Detection of architectural distortion in prior screening mammograms using Gabor filters, phase portraits, fractal dimension, and texture analysis

  • Rangaraj M. Rangayyan
  • Shormistha Prajna
  • Fábio J. Ayres
  • J. E. Leo Desautels
Original article



Mammography is a widely used screening tool for the early detection of breast cancer. One of the commonly missed signs of breast cancer is architectural distortion. The purpose of this study is to explore the application of fractal analysis and texture measures for the detection of architectural distortion in screening mammograms taken prior to the detection of breast cancer.

Materials and methods

A method based on Gabor filters and phase portrait analysis was used to detect initial candidates for sites of architectural distortion. A total of 386 regions of interest (ROIs) were automatically obtained from 14 “prior mammograms”, including 21 ROIs related to architectural distortion. From the corresponding set of 14 “detection mammograms”, 398 ROIs were obtained, including 18 related to breast cancer. For each ROI, the fractal dimension and Haralick’s texture features were computed. The fractal dimension of the ROIs was calculated using the circular average power spectrum technique.


The average fractal dimension of the normal (false-positive) ROIs was significantly higher than that of the ROIs with architectural distortion (p  =  0.006). For the “prior mammograms”, the best receiver operating characteristics (ROC) performance achieved, in terms of the area under the ROC curve, was 0.80 with a Bayesian classifier using four features including fractal dimension, entropy, sum entropy, and inverse difference moment. Analysis of the performance of the methods with free-response receiver operating characteristics indicated a sensitivity of 0.79 at 8.4 false positives per image in the detection of sites of architectural distortion in the “prior mammograms”.


Fractal dimension offers a promising way to detect the presence of architectural distortion in prior mammograms.


Architectural distortion Breast cancer Prior screening mammograms Screen-detected breast cancer Fractal dimension Texture analysis Gabor filters Phase portraits 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    National Cancer Institute of Canada. Canadian cancer statistics, (2007). Accessed on 22 June 2007
  2. 2.
    Schneider MA (2000) Better detection: improving our chances. In: Yaffe MJ(eds) Digital mammography: 5th international workshop on digital mammography, Toronto, ON, Canada, June 2000. Medical Physics Publishing, Madison, pp 3–6Google Scholar
  3. 3.
    Bird RE, Wallace TW, Yankaskas BC (1992) Analysis of cancers missed at screening mammography. Radiology 184(3): 613–617PubMedGoogle Scholar
  4. 4.
    Majid AS, Paredes ES, Doherty RD, Sharma NR, Salvador X (2003) Missed breast carcinoma: Pitfalls and pearls. RadioGraphics 23: 881–895PubMedCrossRefGoogle Scholar
  5. 5.
    Ikeda DM, Birdwell RL, O’Shaughnessy KF, Brenner RJ, Sickles EA (2003) Analysis of 172 subtle findings on prior normal mammograms in women with breast cancer detected at follow-up screening. Radiology 226: 494–503PubMedCrossRefGoogle Scholar
  6. 6.
    Ikeda DM, Birdwell RL, O’Shaughnessy KF, Sickles EA, Brenner RJ (2004) Computer-aided detection output on 172 subtle findings on normal mammograms previously obtained in women with breast cancer detected at follow-up screening mammography. Radiology 230: 811–819PubMedCrossRefGoogle Scholar
  7. 7.
    Peitgen HO (ed) (2002) Proceedings of the 6th international workshop on digital mammography. Springer, Bremen, Germany, June 2002Google Scholar
  8. 8.
    Rangayyan RM, Ayres FJ, Desautels JEL (2007) A review of computer-aided diagnosis of breast cancer: toward the detection of subtle signs. J Franklin Inst 344: 312–348CrossRefGoogle Scholar
  9. 9.
    Doi K (2006) Diagnostic imaging over the last 50 years: research and development in medical imaging science and technology. Phys Med Biol 51: R5–R27PubMedCrossRefGoogle Scholar
  10. 10.
    Doi K (2007) Computer-aided diagnosis in medical imaging: historical review, current status and future potential. Comput Med Imag Graph 31: 198–211CrossRefGoogle Scholar
  11. 11.
    Baker JA, Rosen EL, Lo JY, Gimenez EI, Walsh R, Soo MS (2003) Computer-aided detection (CAD) in screening mammography: sensitivity of commercial CAD systems for detecting architectural distortion. Am J Roentgenol 181: 1083–1088Google Scholar
  12. 12.
    Prajna S, Rangayyan RM, Ayres FJ, Desautels JEL (2008) Detection of architectural distortion in mammograms acquired prior to the detection of breast cancer using texture and fractal analysis. In: Fitzpatrick JM, Sonka M (eds) Proceedings of SPIE medical imaging 2008: image processing, San Diego, CA, February 2008Google Scholar
  13. 13.
    American College of Radiology (ACR) (1998) Illustrated breast imaging reporting and data system (BI-RADS), 3rd edn. American College of Radiology, RestonGoogle Scholar
  14. 14.
    Homer MJ (1997) Mammographic interpretation: a practical approach, 2nd edn. McGraw-Hill, New YorkGoogle Scholar
  15. 15.
    Knutzen AM, Gisvold JJ (1993) Likelihood of malignant disease for various categories of mammographically detected, nonpalpable breast lesions. Mayo Clinic Proc 68: 454–460Google Scholar
  16. 16.
    Yankaskas BC, Schell MJ, Bird RE, Desrochers DA (2001) Reassesment of breast cancers missed during routine screening mammography: a community based study. Am J Roentgenol 177: 535–541Google Scholar
  17. 17.
    Burrell H, Evans A, Wilson A, Pinder S (2001) False-negative breast screening assesment: what lessons we can learn?. Clin Radiol 56: 385–388PubMedCrossRefGoogle Scholar
  18. 18.
    Burrell HC, Sibbering DM, Wilson ARM, Pinder SE, Evans AJ, Yeoman LJ, Elston CW, Ellis IO, Blamey RW, Robertson JFR (1996) Screening interval breast cancers: Mammographic features and prognostic factors. Radiology 199(4): 811–817PubMedGoogle Scholar
  19. 19.
    Broeders MJM, Onland-Moret NC, Rijken HJTM, Hendriks JHCL, Verbeek ALM, Holland R (2003) Use of previous screening mammograms to identify features indicating cases that would have a possible gain in prognosis following earlier detection. Eur J Cancer 39: 1770–1775PubMedCrossRefGoogle Scholar
  20. 20.
    Ayres FJ, Rangayyan RM (2005) Characterization of architectural distortion in mammograms. IEEE Eng Med Biol Mag 24(1): 59–67PubMedCrossRefGoogle Scholar
  21. 21.
    Ayres FJ, Rangayyan RM (2007) Reduction of false positives in the detection of architectural distortion in mammograms by using a geometrically constrained phase portrait model. Int J Comput Assist Radiol Surg 1: 361–369CrossRefGoogle Scholar
  22. 22.
    Rangayyan RM, Ayres FJ (2006) Gabor filters and phase portraits for the detection of architectural distortion in mammograms. Med Biol Eng Comput 44: 883–894PubMedCrossRefGoogle Scholar
  23. 23.
    Guo Q, Shao J, Ruiz V (2005) Investigation of support vector machine for the detection of architectural distortion in mammographic images. J Phys Conf Ser 15: 88–94CrossRefGoogle Scholar
  24. 24.
    Suckling J, Parker J, Dance DR, Astley S, Hutt I, Boggis CRM, Ricketts I, Stamakis E, Cerneaz N, Kok S-L, Taylor P, Betal D, Savage J (1994) The Mammographic Image Analysis Society digital mammogram database. In: Gale AG, Astley SM, Dance DD, Cairns AY(eds) Digital mammography: proceedings of the 2nd international workshop on digital mammography. Elsevier, York, pp 375–378Google Scholar
  25. 25.
    Tourassi GD, Delong DM, Floyd CE Jr (2006) A study on the computerized fractal analysis of architectural distortion in screening mammograms. Phys Med Biol 51(5): 1299–1312PubMedCrossRefGoogle Scholar
  26. 26.
    Mudigonda NR, Rangayyan RM (2001) Texture flow-field analysis for the detection of architectural distortion in mammograms. In: Ramakrishnan AG (ed) Proceedings of biovision. Bangalore, India, December 2001, pp 76–81Google Scholar
  27. 27.
    Matsubara T, Ichikawa T, Hara T, Fujita H, Kasai S, Endo T, Iwase T (2003) Automated detection methods for architectural distortions around skinline and within mammary gland on mammograms. In: Lemke HU, Vannier MW, Inamura K, Farman AG, Doi K, Reiber JHC (eds) International congress series: proceedings of the 17th international congress and exhibition on computer assisted radiology and surgery, London, UK, June 2003. Elsevier, Amsterdam, pp 950–955Google Scholar
  28. 28.
    Ichikawa T, Matsubara T, Hara T, Fujita H, Endo T, Iwase T (2004) Automated detection method for architectural distortion areas on mammograms based on morphological processing and surface analysis. In: Fitzpatrick JM, Sonka M (eds) Proceedings of SPIE medical imaging 2004: image processing, San Diego, CA, February 2004. SPIE, pp 920–925Google Scholar
  29. 29.
    Sampat MP, Whitman GJ, Markey MK, Bovik AC (2005) Evidence based detection of spiculated masses and architectural distortion. In: Fitzpatrick JM, Reinhardt JM (eds) Proceedings of SPIE medical imaging 2005: image processing, vol 5747, San Diego, CA, April 2005, pp 26–37Google Scholar
  30. 30.
    Eltonsy N, Tourassi G, Elmaghraby A (2006) Investigating performance of a morphology-based CAD scheme in detecting architectural distortion in screening mammograms. In: Lemke HU, Inamura K, Doi K, Vannier MW, Farman AG (eds) Proceedings of the 20th international congress and exhibition on computer assisted radiology and surgery (CARS 2006), Osaka, Japan, June 2006. Springer, Heidelberg, pp 336–338Google Scholar
  31. 31.
    Evans WP, Burhenne LJW, Laurie L, O’Shaughnessy KF, Castellino RA (2002) Invasive lobular carcinoma of the breast: mammographic characteristics and computer-aided detection. Radiology 225(1): 182–189PubMedCrossRefGoogle Scholar
  32. 32.
    Burhenne LJW, Wood SA, D’Orsi CJ, Feig SA, Kopans DB, O’Shaughnessy LF, Sickles EA, Tabar L, Vyborny CJ, Castellino RA (2000) Potential contribution of computer-aided detection to the sensitivity of screening mammography. Radiology 215(2): 554–562Google Scholar
  33. 33.
    Birdwell RL, Ikeda DM, O’Shaughnessy KF, Sickles EA (2001) Mammographic characteristics of 115 missed cancers later detected with screening mammography and the potential utility of computer-aided detection. Radiology 219(1): 192–202PubMedGoogle Scholar
  34. 34.
    van Dijck JAAM, Verbeek ALM, Hendriks JHCL, Holland R (1993) The current detectability of breast cancer in a mammographic screening program. Cancer 72(6): 1933–1938PubMedCrossRefGoogle Scholar
  35. 35.
    Sameti M, Morgan-Parkes J, Ward RK, Palcic B (1998) Classifying image features in the last screening mammograms prior to detection of a malignant mass. In: Karssemeijer N, Thijssen M, Hendriks J, van Erning L (eds) Proceedings of the 4th international workshop on digital mammography, Nijmegen, The Netherlands, June 1998, pp 127–134Google Scholar
  36. 36.
    Petrick N, Chan HP, Sahiner B, Helvie MA, Paquerault S (2000) Evaluation of an automated computer-aided diagnosis system for the detection of masses on prior mammograms. In: Proceedings of SPIE, vol 3979. Medical imaging 2000: image processing, pp 967–973Google Scholar
  37. 37.
    Zheng B, Good WF, Armfield DR, Cohen C, Hertzberg T, Sumkin JH, Gur D (2003) Performance change of mammographic CAD schemes optimized with most-recent and prior image databases. Acad Radiol 10: 283–288PubMedCrossRefGoogle Scholar
  38. 38.
    Burnside ES, Sickles EA, Sohlich RE, Dee KE (2002) Differential value of comparison with previous examinations in diagnostic versus screening mammography. Am J Roentgenol 179: 1173–1177Google Scholar
  39. 39.
    Sumkin JH, Holbert BL, Herrmann JS, Hakim CA, Ganott MA, Poller WR, Shah R, Hardesty LA, Gur D (2003) Optimal reference mammography: a comparison of mammograms obtained 1 and 2 years before the present examination. Am J Roentgenol 180: 343–346Google Scholar
  40. 40.
    Varela C, Karssemeijer N, Hendriks JHCL, Holland R (2005) Use of prior mammograms in the classification of benign and malignant masses. Eur J Radiol 56: 248–255PubMedCrossRefGoogle Scholar
  41. 41.
    Ciatto S, Del Turco MR, Burke P, Visioli C, Paci E, Zappa M (2003) Comparison of standard and double reading and computer-aided detection (CAD) of interval cancers at prior negative screening mammograms: blind review. Brit J Canc 89: 1645–1649CrossRefGoogle Scholar
  42. 42.
    Moberg K, Bjurstam N, Wilczek B, Rostgård L, Egge E, Muren C (2001) Computer assisted detection of interval breast cancers. Eur J Radiol 39: 104–110PubMedCrossRefGoogle Scholar
  43. 43.
    Garvican L, Field S (2001) A pilot evaluation of the R2 Image Checker System and users’ response in the detection of interval breast cancers on previous screening films. Clin Radiol 56: 833–837PubMedCrossRefGoogle Scholar
  44. 44.
    Mandelbrot BB (1983) The Fractal Geometry of Nature. San Francisco, CA, FreemanGoogle Scholar
  45. 45.
    Fortin C, Kumaresan R, Ohley W (1992) Fractal dimension in the analysis of medical images. IEEE Eng Med Biol Mag 11(2): 65–71CrossRefGoogle Scholar
  46. 46.
    Rangayyan RM, Nguyen TM (2007) Fractal analysis of contours of breast masses in mammograms. J Dig imag 20(3): 223–237CrossRefGoogle Scholar
  47. 47.
    Huang Q, Lorch JR, Dubes RC (1994) Can the fractal dimension of images be measured?. Pattern Recognition 27: 1569–1579Google Scholar
  48. 48.
    Aguilar M, Anguiano E, Pancorbo MA (1993) Fractal characterization by frequency analysis: II. A new method. J Microsc 172: 233–238Google Scholar
  49. 49.
    Anguiano E, Pancorbo MA, Aguilar M (1993) Fractal characterization by frequency analysis: I. Surfaces. J Microsc 172: 223–232Google Scholar
  50. 50.
    Schepers HE, van Beek JHGM, Bassingthwaighte JB (1992) Four methods to estimate the fractal dimension from self-affine signals. IEEE Eng Med Biol Mag 11(2): 57–64CrossRefGoogle Scholar
  51. 51.
    Bak P, Tang C, Wiesenfeld K (1987) Self-organized criticality: An explanation of 1/f noise. Am Phys Soc 59: 381–384Google Scholar
  52. 52.
    Lowen SB, Teich MC (1993) Fractal renewal processes generate 1/f noise. Am Phys Soc 47: 992–1001Google Scholar
  53. 53.
    DeLos Rios P, Zhang Y-C (1999) Universal/noise from dissipative self-organized criticality models. Am Phys Soc 82: 472–475Google Scholar
  54. 54.
    Billock VA, De Guzman GC, Kelso JAS (2001) Fractal time and 1/f spectra in dynamic images and human vision. Physica D: Nonlinear Phenom 148: 136–146CrossRefGoogle Scholar
  55. 55.
    Uss M, Lukin VV, Abramov S, Vozel B, Chehdi K (2007) Joint estimation of multiplicative and impulsive noise parameters in remote sensing with fractal structure. In: IEEE international conference on acoustics, speech, and signal processing, Honolulu, HI, pp 581–584Google Scholar
  56. 56.
    StǑsić T, StǑsić BD (2006) Multifractal analysis of human retinal vessels. IEEE Trans Med Imag 25: 1101–1107CrossRefGoogle Scholar
  57. 57.
    Otsu N (1979) A threshold selection method from gray-level histograms. IEEE Trans Syst Man Cybernet 9(1): 62–66CrossRefGoogle Scholar
  58. 58.
    Gonzalez RC, Woods RE (2002) Digital image processing, 2nd edn. Prentice-Hall, Upper Saddle RiverGoogle Scholar
  59. 59.
    Ayres FJ, Rangayyan RM (2007) Design and performance analysis of oriented feature detectors. J Electronic Imag 16(2): 023007:1–12Google Scholar
  60. 60.
    Oppenheim AV, Schafer RW (1989) Discrete-time signal processing. Prentice-Hall, Englewood CliffsGoogle Scholar
  61. 61.
    Haralick RM (1979) Statistical and structural approaches to texture. Proc IEEE 67(5): 786–804Google Scholar
  62. 62.
    Haralick RM, Shanmugam K, Dinstein I (1973) Textural features for image classification. IEEE Trans Syst Man Cybernet 3(6): 610–622CrossRefGoogle Scholar
  63. 63.
    Rangayyan RM (2005) Biomedical image analysis. CRC Press, Boca RatonGoogle Scholar
  64. 64.
    Rangayyan RM, Nguyen TM, Ayres FJ, Nandi AK (2007) Analysis of the effect of spatial resolution on texture features in the classification of breast masses in mammograms. In: Lemke HU, Inamura K, Doi K, Vannier MW, Farman AG (eds) Proceedings of the 21st international congress and exhibition on computer assisted radiology and surgery (CARS 2007), Berlin, Germany, June 2007. Springer, Heidelberg, pp 334–336Google Scholar
  65. 65.
    Nandi RJ, Nandi AK, Rangayyan RM, Scutt D (2006) Classification of breast masses in mammograms using genetic programming and feature selection. Med Biol Eng Comput 44: 683–694PubMedCrossRefGoogle Scholar
  66. 66.
    Ware JH, Mosteller F, Delgado F, Donnelly C, Ingelfinger JA (1992) P values. In: Bailar JC III, Mosteller F(eds) Medical uses of statistics, 2nd edn. NEJM Books, Boston, pp 181–200Google Scholar
  67. 67.
    Metz CE (1986) ROC methodology in radiologic imaging. Investigative Radiology 21: 720–733PubMedCrossRefGoogle Scholar
  68. 68.
    Duda RO, Hart PE, Stork DG (2001) Pattern classification, 2nd edn. Wiley–Interscience, New YorkGoogle Scholar
  69. 69.
    Alto H, Rangayyan RM, Paranjape RB, Desautels JEL, Bryant H (2003) An indexed atlas of digital mammograms for computer-aided diagnosis of breast cancer. Ann Télécommun 58(5–6): 820–835Google Scholar
  70. 70.
    Alberta Cancer Board,, Alberta, Canada (2004). Screen Test: Alberta Program for the Early Detection of Breast Cancer—2001/03 Biennial Report
  71. 71.
    Byng JW, Boyd NF, Fishell E, Jong RA, Yaffe MJ (1996) Automated analysis of mammographic densities. Phys Med Biol 41: 909–923PubMedCrossRefGoogle Scholar
  72. 72.
    Caldwell CB, Stapleton SJ, Holdsworth DW, Jong RA, Weiser WJ, Cooke G, Yaffe MJ (1990) Characterization of mammographic parenchymal pattern by fractal dimension. Phys Med Biol 35(2): 235–247PubMedCrossRefGoogle Scholar
  73. 73.
    Zheng L, Chan AK (2001) An artificial intelligent algorithm for tumor detection in screening mammogram. IEEE Trans Med Imag 20(7): 559–567CrossRefGoogle Scholar
  74. 74.
    Pohlman S, Obuchowski KA, Chilcote WA, Grundfest-Broniatowski S (1996) Quantitative classification of breast tumours in digitized mammograms. Med Phys 23(8): 1337–1345PubMedCrossRefGoogle Scholar

Copyright information

© CARS 2008

Authors and Affiliations

  • Rangaraj M. Rangayyan
    • 1
    • 2
  • Shormistha Prajna
    • 1
  • Fábio J. Ayres
    • 1
  • J. E. Leo Desautels
    • 1
  1. 1.Department of Electrical and Computer Engineering, Schulich School of EngineeringUniversity of CalgaryCalgaryCanada
  2. 2.Department of RadiologyUniversity of CalgaryCalgaryCanada

Personalised recommendations