The Perona–Malik Method as an Edge Pruning Algorithm

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• 作者：Satyanad Kichenassamy
• 关键词：Computer vision ; Perona–Malik equation ; Semi ; group theory ; Image model ; Non ; convex variational principle
• 刊名：Journal of Mathematical Imaging and Vision
• 出版年：2008
• 出版时间：February, 2008
• 年：2008
• 卷：30
• 期：2
• 页码：209-219
• 全文大小：413.3 KB
• 刊物类别：Computer Science
• 刊物主题：Computer Imaging, Vision, Pattern Recognition and Graphics
  Image Processing and Computer Vision
  Artificial Intelligence and Robotics
  Automation and Robotics
  
• 出版者：Springer Netherlands
• ISSN：1573-7683

文摘

The Perona–Malik equation (PM), in the continuum limit, is interpreted as the gradient flow for a functional, corresponding to the reconstruction of an image with edges with non-zero thickness. This result is based on an image model (u,Γ) where Γ is an edge set, and u is a slowly-varying function. PM simplifies the image by reducing the jump across each component of Γ, resulting in an automatic edge pruning procedure. The initial-value problem thus defined is well-posed, but practically stable only for small times: it leads to a semi-group with exponential growth. The rigorous analysis gives a mathematical basis for empirical observations, including edge localization and the need to use a small number of iterations. The variational formulation enables an easy comparison with earlier methods.