A Research About Different Modeling and Application of Higher Order Derivatives: Applications of Higher Order Derivatives in Geometric Modeling and Image Processing

Abstract

Modeling of high quality surfaces is the core ofgeometric modeling. Such models are used in many computer-aided design andcomputer graphics applications. Irregular behavior of higher-order differentialparameters of the surface (e.g. curvature variation) may lead to aesthetic orphysical imperfections. In this work, we consider methods for constructingsurfaces with high degree of smoothness. This is an overview of recent research of the authors onthe application of variational methods with higher–order derivatives in imageprocessing. We focus on gray-valued and matrix-valued images and deal with apurely discrete setting. We show that regularization methods with second–orderderivatives can be successfully applied to the denoising of gray–value images.