework of regular arrays, but applicability extends to arbitrary finite discrete sampling strategies. The mathematical model and computations use concepts from vector calculus and introductory linear algebra so the discussion is accessible for upper-division undergraduate students.

References

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