Morphological shape descriptors of binary images based on elliptical structuring elements
S.V. Sidyakin, Yu.V. Vizilter


PDF, 464 kB

Full text of article: Russian language.

DOI: 10.18287/0134-2452-2014-38-3-511-520

Pages: 511-520.

In this paper, we proposed algorithms for constructing continuous skeletons with elliptical structuring element (SE). The transformation between disk and elliptical skeletons is described.  Computationally efficient discrete-continuous approach for the construction of morphological descriptors (spectra and maps) with fixed elliptical SE is proposed based on elliptical skeletons. The definitions of morphological elliptical maps, size spectra, directions spectra, elongation spectra with arbitrary elliptical structuring element is proposed. Definitions of two-dimensional spectra with various combinations of size and shape factors is given. Proposed morphological descriptors can be used directly for shape comparison or for shape segmentation into simple geometric parts of specified thickness, direction and elongation.

Key words:
mathematical morphology, pattern spectra, continuous skeleton, ellipse.


  1. Mestetskiy, L.M. Continuous morphology of binary images: figures, skeletons, circulars. – Moscow: “Fizmatlit” Publisher, 2009. – 288 p. – (In Russian).
  2. Serra, J. Image Analysis and Mathematical Morphology. – London: Academic Press, 1982. – 610 p.
  3. Maragos, P. Pattern Spectrum, Multiscale Shape Representation // Pattern Analysis and Machine Intelligence, IEEE Transactions on. – 1989, July – Vol. 11, Issue 7. – P. 701-716.
  4. Vizilter, Yu.V. Morphological spectrum computation of flat figures using continuous skeletal representations / S.V. Sidyakin, A.Yu Rubis // Proceedings of 15th Conference on Mathematical Methods in Pattern Recognition – Moscow: “MAKS Press” Publisher, 2011 – P. 416-419. – (In Russian).
  5. Sidyakin, S.V. Morphological pattern spectra algorithm 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).
  6. Mestetskiy, L.M. Skeleton of polygonal figure – representation by planar linear graph // Proceedings of the 20th International Conference on Computer Graphics and Vision “Graphicon 2010” Publisher. – Saint Petersburg, 2010. – P. 222-229 – (In Russian).
  7. Mestetskiy, L.M. Segment Voronoi Diagram Representation by Bezier Control Graph // Proc. of the 10th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2013). – Saint Petersburg, 2013. – P. 75-81
  8. Bronstein, A.M. Analysis of two-dimensional non-rigid shapes / M.M. Bronstein, A.M. Bruckstein, R. Kimmel // International Journal of Computer Vision (IJCV). – 2008. –Vol. 78(1). – P. 67-88.
  9. Rubner, Y. The Earth Mover’s Distance as a Metric for Image Retrieval / C. Tomasi, L.J. Guibas // International Journal of Computer Vision. – 2000. – Vol. 40(2). – P. 99-121.
    © 2009, IPSI RAS
    Institution of Russian Academy of Sciences, Image Processing Systems Institute of RAS, Russia, 443001, Samara, Molodogvardeyskaya Street 151; e-mail:; Phones: +7 (846 2) 332-56-22, Fax: +7 (846 2) 332-56-20