Skip to main content

Morphological Image Analysis for Computer Vision Applications

  • Chapter
  • First Online:
Computer Vision in Control Systems-1

Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 73))

Abstract

Some original and novel morphological concepts and tools are presented in this chapter as well as required amount of mathematical morphological basics. The continuous binary morphology based on a computational geometry is presented as a very fast approach to shape representation via real-time computation of figures’ skeletons. A skeletal representation of the figure is formed as a skeleton graph, and the radial function is determined in skeleton points. The proposed morphological spectrum is the multi-scale morphological shape description and analysis tools based on granulometry. It is shown how the tasks of change detection and shape matching in images can be solved using a morphological image analysis. The projective morphology as a generalized framework based on the mathematical morphology and the morphological image analysis provides fast and efficient solutions of morphological segmentation problem in complex images.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Serra J (1982) Image analysis and mathematical morphology. Academic Press, London

    MATH  Google Scholar 

  2. Matheron G (1975) Random sets and integral geometry. Wiley, New York

    MATH  Google Scholar 

  3. Serra J (1988) Image analysis and mathematical morphology. Theoretical advances. Academic Press, London

    Google Scholar 

  4. Dougherty ER (1992) An introduction to morphological image processing. SPIE Optical Engineering Press, Bellingham, Washington, USA

    Google Scholar 

  5. Najman L, Talbot H (2010) Mathematical morphology: from theory to applications. Wiley, Hoboken, NJ

    Google Scholar 

  6. Serra J, Soille P (1994) Mathematical morphology and its applications to image processing. Kluwer Academic Publishers, Dordrecht

    Book  MATH  Google Scholar 

  7. Shih FY, Mitchell OR (1989) Threshold decomposition of gray scale morphology into binary morphology. IEEE Trans Pattern Anal Mach Intell 11(1):31–42

    Article  MATH  Google Scholar 

  8. Grätzer G (2011) Lattice theory: foundation Springer Basel

    Google Scholar 

  9. Nachtegael M, Sussner P, Mélange T, Kerre E (2011) On the role of complete lattices in mathematical morphology: from tool to uncertainty model. Inf Sci 181(10):1971–1988

    Article  MATH  Google Scholar 

  10. Ronse C, Najman L, Decencière E (eds) (2005) Mathematical morphology: 40 years on 7th international symposium on mathematical morphology, vol 30

    Google Scholar 

  11. Salembier P, Wilkinson MHF (2009) Connected operators: a review of region-based morphological image processing techniques. IEEE Signal Process Mag 26(6):136–157

    Article  Google Scholar 

  12. Vizilter YV (2002) Design of morphological operators based on selective morphology. In: Dougherty ER, Astola JT, Egiazarian KO (eds) Proceedings of SPIE—the international society for optical engineering image processing: algorithms and systems, pp 215–226

    Google Scholar 

  13. Lantuéjoul Ch (1977) Sur le modèle de Johnson-Mehl generalize. Internal report of the Centre de Morph. Math., Fontainebleau, France

    Google Scholar 

  14. Aichholzer O, Aurenhammer F (1996) Straight skeletons for general polygonal figures in the plane. In: Cai JY, Wong CK (eds) Computing and combinatorics, vol 1090. LNCS Springer, pp 117–126

    Google Scholar 

  15. Blum H (1967) A transformation for extracting new descriptors of shape. In: Wathen-Dunn W (ed) Models for the perception of speech and visual form, pp 362–380

    Google Scholar 

  16. Costa L, Cesar R (2001) Shape analysis and classification. CRC Press, USA

    MATH  Google Scholar 

  17. Siddiqi K, Pizer SM (2008) Medial representations: mathematics, algorithms and applications. Springer, Berlin

    Book  Google Scholar 

  18. Mestetskiy L (2006) Skeletonization of a multiply connected polygonal domain based on its boundary adjacent tree. Siberian J Numer Math 9(3):299–314 (in Russian)

    MATH  Google Scholar 

  19. Mestetskiy L (2007) Shape comparison of flexible objects—similarity of palm silhouettes. In: 2nd international conference on computer vision theory and applications VISAPP’2007, pp 390–393

    Google Scholar 

  20. Mestetskiy L (2009) Continuous morphology of binary images: figures, skeletons and circulars. Fizmatlit, Moscow (in Russian)

    Google Scholar 

  21. Mestetskiy L (2010) Skeleton representation based on compound Bezier curves. In: 5th International conference on computer vision theory and applications VISAPP’2010, vol 1. INSTICC Press, pp 44–51

    Google Scholar 

  22. Mestetskiy L, Semenov A (2008) Binary image skeleton—continuous approach. In: 3rd international conference on computer vision theory and applications VISAPP’2008, vol 1. INSTICC Press, pp 251–258

    Google Scholar 

  23. Deng W, Iyengar S, Brener N (2000) A fast parallel thinning algorithm for the binary image skeletonization. Int J High Perform Comput Appl 14(1):65–81

    Article  Google Scholar 

  24. Drysdale R, Lee D (1978) Generalized Voronoi diagrams in the plane. In: 16th Ann Allerton conference on communications, control and computing, pp 833–842

    Google Scholar 

  25. Kirkpatrick D (1979) Efficient computation of continuous skeletons. In: 20th Ann IEEE symposium foundations of computer science, pp 18–27

    Google Scholar 

  26. Fortune S (1987) A sweepline algorithm for Voronoi diagrams. Algorithmica 2:153–174

    Article  MathSciNet  MATH  Google Scholar 

  27. Yap C (1987) An O(n log n) algorithm for the Voronoi diagram of the set of simple curve segments. Discrete Comput Geom 2:365–393

    Article  MathSciNet  MATH  Google Scholar 

  28. Lee D (1982) Medial axis transformation of a planar shape. IEEE Trans Pattern Anal Mach Intell PAMI-4 4:363–369

    Google Scholar 

  29. Lee DT, Schachter BJ (1980) Two algorithms for constructing a Delaunay triangulation. Int J Comput Inf Sci 9(3):219–242

    Article  MathSciNet  MATH  Google Scholar 

  30. Manzanera A, Bernard T, Preteux F, Longuet B (1999) Ultra-fast skeleton based on an isotropic fully parallel algorithm. In: Bertrand G, Couprie M, Perroton L (eds) Discrete geometry for computer imagery, vol 1568. LNCS Springer, Berlin, pp 313–324

    Google Scholar 

  31. Karavelas MI (2006) Voronoi diagrams in CGAL. In: 22nd European workshop on computational geometry, pp 229–232

    Google Scholar 

  32. Srinivasan V, Nackman L, Tang J, Meshkat S (1992) Automatic mesh generation using the symmetric axis transform of polygonal domains. Proc IEEE 80(9):1485–1501

    Article  Google Scholar 

  33. Ogniewicz R, Kubler O (1995) Hierarchic Voronoi skeletons. Pattern Recogn 28(3):343–359

    Article  Google Scholar 

  34. Strzodka R, Telea A (2004) Generalized distance transforms and skeletons in graphics hardware. Joint eurographics—IEEE TCVG symposium on visualization

    Google Scholar 

  35. Maragos P (1989) Pattern spectrum and multiscale shape representation. IEEE Trans Pattern Anal Mach Intell 11:701–715

    Article  MATH  Google Scholar 

  36. Suruliandi A, Ramar K (2008) Local texture patterns—a univariate texture model for classification of images. In: 16th IEEE International conference on advanced computing and communications, ADCOM 2008, pp 32–39

    Google Scholar 

  37. Asano A (1999) Texture analysis using morphological pattern spectrum and optimization of structuring elements. In: 10th international conference on image analysis and processing, ICIAP ’99, pp 209–214

    Google Scholar 

  38. Mestetskiy LM (2009) Continuous morphology of the binary images. The figures. Skeletons. Circulars. Moscow Physmatlit (in Russian)

    Google Scholar 

  39. Shih FY, Mitchell OR (1991) Decomposition of gray-scale morphological structuring elements. Pattern Recogn 24(3):195–203

    Article  MathSciNet  Google Scholar 

  40. Wilkinson MHF (2002) Generalized pattern spectra sensitive to spatial information. In: 16th international conference pattern recognition, vol 1, pp 21–24

    Google Scholar 

  41. Urbach ER, Roerdink JBTM, Wilkinson MHF (2007) Connected shape-size pattern spectra for rotation and scale-invariant classification of gray-scale images. IEEE Trans Pattern Anal Mach Intell 29(2):272–285

    Article  Google Scholar 

  42. van Herk M (1992) A fast algorithm for local minimum and maximum filters on rectangular and octagonal kernels. Pattern Recogn Lett 13(7):517–521

    Article  Google Scholar 

  43. Liang EH, Wong EK (1993) Hierarchical algorithms for morphological image processing. Pattern Recogn 26(4):511–529

    Article  Google Scholar 

  44. Park H, Chin RT (1995) Decomposition of arbitrarily shaped morphological structuring elements. IEEE Trans Pattern Anal Mach Intell 17(1):2–15

    Article  Google Scholar 

  45. Soille P, Breen E, Jones R (1996) Recursive implementation of erosions and dilations along discrete lines at arbitrary angles. IEEE Trans Pattern Anal Mach Intell 18(5):562–567

    Article  Google Scholar 

  46. Van Droogenbroeck M, Talbot H (1996) Fast computation of morphological operations with arbitrary structuring elements. Pattern Recogn Lett 17(14):1451–1460

    Article  Google Scholar 

  47. Anelli G, Broggi A, Destri G (1998) Decomposition of arbitrarily shaped binary morphological structuring elements using genetic algorithms. IEEE Trans Pattern Anal Mach Intell 20(2):217–224

    Article  Google Scholar 

  48. Van Droogenbroeck M, Buckley M (2005) Morphological erosions and openings: fast algorithms based on anchors. J Math Imag Vis 22:121–142

    Article  Google Scholar 

  49. Gil J, Kimmel R (2002) Efficient dilation, erosion, opening and closing algorithms. IEEE Trans Pattern Anal Mach Intell 24(12):1606–1617

    Article  Google Scholar 

  50. Urbach ER, Wilkinson MHF (2008) Efficient 2-D gray-scale morphological transformations with arbitrary flat structuring elements. IEEE Trans Image Proc 17(1):1–8

    Article  MathSciNet  Google Scholar 

  51. Preparata F, Sheimos M (1985) Computational geometry: an introduction. Springer, New York, NY, USA

    Book  Google Scholar 

  52. Vizilter YV, Sidyakin SV, Rubis A Y (2011) Calculation of morphological spectra of flat figures with the use of continuous skeletal representation. In: 15th Russian conference on mathematical methods of pattern recognition, pp 416–420 (in Russian)

    Google Scholar 

  53. Vizilter YV, Zheltov SY, Laretina NA (2009) Projective morphology on the basis of the operators filtering and image segmentation, computable by the method of dynamic programming. Vestnik Comput Inf Technol 6:18–27 (in Russian)

    Google Scholar 

  54. Vizilter YV, Sidyakin SV (2012) Calculation of morphological pattern spectra of gray scale images. Vestnik Comput Inf Technol 4:8–17 (in Russian)

    Google Scholar 

  55. Sidyakin SV (2013) Morphological pattern spectra algorithm development for digital image and video sequences analysis. PhD thesis, Moscow (in Russian)

    Google Scholar 

  56. Zingl A (2012) A rasterizing algorithm for drawing curves. Multimedia und Software entwicklung. Technikum-Wien, Wien

    Google Scholar 

  57. Tikhonov AN (1983) The theory of recovery signals Moscow, Science (in Russian)

    Google Scholar 

  58. Pyt’ev Y (1975) Morphological notions in problems of image analysis. Reports of USSR Academy of Science 224(6):1283–1286 (in Russian)

    Google Scholar 

  59. Pyt’ev Y (1975) Projection-based image analysis. Cybernetics 3:130–139 (in Russian)

    MathSciNet  Google Scholar 

  60. Pyt’ev Y (1983) Morphological image analysis. Reports of USSR Academy of Science 3:1061–1064 (in Russian)

    Google Scholar 

  61. Pyt’ev Y, Chulichkov A (2010) Morphological methods for image analysis. Fizmatlit Publisher, Moscow (in Russian)

    Google Scholar 

  62. Pyt’ev Yu (1993) Morphological image analysis. Pattern Recogn Image Anal 3(1):19–28

    MathSciNet  Google Scholar 

  63. Pyt’ev Y (1997) The morphology of color (multispectral) images. Pattern Recogn Image Anal 7(4):467–473

    MathSciNet  Google Scholar 

  64. Pyt’ev Y (1998) Methods for morphological analysis of color images. Pattern Recogn Image Anal 8(4):517–531

    MathSciNet  Google Scholar 

  65. Antonjuk V (1984) Hardware and techniques for morphological analysis of experimental multidimensional signals. Ph.D thesis (in Russian)

    Google Scholar 

  66. Pyt’ev Yu, Kalinin A, Loginov E, Smolovik V (1998) Morphological analysis of color images in the Chebyshev and quadratic metrics. Pattern Recogn Image Anal 8(2):234–235

    Google Scholar 

  67. Pyt’ev Y, Kalinin A, Loginov E, Smolovik V (1998) Comparison of black-and-white and Lambertian morphologies in the problem of pattern recognition. Pattern Recogn Image Anal 8(2):239–241

    Google Scholar 

  68. Pyt’ev Y, Kalinin A, Loginov E, Smolovik V (1998) On the problem of object detection by black-and-white and color morphologies. Pattern Recogn Image Anal 8(4):532–536

    Google Scholar 

  69. Chulichkov A, Grachev E, Ustinin D, Cheremukhin E (2003) Metrological measurements and signal processing in SEM based on model of signal formation. Microelectron Eng 69(2–4):555–564

    Article  Google Scholar 

  70. Pyt’ev YP, Falomkin II, Chulichkov AI (2006) Morphological compression of grayscale images of text. Pattern Recogn Image Anal 16(3):523–528

    Google Scholar 

  71. Evsegneev SO, Pyt’ev YP (2006) Analysis and recognition of piecewise constant texture images. Pattern Recogn Image Anal 16(3):398–405

    Article  Google Scholar 

  72. Falomkin II, Pyt’ev YP (2007) Algorithm of adaptive morphological filtering of images. Pattern Recog Image Anal 17(3):408–420

    Article  Google Scholar 

  73. Pyt’ev Y, Chulichkov A (2011) Methods of morphological image analysis. Bilateral Russian–Indian scientific workshop on emerging applications of computer vision

    Google Scholar 

  74. Visilter Y, Zheltov S, Stepanov A (1994) Shape analysis using Pyt’ev morphologic paradigm and its use in machine vision. SPIE Proc 2350:163–167

    Article  Google Scholar 

  75. Vizilter Y, Zheltov S (2008) Projective morphologies for image analysis. In: 9th international conference on pattern recognition and image analysis: new information technologies (PRIA-9-2008), vol 2, pp 287–290

    Google Scholar 

  76. Vizilter Y, Zheltov S (2010) Image segmentation in the framework of projective morphology. In: 10th international conference on pattern recognition and image analysis: new information technologies (PRIA-10-2010)

    Google Scholar 

  77. Vizilter YV (2011) Development of applied computer vision systems using projective morphologies and evidence-based image analysis. Bilateral Russian–Indian scientific workshop on emerging applications of computer vision (EACV-2011), pp 82–94

    Google Scholar 

  78. Vizilter YV, Sidyakin SV, Rubis AY, Gorbatsevich V (2011) Skeleton-based morphological shape comparison. Pattern Recogn Image Anal 21(2):357–360

    Article  Google Scholar 

  79. Vizilter YV, Zheltov SY (2009) The use of projective morphologies for object detection and identification in images. J Comput Syst Sci Int 48(2):282–294

    Article  MathSciNet  MATH  Google Scholar 

  80. Vizilter YV (2009) Design of data segmentation and data compression operators based on projective morphological decompositions. J Comput Syst Sci Int 48(3):415–429

    Article  MathSciNet  Google Scholar 

  81. Vizilter YV, Zheltov SY (2012) Geometrical correlation and matching of 2D image shapes. ISPRS Ann Photogramm Remote Sens Spatial Inf Sci 1–3:191–196

    Google Scholar 

  82. Pyt’ev YP (2013) Oblique projectors and relative forms in image morphology. J Comput Math Math Phys 53(1):21916–21937

    MathSciNet  Google Scholar 

  83. Maes F, Collignon A, Vandermeulen D, Marchal G, Suetens P (1997) Multimodality image registration by maximization of mutual information. IEEE Trans Med Imaging 16(2P):187–198

    Article  Google Scholar 

  84. Vizilter Y, Zheltov S (2008) Projective morphologies and their application in structural analysis of digital images. J Comput Syst Sci Int 47(6):944–958

    Article  MathSciNet  Google Scholar 

  85. Vizilter YV, Rubis AY (2009) Metric space of image shapes. Intell Inf Process IIP 9:406–409 (in Russian)

    Google Scholar 

  86. Vizilter YV, Rubis AY (2013) Comparison of 2D image shape similarity measures. In: 11th international conference on pattern recognition and image analysis: new information technologies (PRIA-11-2013), vol 1, pp 345–348

    Google Scholar 

  87. Pavel M (1989) Fundamentals of pattern recognition. Marcel Dekker Inc., New York

    MATH  Google Scholar 

  88. Hough PVC (1962) Methods, means for recognizing complex patterns. U.S., patent 3069654

    Google Scholar 

  89. Ballard DH, Brown CM (1982) Computer vision. Prentice-Hall, Englewood Cliffs, New Jersey

    Google Scholar 

  90. Davies ER (1992) Locating objects from their point features using an optimised Hough-like accumulation technique. Pattern Recogn 13(2):113–121

    Article  Google Scholar 

  91. Davies ER (1993) Computationally efficient Hough transform for 2-D object location. In: 4th conference on British machine vision association, vol 1, pp 259–268

    Google Scholar 

  92. Davies ER (2004) Machine vision: theory, algorithms, practicalities, 3rd edn. Academic Press, San Diego

    Google Scholar 

  93. Visilter Y, Zheltov S, Stepanov A (1996) Object detection and recognition using events-based image analysis. SPIE Proc 2823:184–195

    Article  Google Scholar 

  94. Visilter Y, Zheltov S, Stepanov A (1996) Events-based image analysis for machine vision and digital photogrammetry. In: ISPRS Proceedings of international archives of photogrammetry and remote sensing V.XXXI, Part B, pp 898–902

    Google Scholar 

  95. Visilter Y, Zheltov S, Bondarenko AV, Ososkov MV, Morzhin AV (2010) Image processing and analysis in machine vision applications. Moscow Phismathkniga (in Russian)

    Google Scholar 

  96. Ballard DH (1981) Generalizing the Hough transform to detect arbitrary shapes. Pattern Recogn 13(2):111–122

    Article  MATH  Google Scholar 

  97. Visilter Y, Gorbatsevich V (2011) Morphological image analysis using dynamic programming and stacked representations. Vestnik Comput Inf Technol 3:7–15 (in Russian)

    Google Scholar 

  98. Ford L, Fulkerson D (1962) Flows in networks. Princeton University Press, Princeton

    Google Scholar 

  99. Greig D, Porteous B, Seheult A (1989) Exact maximum a posteriori estimation for binary images. J Royal Stat Soc 51(2):271–279

    Google Scholar 

  100. Boykov Y, Kolmogorov V (2003) Computing geodesics and minimal surfaces via graph cuts. IEEE Int Conf Computer Vision (ICCV’2003), pp 26–33

    Google Scholar 

  101. Boykov Y, Kolmogorov V (2004) An experimental comparison of min-cut/max-ow algorithms for energy minimization in vision. IEEE Trans Pattern Anal Mach Intell (PAMI) 26(9):1124–1137

    Article  Google Scholar 

  102. Darbon J, Sigelle M (2006) Image restoration with discrete constrained total variation part i: fast and exact optimization. J Math Imaging Vision 26(3):261–276

    Article  MathSciNet  Google Scholar 

  103. Darbon J, Sigelle M (2006) Image restoration with discrete constrained total variation part ii: levelable functions, convex and non-convex cases. J Math Imaging Vision 26(3):277–291

    Article  MathSciNet  Google Scholar 

  104. Zheltov SY, Vizilter YV (2004) Robust computer image analysis for flight vehicles navigation and guidance. In: 16th IFAC symposium on automatic control in aerospace, vol 2, pp 164–167

    Google Scholar 

  105. Vizilter YV (2008) Generalized projective morphology. Comput Opt 32(4):384–399 (in Russian)

    Google Scholar 

Download references

Acknowledgments

Authors thank all colleagues from Moscow Morphological Workshop in the Lomonosov Moscow state university (supervised by Prof. Y. Pyt’ev) for many-years fruitful and kind discussions. Special thanks are to Russian Fund of Basic Researches supported the morphological researches by a series of grants.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Y.V. Vizilter .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Vizilter, Y., Pyt’ev, Y., Chulichkov, A., Mestetskiy, L.M. (2015). Morphological Image Analysis for Computer Vision Applications. In: Favorskaya, M., Jain, L. (eds) Computer Vision in Control Systems-1. Intelligent Systems Reference Library, vol 73. Springer, Cham. https://doi.org/10.1007/978-3-319-10653-3_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-10653-3_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10652-6

  • Online ISBN: 978-3-319-10653-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics