Bézier Curves in the Space of Images

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• 关键词：De Casteljau algorithm ; Shape manifolds ; Metamorphosis
• 刊名：Lecture Notes in Computer Science
• 出版年：2015
• 出版时间：2015
• 年：2015
• 卷：9087
• 期：1
• 页码：372-384
• 全文大小：1,412 KB
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• 作者单位：Alexander Effland (16)
  Martin Rumpf (16)
  Stefan Simon (16)
  Kirsten Stahn (16)
  Benedikt Wirth (17)
  
  16. Institute for Numerical Simulation, Universit?t Bonn, Bonn, Germany
  17. Institute for Computational and Applied Mathematics, University of Muenster, Muenster, Germany
  
• 丛书名：Scale Space and Variational Methods in Computer Vision
• ISBN：978-3-319-18461-6
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349

文摘

Bézier curves are a widespread tool for the design of curves in Euclidian space. This paper generalizes the notion of Bézier curves to the infinite-dimensional space of images. To this end the space of images is equipped with a Riemannian metric which measures the cost of image transport and intensity variation in the sense of the metamorphosis model [MY01]. Bézier curves are then computed via the Riemannian version of de Casteljau’s algorithm, which is based on a hierarchical scheme of convex combination along geodesic curves. Geodesics are approximated using a variational discretization of the Riemannian path energy. This leads to a generalized de Casteljau method to compute suitable discrete Bézier curves in image space. Selected test cases demonstrate qualitative properties of the approach. Furthermore, a Bézier approach for the modulation of face interpolation and shape animation via image sketches is presented.