Skip to main content

Development of Mathematical Theory in Computer Vision

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

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

Abstract

This chapter presents a brief description of chapters devoted to the theoretical development of computer vision. Original investigations in mathematical morphology, estimations of structural changes, the hierarchical adaptive Karhunen-Loeve and projective transforms, among others, provide the great contribution in mathematical foundations of computer vision. Each theoretical chapter involves practical implementations, which demonstrate the merit of proposed methods in practice.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
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 (1988) Image analysis and mathematical morphology. Theoretical advances. Academic Press, London

    Google Scholar 

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

    MATH  Google Scholar 

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

    MathSciNet  Google Scholar 

  4. 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 

  5. 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 

  6. Sheikh HR, Bovik FC (2011) Image information and visual quality. IEEE Trans Image Process 20(1):88–98

    Article  MathSciNet  Google Scholar 

  7. Pratt WK (2001) Digital image processing. PIKS inside, 3rd edn. Wiley, New York

    Book  Google Scholar 

  8. Dony R (2001) Karhunen-Loeve transform. In: Rao K, Yip P (eds) The transform and data compression handbook. CRC Press, Boca Raton, London, New York, Washington, DC

    Google Scholar 

  9. Kountchev R, Kountcheva R (2013) Decorrelation of multispectral images, based on hierarchical adaptive PCA. Int J WSEAS Trans Sign Proc 3(9):120–137

    Google Scholar 

  10. Ivanov P, Kountchev R (2013) Hierarchical principal component analysis-based transformation of multispectral images. Int J Reasoning-Based Intell Syst (IJRIS) 5(4):260–273

    Article  Google Scholar 

  11. Rao K, Kim D, Hwang J (2010) Fast Fourier transforms: algorithms and applications. Springer, Dordrecht, Heidelberg, London, New York

    Google Scholar 

  12. Shapiro LG, Stockman GC (2001) Computer vision. Prentice Hall, Upper Saddle River, New Jersey

    Google Scholar 

  13. Lutsiv V (2009) Method of iteratively compensating projective image distortions. J Opt Technol 76(7):417–422

    Article  Google Scholar 

  14. Jähne B (2005) Digital image processing, 6th edn. Springer, Berlin

    Google Scholar 

  15. Xiao Z, Hou Z (2004) Phase based feature detector consistent with human visual system characteristics. Pattern Recogn Lett 25(10):1115–1121

    Article  Google Scholar 

  16. Marr D (1982) Vision: a computational investigation into the human representation and processing of visual information. W. H. Freeman, San Francisco

    Google Scholar 

  17. Gepshtein S, Tyukin I, Kubovy M (2011) A failure of the proximity principle in the perception of motion. Humana Mente 17:21–34

    Google Scholar 

  18. Ilea DE, Whelan PF (2011) Image segmentation based on the integration of colour-texture descriptors—a review. Pattern Recogn 44(10):2479–2501

    Article  MATH  Google Scholar 

  19. Marquez-Neila P, Baumela L, Alvarez L (2014) A morphological approach to curvature-based evolution of curves and surfaces. IEEE Trans Pattern Anal Mach Intell 36(1):2–17

    Article  Google Scholar 

  20. Fox V, Milanova M, Al-Ali S (2013) A morphological multiphase active contour for vascular segmentation. Int J Bioinform Biosci 3(3):1–12

    Article  Google Scholar 

  21. Battiato S, Lukac R (2008) Video stabilization techniques. Encyclopedia of multimedia. Springer, New York, pp 941–945

    Google Scholar 

  22. Rawat P, Singhai J (2011) Review of motion estimation and video stabilization techniques for hand held mobile video. Int J Signal Image Process 2(2):159–168

    Article  Google Scholar 

  23. Mironowsky LA, Slaev VA (2011) Strip-method for image and signal transformation. De Gruyter, Berlin

    Book  Google Scholar 

  24. Hadamard J (1893) Resolution d’une Question Relative aux Determinants. Bull Sci Math ser 2 17(1):240–246

    Google Scholar 

  25. Yüksel S, Başar T (2013) Stochastic networked control systems. Springer, New York, Heidelberg

    Book  MATH  Google Scholar 

  26. Govindan M, Tang CM (2010) Information system evaluation: an ongoing measure. Int J Business Inform Syst 6(3):336–353

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Margarita N. Favorskaya .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Favorskaya, M.N., Jain, L.C. (2015). Development of Mathematical Theory in Computer Vision. 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_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-10653-3_1

  • 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