Parametrical and morphological spectra
Vizilter Yu.V., Sidyakin S.V.

 

FGUP «GosNIIAS»

 

DOI: 10.18287/0134-2452-2015-39-1-109-118

Full text of article: Russian language.

Abstract:
A generic formalism of parametric spectra is proposed for describing all spectra of this type from a common viewpoint. The parametric spectrum represents the density of distribution of some pattern/image measure (numerical characteristic) over the parameter under analysis. The measure depends monotonically on the analyzed parameter. The classification of parametric spectra is made. The most general case of parametric spectra are the spectra of the measurement accuracy as a function of the resolution parameter. They include as special cases: spectra based on descriptors, spectra based on filtering, partial order spectra, spectra based on monotone filtering operators, spectra based on enclosed projectors and distance, spectra based on normalized linear spaces. A subclass of morphological spectra that represent reconstruction accuracy spectra by the description complexity parameter is considered. The connection between the parametrical spectra and relevant parametrical decompositions is shown.

Keywords:
image morphology, pattern spectra.

References:

  1. Maragos, P. Pattern Spectrum, Multiscale Shape Representation // Pattern Analysis and Machine Intelligence, IEEE Transactions on. – 1989, July. – Vol. 11, Issue 7. – P. 701-716.
  2. Serra, J. Image Analysis and Mathematical Morphology / J. Serra. – London: Academic Press, 1982. – 610 p.
  3. Wilkinson, M. Generalized pattern spectra sensitive to spatial information // Proceedings of 16th International Conference on Pattern Recognition. – 2002. – Vol. 1. – P. 21-24.
  4. Urbach, E.R. Connected Shape-Size Pattern Spectra for Rotation and Scale-invariant Classification of Gray-scale Images / E.R. Urbach, J.B. Roerdink, M.H. Wilkinson // IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI) – 2007. – Vol. 29(2). – P. 272-285.
  5. Sidyakin, S.V. omputation of morphological spectrum for grayscale images / S.V. Sidyakin, Yu.V. Vizilter // Herald of Computer and Information Technologies. – 2012. – Vol. 4. – P. 8-17. – (In Russian).
  6. Vizilter, Yu.V. Morphological complexity spectrums of 2D figures and images / Yu.V. Vizilter, S.V. Sidyakin // Herald of Computer and Information Technologies. – 2012. – Vol. 11. – P. 3-8. – (In Russian).
  7. Vishnyakov, B.V. Autoregression pseudo-spectra development for detection and tracking of objects in video surveillance system / B.V. Vishnyakov, Yu.V. Vizilter, O.V. Vi­golov // Proceedings of 15th Conference on Mathematical Methods in Pattern Recognition. – Moscow: “MAKS Press” Publisher, 2011. – P. 463-466. – (In Russian).
  8. Pytiev, Yu.P. Methods of Morphological image analysis / Yu.P. Pytiev, A.I. Chulichkov. – Moscow: “Fizmatlit” Publisher, 2010. – 336 p. – (In Russian).
  9. Daubechies, I. Ten lectures on wavelets / I. Daubechies. – Izhevsk: SIC “Regular and Chaotic Dynamics” Publisher, 2001. – 464 p. – (In Russian).
  10. Sidyakin, S.V.  Morphological pattern spectra algorithm
  11. development for digital image and video sequences analysis // PhD Thesis. – Moscow: Institution of Russian Academy of Sciences Dorodnicyn Computing Centre of RAS (CC RAS), 2013. – 163 p. – (In Russian).
  12. Dougherty, E.R. The dual representation of gray-scale mor-phological filters // Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR). – San Diego, CA: 1989. – P. 172-177.

© 2009, IPSI RAS
Institution of Russian Academy of Sciences, Image Processing Systems Institute of RAS, Russia, 443001, Samara, Molodogvardeyskaya Street 151; e-mail: ko@smr.ru; Phones: +7 (846 2) 332-56-22, Fax: +7 (846 2) 332-56-20