Professional paper

Application of Linear and Nonlinear Heat Equation in Digital Image Processing

Andrej Novak ; University of Dubrovnik, Dubrovnik, Croatia
Andrija Štajduhar ; School of Medicine, University of Zagreb, Zagreb, Croatia

Abstract

We will explore the application of partial differential equations on digital images. We will show how to use the heat equation to eliminate noise in an image, highlight important elements and prepare it for possible further processing. We also show known heat equation’s theoretical results in a methodical sequence and then derive simple numerical schemes based on the finite differences method. Guided by the idea of image structure preservation, for example edge preservation, the central part of this article introduces Perona-Malik equation as an example of a nonlinear heat equation. We conclude by comparing linear and nonlinear heat equation application on a couple of test images.

Keywords

heat equation; Perona-Malik equation

Hrčak ID:

133846

URI

https://hrcak.srce.hr/133846

Publication date:

30.1.2015.

Article data in other languages: croatian

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