Theoretical foundations for spatially discrete 1-D shock filtering

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• 作者：Martin Welk ; Joachim Weickert ; Irena Galić
• 关键词：Shock filters ; Analytical solution ; Well-posedness ; Dynamical systems ; Mode filters
• 刊名：Image and Vision Computing
• 出版年：2007
• 出版时间：April 2007
• 年：2007
• 卷：25
• 期：4
• 页码：455-463
• 全文大小：311 K

文摘

While shock filters are popular morphological image enhancement methods, no well-posedness theory is available for their corresponding partial differential equations (PDEs). By analysing the dynamical system of ordinary differential equations that results from a space discretisation of a PDE for 1-D shock filtering, we derive an analytical solution and prove well-posedness. We show that the results carry over to the fully discrete case when an explicit time discretisation is applied. Finally we establish an equivalence result between discrete shock filtering and local mode filtering.