Definition of rotation parameters of spatial group point object at unknown numbering of dot marks
D. G. Khafizov

Mari State Technical University

Full text of article: Russian language.

Abstract:
Questions of rotation parameters of spatial group point objects images on the basis of the main things method are considered. The application of the given method allows to receive an estimation of rotation parameters of spatial group point object at the absence of the information on numbering of points in object that essentially simplifies the decision of problems of processing of spatial group points objects.

Key words:
spatial group point object, hypercomplex number, quaternion, quaternion signals, rotation quaternion, rotational variables, rotational matrix.

References:

  1. Contour Analysis introduction and its image and signal processing application / Ya.A. Furman, A.V. Krevetsky, A.K. Peredreyev [and etc.]; under edition of Ya.A. Furman. – Secondary Edition – Moscow: Fizmatlit, 2003. – 592 p. – (in Russian).
  2. Complex and hypercomplex systems at tasks of multidimensional signal processing / Ya.A. Furman, A.V. Krevetsky, A.A. Rozhentsov [and etc.]; under edition of Ya.A. Furman. – Moscow: Fizmatlit, 2004. – 456 p. – (in Russian).
  3. Furman, Ya.A. Recognition of group point objects in three-dimensional space / Ya.A. Furman, D.G. Khafizov// Avtometriya. – 2003. – V. 39, 1. – P. 3-18. – (in Russian).
  4. Furman, Ya.A. Processing of quaternion signals specifying spatially located group point objects / Ya.A. Furman // Pattern Recognition and Image Analysis. – 2002. – Vol.12, 2. – p. 175-193.
  5. Khafizov, D.G. Sequencing points of the spatial image of a group point object based on amplitude-phase representation / D.G. Khafizov // Avtometriya. – 2007. – V. 43, 1. – P. 10-23. – (in Russian).
  6. Leukhin, A.N. Estimation of rotation parameters of three-dimensional group point object without preliminary numbering points / A.N. Leukhin, D.G. Khafizov // «Mathematical methods of image recognition»: Reports of 11th All-Russia conference. – Moscow, 2003. – P. 130-133.
  7. Furman, Ya.A. Inverse problem of rotation of three-dimensional vector signals / Ya.A. Furman, I.L. Egoshina // Avtometriya. – 2010. – V. 46, 1. – P. 46-56. – (in Russian).
  8. Furman, Ya.A. Determining the rotational variables of a spatial group point object / Ya.A. Furman, K.B. Ryabinin // Radioengineering and electronics. – 2008. – V. 53, 1. – P. 86-97. – (in Russian).
  9. Dronov, S.V. The multidimensional statistical analysis / S.V. Dronov. – Barnaul: Publishing house of the Altay state university, 2003. – 213 p. – (in Russian).
  10. Kalinina, V.N. Introduction in the multidimensional statistical analysis / V.N. Kalinina, V.I. Solov’ev. – SUM. – Moscow, 2003. – 66 p. – (in Russian).
  11. Kantor, I.L. Hypercomplex numbers / I.L. Kantor, A.S. Solodovnikov. – Moscow: Nauka, 1973. – (in Russian).
  12. Khafizov, D.G. Getting an analytical representation of the spatial group point objects form/ D.G. Khafizov// The bulletin of MarSTU Radioengineering and infocommunication systems. – 2008. – 2. – P. 35-41. (in Russian).
  13. Korn, G. The directory on the mathematician for scientist and engineers / G. Korn, T. Korn. – Moscow: Nauka, 1968. – 720 p. – (in Russian).

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