Abstract
In this chapter we consider the numerical solution of the hyperbolic partial differential equations of mathematical morphology in image processing. First we review our completely discrete flux-corrected transport (DFCT) approach. It uses the viscosity form of a specific upwind scheme in order to quantify viscous artifacts. In a subsequent corrector step that viscosity is compensated by a stabilised inverse diffusion step. We present a thorough analysis of the method including a proof of convergence. After that we introduce a useful framework for processing tensor-valued data. Such data appear in important applications in medical image analysis and engineering. We indicate how to extend the DFCT scheme to that setting and present numerical results proving desirable qualities of our method.
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