Mammogram Analysis Using Two-Dimensional Autoregressive Models: Sufficient or Not?

  • Sarah Lee
  • Tania Stathaki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3617)

Abstract

Two-dimensional (2–D) autoregressive (AR) models have been used as one of the methods to characterise the textures of tumours in mammograms. Previously, the 2–D AR model coefficients were estimated for the block containing the tumour and the blocks in its 3 × 3 neighbourhood. In this paper, the possibility of having the estimated set of AR model coefficients of the block containing the tumour as a unique set of AR model coefficients for the entire mammogram is looked into. Based on the information given from the MiniMammography database, the possible number of blocks of the same size of the block containing the tumour is obtained from the entire mammogram and for each block a set of AR model coefficients is estimated using a method that combines both the Yule-Walker system of equations and the Yule-Walker system of equations in the third-order statistical domain. These sets of AR model coefficients are then compared. The simulation results show that 98.6% of the time we can not find another set of AR model coefficients representing the blocks of pixels in the possible neighbourhood of the entire mammogram for the data (95 mammograms with 5 of them having two tumours) available in the MiniMammography database.

Keywords

Tumour Block Digital Mammogram Diagonal Weighting Matrix International Congress Series European Signal Processing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Kay, S.M.: Modern spectral estimation: theory and application. Prentice-Hall, Englewood Cliffs (1988)MATHGoogle Scholar
  2. 2.
    Lee, S., Stathaki, T.: Texture Characterisation Using Constrained Optimisation Techniques with Application to Mammography. In: Fifth International Workshop on Image Analysis for Multimedia Interactive Services (WIAMIS 2004), on CD-ROM (2004)Google Scholar
  3. 3.
    Lee, S., Stathaki, T.: Two-Dimensional Autoregressive Modelling Using Joint Second and Third Order Statistics and a Weighting Scheme. In: Twelfth European Signal Processing Conference (EUSIPCO), on CD-ROM (2004)Google Scholar
  4. 4.
    Lee, S.H.-H.: Novel Approaches to Two Dimensional Autoregressive Modelling, Ph.D. and DIC thesis, Imperial College London (2004)Google Scholar
  5. 5.
    The Mammographic Image Analysis Society (MIAS): MiniMammography Database. last access: February 11 (2005), http://www.wiau.man.ac.uk/services/MIAS/MIASmini.html
  6. 6.
    Stathaki, T.: 2-D autoregrssive modelling using joint and weighted second and third order statistics. Electronics Letters 32(14), 1271–1273 (1996)CrossRefGoogle Scholar
  7. 7.
    Suckling, J., Parker, J., Dance, D., Astley, S., Hutt, I., Boggis, C., Ricketts, I., Stamatakis, E., Cerneaz, N., Kok, S., Taylor, P., Betal, D., Savage, J.: The Mammographic Image Analysis Society Digital Mammogram Database. In: Exerpta Medica. International Congress Series, vol. 1069, pp. 375–378 (1994)Google Scholar
  8. 8.
    Swami, A., Giannakis, G.B., Mendel, J.M.: Linear modeling of multidimensional non-Gaussian processes using cumulants. Multidimensional Systems and Signal Processing 1, 11–37 (1990)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Sarah Lee
    • 1
    • 2
  • Tania Stathaki
    • 3
  1. 1.Department of Diabetes, Endocrinology & Internal Medicine, Guy’s, King’s and St Thomas’ School of MedicineKing’s College, LondonLondonUK
  2. 2.Brain Image Analysis UnitCentre for Neuroimaging Sciences, Institute of PsychiatryLondonUK
  3. 3.Communications and Signal Processing Group, Department of Electrical and Electronic EngineeringImperial College, LondonLondonUK

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