Bijectivity Certification of 3D Digitized Rotations

详细信息    查看全文

• 刊名：Lecture Notes in Computer Science
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：9667
• 期：1
• 页码：30-41
• 全文大小：1,643 KB
• 参考文献：1.Andres, E.: The quasi-shear rotation. In: Miguet, S., Ubéda, S., Montanvert, A. (eds.) DGCI 1996. LNCS, vol. 1176. Springer, Heidelberg (1996)
  2.Conway, J., Smith, D.: On Quaternions and Octonions. Taylor & Francis, Ak Peters Series, Boca Raton (2003)MATH
  3.Cremona, J.: Letter to the editor. American Mathematical Monthly 94(8), 757–758 (1987)MathSciNet
  4.Hardy, G.H., Wright, E.M.: Introduction to the Theory of Numbers, vol. IV. Oxford University Press, Cambridge (1979)MATH
  5.Jacob, M.A., Andres, E.: On discrete rotations. In: DGCI. pp. 161–174 (1995)
  6.Kanatani, K.: Understanding Geometric Algebra: Hamilton, Grassmann, and Clifford for Computer Vision and Graphics. CRC Press, Boca Raton (2015)CrossRef MATH
  7.Micciancio, D., Warinschi, B.: A linear space algorithm for computing the Hermite Normal Form. In: ISSAC. pp. 231–236. ACM (2001)
  8.Murray, R., Li, Z., Sastry, S.: A Mathematical Introduction to Robotic Manipulation. CRC Press, Boca Raton (1994)MATH
  9.Ngo, P., Kenmochi, Y., Passat, N., Talbot, H.: Combinatorial structure of rigid transformations in 2D digital images. Comput. Vis. Image Underst. 117(4), 393–408 (2013)CrossRef MATH
  10.Ngo, P., Kenmochi, Y., Passat, N., Talbot, H.: Topology-preserving conditions for 2D digital images under rigid transformations. J. Math. Imaging Vis. 49(2), 418–433 (2014)MathSciNet CrossRef MATH
  11.Ngo, P., Passat, N., Kenmochi, Y., Talbot, H.: Topology-preserving rigid transformation of 2D digital images. IEEE Trans. Image Process. 23(2), 885–897 (2014)MathSciNet CrossRef MATH
  12.Nouvel, B., Rémila, É.: On colorations induced by discrete rotations. In: Nyström, I., Sanniti di Baja, G., Svensson, S. (eds.) DGCI 2003. LNCS, vol. 2886, pp. 174–183. Springer, Heidelberg (2003)CrossRef
  13.Nouvel, B., Rémila, É.: Characterization of bijective discretized rotations. In: Klette, R., Žunić, J. (eds.) IWCIA 2004. LNCS, vol. 3322, pp. 248–259. Springer, Heidelberg (2004)CrossRef
  14.Nouvel, B., Rémila, E.: Configurations induced by discrete rotations: Periodicity and quasi-periodicity properties. Discrete Appl. Math. 147(2–3), 325–343 (2005)MathSciNet CrossRef MATH
  15.Pernet, C., Stein, W.: Fast computation of Hermite normal forms of random integer matrices. J. Number Theory 130(7), 1675–1683 (2010)MathSciNet CrossRef MATH
  16.Pluta, K., Romon, P., Kenmochi, Y., Passat, N.: Bijective rigid motions of the 2D Cartesian grid. In: Normand, N., Guédon, J., Autrusseau, F. (eds.) DGCI 2016. LNCS, vol. 9647, pp. 359–371. Springer, Heidelberg (2016). doi:10.​1007/​978-3-319-32360-2_​28 CrossRef
  17.Roussillon, T., Cœurjolly, D.: Characterization of bijective discretized rotations by Gaussian integers. Research report, LIRIS UMR CNRS 5205 (2016). https://​hal.​archives-ouvertes.​fr/​hal-01259826
  18.Schrijver, A.: Theory of Linear and Integer Programming. Wiley, Chichester (1998)MATH
  19.Vince, J.: Quaternions for Computer Graphics. Springer, London (2011)CrossRef MATH
  
• 作者单位：Kacper Pluta (15) (16)
  Pascal Romon (16)
  Yukiko Kenmochi (15)
  Nicolas Passat (17)
  
  15. Université Paris-Est, LIGM, CNRS, ESIEE, Paris, France
  16. Université Paris-Est, LAMA, UPEM, Paris, France
  17. Université de Reims Champagne-Ardenne, CReSTIC, Reims, France
  
• 丛书名：Computational Topology in Image Context
• ISBN：978-3-319-39441-1
• 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
• 卷排序：9667

文摘

Euclidean rotations in \(\mathbb {R}^n\) are bijective and isometric maps. Nevertheless, they lose these properties when digitized in \(\mathbb {Z}^n\). For \(n=2\), the subset of bijective digitized rotations has been described explicitly by Nouvel and Rémila and more recently by Roussillon and Cœurjolly. In the case of 3D digitized rotations, the same characterization has remained an open problem. In this article, we propose an algorithm for certifying the bijectivity of 3D digitized rational rotations using the arithmetic properties of the Lipschitz quaternions.