Convergent Geometric Estimators with Digital Volume and Surface Integrals

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• 关键词：Digital geometry ; Volume estimation ; Moments estimation ; Normal estimation ; Curvatures estimation ; Area estimation ; Multigrid convergence ; Digital integration ; Integral invariants ; Digital moments ; Voronoi covariance measure ; Stability
• 刊名：Lecture Notes in Computer Science
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：9647
• 期：1
• 页码：3-17
• 全文大小：928 KB
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• 作者单位：Jacques-Olivier Lachaud (16)
  
  16. Laboratoire de Mathématiques (LAMA), CNRS, UMR 5127, Université Savoie Mont Blanc, Chambéry, France
  
• 丛书名：Discrete Geometry for Computer Imagery
• ISBN：978-3-319-32360-2
• 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

This paper presents several methods to estimate geometric quantities on subsets of the digital space \(\mathbb {Z}^d\). We take an interest both on global geometric quantities like volume and area, and on local geometric quantities like normal and curvatures. All presented methods have the common property to be multigrid convergent, i.e. the estimated quantities tend to their Euclidean counterpart on finer and finer digitizations of (smooth enough) Euclidean shapes. Furthermore, all methods rely on digital integrals, which approach either volume integrals or surface integrals along shape boundary. With such tools, we achieve multigrid convergent estimators of volume, moments and area in \(\mathbb {Z}^d\), of normals, curvature and curvature tensor in \(\mathbb {Z}^2\) and \(\mathbb {Z}^3\), and of covariance measure and normals in \(\mathbb {Z}^d\) even with Hausdorff noise.