On the Characterization of Absentee-Voxels in a Spherical Surface and Volume of Revolution in  \({\mathbb Z}^3\)

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• 作者：Sahadev Bera ; Partha Bhowmick…
• 刊名：Journal of Mathematical Imaging and Vision
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：56
• 期：3
• 页码：535-553
• 全文大小：5,915 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
• 卷排序：56

文摘

We show that the construction of a digital sphere by circularly sweeping a digital semi-circle (generatrix) around its diameter results in the appearance of some holes (absentee-voxels) in its spherical surface of revolution. This incompleteness calls for a proper characterization of the absentee-voxels whose restoration in the surface of revolution can ensure the required completeness. In this paper, we present a characterization of the absentee-voxels using certain techniques of digital geometry and show that their count varies quadratically with the radius of the semi-circular generatrix. Next, we design an algorithm to fill up the absentee-voxels so as to generate a spherical surface of revolution, which is complete and realistic from the viewpoint of visual perception. We also show how the proposed technique for absentee-filling can be used to generate a variety of digital surfaces of revolution by choosing an arbitrary curve as the generatrix. We further show that covering a solid sphere by a set of complete spheres also results to an asymptotically larger count of absentees, which is cubic in the radius of the sphere. A complete characterization of the absentee-voxels that aids the subsequent generation of a solid digital sphere is also presented. Test results have been furnished to substantiate our theoretical findings.Keywords3D modellingDigital circleDigital sphereDigital geometryGeometry of numbers