AIMS Mathematics, 2019, 4(3): 576-592. doi: 10.3934/math.2019.3.576

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Anisotropic variation formulas for imaging applications

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

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 $R^2$. 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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