摘要：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.
