Research article

Anisotropic variation formulas for imaging applications

  • 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.

    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

    Related Papers:

  • 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.


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  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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