Phase portrait analysis for automatic initialization of multiple snakes for segmentation of the ultrasound images of breast cancer | Pattern Analysis and Applications Skip to main content

Advertisement

Log in

Phase portrait analysis for automatic initialization of multiple snakes for segmentation of the ultrasound images of breast cancer

  • Short Paper
  • Published:
Pattern Analysis and Applications Aims and scope Submit manuscript

Abstract

Segmentation of ultrasound (US) images of breast cancer is one of the most challenging problems of modern medical image processing. A number of popular codes for US segmentation are based on the active contours (snakes) and on a variety of modifications of gradient vector flow. The snakes have been used to locate objects in various applications of medical images. However, the main difficulty in applying the method is initialization. Therefore, we suggest a new method for automatic initialization of active contours based on phase portrait analysis (PPA) of the underlying vector field and a sequential initialization of trial multiple snakes. The PPA makes it possible to exclude the noise and artifacts and properly initialize the multiple snakes. In turn, the trial snakes allow us to differentiate between the seeds initialized inside and outside the desired object. While preceding methods require the manual selection of at least one seed point inside the object or rely on the particular distribution of the gray levels, the proposed method is fully automatic and robust to the noise, as can be seen from the tests with synthetic and real images.

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

Access this article

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

References

  1. Ma Z, Tavares JMRS, Jorge RMN (2009) A review on the current segmentation algorithms for medical images. In: Proceedings of the 1st international conference on Imaging Theory and Applications (IMAGAPP), Portugal, pp. 135–140.

  2. Noble JA, Boukerroui D (2006) Ultrasound image segmentation: a survey. IEEE Trans Med Imaging 25(8):987–1010

    Article  Google Scholar 

  3. Horsch K, Giger ML, Venta LA, Vyborny CJ (2001) Automatic segmentation of breast lesions on ultrasound. Med Phys 28(8):1652–1659

    Article  Google Scholar 

  4. Horsch K, Giger ML, Venta LA, Vyborny CJ (2002) Computerized diagnosis of breast lesions on ultrasound. Med Phys 29(2):157–164

    Article  Google Scholar 

  5. Horsch K, Giger ML, Vyborny CJ, Venta LA (2004) Performance of computer-aided diagnosis in the interpretation of lesions on breast sonography. Acad Radiol 11(3):272–280

    Article  Google Scholar 

  6. Drukker K, Giger ML, Horsch K, Kupinski MA, Vyborny CJ, Mendelson EB (2002) Computerized lesion detection on breast ultrasound. Med Phys 29(7):1438–1446

    Article  Google Scholar 

  7. Drukker K, Giger ML, Vyborny CJ, Mendelson EB (2004) Computerized detection and classification of cancer on breast ultrasound. Acad Radiol 11(5):526–535

    Article  Google Scholar 

  8. Shan J, Cheng HD, Wang Y (2012) Completely automated segmentation approach for breast ultrasound images using multiple-domain features. Ultrasound Med Biol 38(2):262–275

    Article  Google Scholar 

  9. Jiang P, Peng J, Zhang G, Cheng E, Megalooikonomou V, Ling H (2012) Learning-based automatic breast tumor detection and segmentation in ultrasound images. In: the 9th IEEE international symposium biomedical imaging (ISBI), pp. 1587–1590

  10. Jesneck JL, Lo JY, Baker JA (2007) Breast mass lesions: computer-aided diagnosis models with mammographic and sonographic descriptors. Radiology 244(2):390–398

    Article  Google Scholar 

  11. Chen CM, Chou YH, Han KC, Hung GS, Tiu CM, Chiou HJ, Chiou SY (2003) Breast lesions on sonograms: computer-aided diagnosis with nearly setting-independent features and artificial neural networks. Radiology 226(2):504–514

    Article  Google Scholar 

  12. Song JH, Venkatesh SS, Conant EF, Cary TW, Arger PH, Sehgal CM (2005) Artificial Neural Network to aid differentiation of malignant and benign breast masses by ultrasound imaging. In: Proceedings of SPIE, progress in biomedical optics and imaging, pp.148–152

  13. Joo S, Yang YS, Moon WK, Kim HC (2004) Computer-aided diagnosis of solid breast nodules: use of an artificial neural network based on multiple sonographic features. IEEE Trans Med Imaging 23(10):1292–1300

    Article  Google Scholar 

  14. Huang YL, Wang KL, Chen DR (2005) Diagnosis of breast tumors with ultrasonic texture analysis using support vector machines. Neural Comput Appl 15(2):164–169

    Article  Google Scholar 

  15. Huang YL, Chen DR (2004) Watershed segmentation for breast tumor in 2-D sonography. Ultrasound Med Biol 30(5):625–632

    Article  Google Scholar 

  16. Xiao G, Brady M, Noble JA, Zhang Y (2002) Segmentation of ultrasound B-mode images with intensity inhomogeneity correction. IEEE Trans Med Imaging 21(1):48–57

    Article  Google Scholar 

  17. Boukerroui D, Baskurt A, Noble JA, Basset O (2003) Segmentation of ultrasound images-multiresolution 2D and 3D algorithm based on global and local statistics. Pattern Recognit Lett 24(45):779–790

    Article  Google Scholar 

  18. Kannan SR, Devi R, Ramathilagam S, Takezawa K (2013) Effective FCM noise clustering algorithms in medical images. Comput Biol Med 43(2):73–83

    Article  Google Scholar 

  19. Son LH, Tuan TM (2016) A cooperative semi-supervised fuzzy clustering framework for dental X-ray image segmentation. Expert Syst Appl 46(C):380–393

    Article  Google Scholar 

  20. Zhang X, Li X, Feng Y (2015) A medical image segmentation algorithm based on bi-directional region growing. Optik—Int J Light Electron Optics 126(20):2398–2404

    Article  Google Scholar 

  21. Madabhushi A, Metaxas DN (2003) Combining low-, high-level and empirical domain knowledge for automated segmentation of ultrasonic breast lesions. IEEE Trans Med Imaging 22(2):155–169

    Article  Google Scholar 

  22. Chen D, Chang R, Wu WJ, Moon W, Wu WL (2003) 3-D breast ultrasound segmentation using active contour model. Ultrasound Med Biol 29(7):1017–1026

    Article  Google Scholar 

  23. Chang RF, Wu WJ, Moon WK, Chen WM, Lee W, Chen DR (2003) Segmentation of breast tumor in three-dimensional ultrasound images using three-dimensional discrete active contour model. Ultrasound Med Biol 29(11):1571–1581

    Article  Google Scholar 

  24. Chang RF, Wu WJ, Tseng CC, Chen DR, Moon WK (2003) 3-D snake for US in margin evaluation for malignant breast tumor excision using Mammotome. IEEE Trans Inform Technol Biomed 7(3):197–201

    Article  Google Scholar 

  25. Sahiner B, Chan HP, Roubidoux MA, Helvie MA, Hadjiiski LM, Ramachandran A, Paramagul C, LeCarpentier GL, Nees A, Blane C (2004) Computerized characterization of breast masses on three-dimensional ultrasound volumes. Med Phys 31(4):744–754

    Article  Google Scholar 

  26. Liu Q, Jiang M, Bai P, Yang G (2016) A novel level set model with automated initialization and controlling parameters for medical image segmentation. Comput Med Imaging Graph 48:21–29

    Article  Google Scholar 

  27. Chen DR, Chang RF, Kuo WJ, Chen MC, Huang YL (2002) Diagnosis of breast tumors with sonographic texture analysis using wavelet transform and neural networks. Ultrasound Med Biol 28(10):1301–1310

    Article  Google Scholar 

  28. Cheng HD, Shan J, Ju W, Guo Y, Zhang L (2010) Automated breast cancer detection and classification using ultrasound images: a survey. Pattern Recognit 43(1):299–317

    Article  MATH  Google Scholar 

  29. James AP, Dasarathy BV (2014) Medical image fusion: a survey of the state of the art. Inf Fusion 19:4–19

    Article  Google Scholar 

  30. Smistad E, Falch TL, Bozorgi M, Elster AC, Lindseth F (2015) Medical image segmentation on GPUs—A comprehensive review. Med Image Anal 20(1):1–18

    Article  Google Scholar 

  31. Iglesias JE, Sabuncu MR (2015) Multi-atlas segmentation of biomedical images: a survey. Med Image Anal 24(1):205–219

    Article  Google Scholar 

  32. Ghosh P, Mitchell M, Tanyi JA, Hung AY (2016) Incorporating priors for medical image segmentation using a genetic algorithm. Neurocomputing. doi:10.1016/j.neucom.2015.09.123

    Google Scholar 

  33. Ma Z, Jorge RN, Tavares JM (2010) A shape guided C–V model to segment the levator ani muscle in axial magnetic resonance images. Med Eng Phys 32(7):766–774

    Article  Google Scholar 

  34. Wang J, Yeung S-K, Chan KL (2015) Matching-constrained active contours with affine-invariant shape prior. Comput Vis Image Underst 132:39–55

    Article  Google Scholar 

  35. el Diop HS, Burdin V (2013) Bi-planar image segmentation based on variational geometrical active contours with shape priors. Med Image Anal 17(2):165–181

    Article  Google Scholar 

  36. Wang B, Gao X, Li J, Li X, Tao D (2015) A level set method with shape priors by using locality preserving projections. Neurocomputing 170:188–200

    Article  Google Scholar 

  37. Li C, Xu C, Gui C, Fox MD (2010) Distance regularized level set evolution and its application to image segmentation. IEEE Trans Image Process 19(12):3243–3254

    Article  MathSciNet  Google Scholar 

  38. Li C. (2006) Level set for image segmentation. Matlab File Exchange MathWorks. http://www.mathworks.com/matlabcentral/fileexchange/12711-level-set-for-image-segmentation Accessed 10 Jan 2016

  39. Li BN, Chui CK, Chang S, Ong SH (2011) Integrating spatial fuzzy clustering with level set methods for automated medical image segmentation. Comput Biol Med 41(1):1–10

    Article  Google Scholar 

  40. ABing (2011) Spatial fuzzy clustering and level set segmentation. Matlab File Exchange MathWorks. http://www.mathworks.com/matlabcentral/fileexchange/31068-spatial-fuzzy-clustering-and-level-set-segmentation. Accessed 10 Jan 2016

  41. Ma Z, Tavares JMRS (2016) A novel approach to segment skin lesions in dermoscopic images based on a deformable model. IEEE J Biomed Health Inform 20(2):615–621

    Article  Google Scholar 

  42. Ma Z, Jorge RMN, Mascarenhas T, Tavares JMRS (2013) A level set based algorithm to reconstruct the urinary bladder from multiple views. Med Eng Phys 35(12):1819–1824

    Article  Google Scholar 

  43. Ma Z, Jorge RMN, Mascarenhas T, Tavares JMRS (2012) Segmentation of female pelvic cavity in axial T2-weighted MR images towards the 3D reconstruction. Int J Numer Method Biomed Eng 28:714–726

    Article  MathSciNet  Google Scholar 

  44. Xie X, Wu J, Jing M (2013) Fast two-stage segmentation via non-local active contours in multiscale texture feature space. Pattern Recognit Lett 34(11):1230–1239

    Article  Google Scholar 

  45. Krawczyk B, Schaefer G (2014) A hybrid classifier committee for analysing asymmetry features in breast thermograms. Appl Soft Comput 20:112–118

    Article  Google Scholar 

  46. Krawczyk B, Schaefer G, Woźniak M (2015) A hybrid cost-sensitive ensemble for imbalanced breast thermogram classification. Artif Intell Med 65(3):219–227

    Article  Google Scholar 

  47. Ozdemir A, Ozdemir H, Maral I, Konus O, Yucel S, Isik S (2001) Differential diagnosis of solid breast lesions: contribution of Doppler studies to mammography and gray scale imaging. J Ultrasound Med 20(10):1091–1101

    Article  Google Scholar 

  48. Cho N, Jang M, Lyou CY, Park JS, Choi HY, Moon WK (2012) Distinguishing benign from malignant masses at breast US: combined US elastography and color Doppler US—Influence on radiologist accuracy. Radiology 262(1):80–90

    Article  Google Scholar 

  49. Berg WA, Cosgrove DO, Doré CJ, Schäfer FKW, Svensson WE, Hooley RJ, Ohlinger R, Mendelson EB, Balu-Maestro C, Locatelli M, Tourasse C, Cavanaugh BC, Juhan V, Stavros AT, Tardivon A, Gay J, Henry JP, Cohen-Bacrie C (2012) Shear-wave elastography improves the specificity of breast US: the BE1 multinational study of 939 masses. Radiology 262(2):435–449

    Article  Google Scholar 

  50. Krawczyk B, Filipczuk P (2014) Cytological image analysis with firefly nuclei detection and hybrid one-class classification decomposition. Eng Appl Artif Intell 31:126–135

    Article  Google Scholar 

  51. Filipczuk P, Krawczyk B, Woźniak M (2013) Classifier ensemble for an effective cytological image analysis. Pattern Recognit Lett 34(14):1748–1757

    Article  Google Scholar 

  52. Krawczyk B, Galar M, Jeleń Ł, Herrera F (2016) Evolutionary undersampling boosting for imbalanced classification of breast cancer malignancy. Appl Soft Comput 38:714–726

    Article  Google Scholar 

  53. Kass M, Witkin A, Terzopoulos D (1988) Snakes: active contour models. Int J Comput Vis 1(4):321–331

    Article  MATH  Google Scholar 

  54. Ji Z, Xia Y, Sun Q, Cao G, Chen Q (2015) Active contours driven by local likelihood image fitting energy for image segmentation. Inf Sci 301:285–304

    Article  Google Scholar 

  55. Xu C, Prince JL (1998) Snakes, shapes, and gradient vector flow. IEEE Trans Image Process 7(3):359–369

    Article  MathSciNet  MATH  Google Scholar 

  56. Xu C, Prince JL (1998) Generalized gradient vector flow external forces for active contours. Sig Process 71(2):131–139

    Article  MATH  Google Scholar 

  57. Tang J (2009) A multi-direction GVF snake for the segmentation of skin cancer images. Pattern Recognit 42(6):1172–1179

    Article  Google Scholar 

  58. Wei M, Zhou Y, Wan M (2004) A fast snake model based on non-linear diffusion for medical image segmentation. Comput Med Imaging Graph 28(3):109–117

    Article  Google Scholar 

  59. Li B, Acton ST (2007) Active contour external force using vector field convolution for image segmentation. IEEE Trans Image Process 16(8):2096–2106

    Article  MathSciNet  Google Scholar 

  60. Hsu CY, Chen SH, Wang KL (2003) Active contour model with a novel image force field. In: Proceeding of the conference CVGIP-2003, Taiwan, pp. 477–483

  61. Hsu CY, Liu CY, Chen CM (2008) Automatic segmentation of liver PET images. Comput Med Imaging Graph 32(7):601–610

    Article  Google Scholar 

  62. Li C, Liu J, Fox MD (2005) Segmentation of external force field for automatic initialization and splitting of snakes. Pattern Recognit 38(11):1947–1960

    Article  Google Scholar 

  63. Cheng J, Foo SW (2006) Dynamic directional gradient vector flow for snakes. IEEE Trans Image Process 15(6):1563–1571

    Article  Google Scholar 

  64. Jifeng N, Chengke W, Shigang L, Shuqin Y (2007) NGVF: an improved external force field for active contour model. Pattern Recognit Lett 28(1):58–63

    Article  Google Scholar 

  65. Zhu G, Zhang S, Zeng Q, Wang C (2010) Gradient vector flow active contours with prior directional information. Pattern Recognit Lett 31(9):845–856

    Article  Google Scholar 

  66. Wu Y, Wang Y, Jia Y (2013) Adaptive diffusion flow active contours for image segmentation. Comput Vis Image Underst 117(10):1421–1435

    Article  Google Scholar 

  67. Rodtook A, Makhanov SS (2013) Multi-feature gradient vector flow snakes for adaptive segmentation of the ultrasound images of breast cancer. J Vis Commun Image Represent 24(8):1414–1430

    Article  Google Scholar 

  68. Li Q, Deng T, Xie W (2016) Active contours driven by divergence of gradient vector flow. Sig Process 120:185–199

    Article  Google Scholar 

  69. Malladi R, Sethian J, Vemuri B (1995) Shape modeling with front propagation. IEEE Trans Pattern Anal Mach Intell 17(2):158–171

    Article  Google Scholar 

  70. Osher S, Sethian JA (1988) Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulation. J Comput Phys 79:12–49

    Article  MathSciNet  MATH  Google Scholar 

  71. Caselles V, Kimmel R, Sapiro G (1997) Geodesic active contours. Int J Comput Vis 22(1):61–79

    Article  MATH  Google Scholar 

  72. Siddiqi K, Lauzie`re YB, Tannenbaum A, Zucker SW (1998) Area and length minimizing flows for shape segmentation. IEEE Trans Image Process 7(3):433–443

    Article  Google Scholar 

  73. Wang X, He L, Wee WG (2004) Deformable contour method: a constrained optimization approach. Int J Comput Vis 59(1):87–108

    Article  Google Scholar 

  74. He L, Peng Z, Everding B, Wang X, Han CY, Weiss KL, Wee WG (2008) A comparative study of deformable contour methods on medical image segmentation. Image Vis Comput 26:141–163

    Article  Google Scholar 

  75. Xu C, Pham D, Prince J (2000) Image segmentation using deformable models, In: Beutel JM, Fitzpatrick JM (eds) Handbook of Medical Imaging vol 2: Medical Image Processing and Analysis. SPIE Press, Bellingham, Washington, USA pp. 129–174

  76. McInerney T, Terzopoulos D (2000) T-snakes: topology adaptive snakes. Med Image Anal 4(2):73–91

    Article  Google Scholar 

  77. Shih FY, Zhang K (2007) Locating object contours in complex background using improved snakes. Comput Vis Image Underst 105:93–98

    Article  Google Scholar 

  78. Mille J (2009) Narrow band region-based active contours and surfaces for 2d and 3d segmentation. Comput Vis Image Underst 113:946–965

    Article  Google Scholar 

  79. Cohen LD, Cohen I (1993) Finite-element methods for active contour models and balloons for 2-D and 3-D images. IEEE Trans Pattern Anal Mach Intell 15(11):1131–1147

    Article  Google Scholar 

  80. Cohen LD (1991) On active contour models and balloons. CVGIP: Image Understanding 53(2):211–218

    Article  MathSciNet  MATH  Google Scholar 

  81. Zhu SC, Yuille A (1996) Region competition: unifying snakes, region growing, and Bayes/MDL for multiband image segmentation. IEEE Trans Pattern Anal Mach Intell 18:884–900

    Article  Google Scholar 

  82. Shang Y, Yang X, Zhu L, Deklerck R, Nyssen E (2008) Region competition based active contour for medical object extraction. Comput Med Imaging Graph 32(2):109–117

    Article  Google Scholar 

  83. Fenster SD, Kender JR (2001) Sectored snakes: evaluating learned energy segmentations. IEEE Trans Pattern Anal Mach Intell 23(9):1028–1034

    Article  Google Scholar 

  84. Fenster A, Tong S, Cardinal HN, Blake C, Downey DB (1998) Three-dimensional ultrasound imaging system for prostate cancer diagnosis and treatment. IEEE Trans Instrum Meas 47(6):1439–1447

    Article  Google Scholar 

  85. Jumaat AK, Wan Abdul Rahman WEZ, Ibrahim A, Mahmud R (2010) Segmentation of masses from breast ultrasound images using parametric active contour algorithm. Procedia—Social and Behavioral Sciences 8:640–647

    Article  Google Scholar 

  86. Cvancarova M, Albresgtsen F, Brabrand K, Samset E (2005) Segmentation of ultrasound images of liver tumors applying snake algorithms and GVF. Congr Ser 1281:218–223

    Article  Google Scholar 

  87. Alemán-Flores M, Alemán-Flores P, Álvarez-León L, Esteban-Sánchez MB, Fuentes-Pavón R, Santana-Montesdeoca JM (2005) Computerized ultrasound characterization of breast tumors. Int Congr Ser 1281:1063–1068

    Article  Google Scholar 

  88. Hamarneh G, Gustavsson T (2000) Combining snakes and active shape models for segmenting the human left ventricle in echocardiographic images. In: Computers in cardiology, Cambridge, MA, pp. 115–118

  89. Chen CM, Lu HHS, Lin YC (2000) An early vision-based snake model for ultrasound image segmentation. Ultrasound Med Biol 26(2):273–285

    Article  Google Scholar 

  90. Mignotte M, Meunier J (2001) A multiscale optimization approach for the dynamic contour-based boundary detection issue. Comput Med Imaging Graph 25(3):265–275

    Article  Google Scholar 

  91. Rodtook A, Makhanov SS (2010) Continuous force field analysis for generalized gradient vector flow field. Pattern Recognit 43(10):3522–3538

    Article  MATH  Google Scholar 

  92. Ma Z, Tavares JMRS, Jorge RMN, Mascarenhas T (2010) A review of algorithms for medical image segmentation and their applications to the female pelvic cavity. Comput Methods Biomech Biomed Eng Imaging Vis 13(2):235–246

    Article  Google Scholar 

  93. Ma Z, Jorge RMN, Mascarenhas T, Tavares JMRS (2011) Novel approach to segment the inner and outer boundaries of the bladder wall in T2-weighted magnetic resonance images. Ann Biomed Eng 39(8):2287–2297

    Article  Google Scholar 

  94. Ma Z, Jorge RMN, Mascarenhas T, Tavares JMRS (2013) Segmentation of female pelvic organs in axial magnetic resonance images using coupled geometric deformable models. Comput Biol Med 43(4):248–258

    Article  Google Scholar 

  95. Rochery M, Jermyn IH, Zerubia J (2006) Higher order active contours. Int J Comput Vis 69:27–42

    Article  Google Scholar 

  96. Tauber C, Batatia H, Ayache A (2010) Quasi-automatic initialization for parametric active contours. Pattern Recognit Lett 31(1):83–90

    Article  Google Scholar 

  97. Tauber C, Batatia H, Ayache A (2005) A general Quasi-automatic initialization for Snakes: application to ultrasound images. In: Proceedings of international conference on image processing, pp. 806-809

  98. Xingfei G, Jie T (2002) An automatic active contour model for multiple objects. In: Proceedings of international conference on pattern recognition, 2, pp. 881–884

  99. Hsua CY, Wang HF, Wang HC, Tseng KK (2012) Automatic extraction of face contours in images and videos. Future Gener Comput Syst 28:322–335

    Article  Google Scholar 

  100. Veronesea E, Stramarec R, Campiona A, Raffeinerb B, Beltramec V, Scagliori E, Coranc A, Ciprianb L, Fioccob U, Grisana E (2013) Improved detection of synovial boundaries in ultrasound examination by using a cascade of active-contours. Med Eng Phys 35:188–194

    Article  Google Scholar 

  101. Doshi DJ, March DE, Crisi GM, Coughlin BF (2007) Complex cystic breast masses: diagnostic approach and imaging-pathologic correlation. Radiographics 27:53–64

    Article  Google Scholar 

  102. Jung IS, Thapa D, Wang GN (2005) Automatic segmentation and diagnosis of breast lesions using morphology method based on ultrasound. In: Wang L, Jin Y (ed) Proceedings of international conference on fuzzy systems and knowledge discovery (FSKD), LNAI 3614, pp. 1079–1088

  103. Selvan S, Shenbagadevi S (2015) Automatic seed point selection in ultrasound echography images of breast using texture features. Biocybern Biomed Eng 35(3):157–168

    Article  Google Scholar 

  104. Fergani K, Lui D, Scharfenberger C, Wong A, Clausi DA (2014) Hybrid structural and texture distinctiveness vector field convolution for region segmentation. Comput Vis Image Underst 125:85–96

    Article  Google Scholar 

  105. Liu S, Peng Y (2012) A local region-based Chan-Vese model for image segmentation. Pattern Recognit 45:2769–2779

    Article  MATH  Google Scholar 

  106. Akgul YS, Kambhamettu C, Stone M (1998) Extraction and tracking of the tongue surface from ultrasound image sequences. In: Proceedings of IEEE Computer Society conference computer vision and pattern recognition, pp. 298–303.

  107. Cohen I, Herlin I (1995) A motion computation and interpretation framework for oceanographic satellite images. In: Proceedings of international symposium computer vision, pp. 13–18

  108. Cohen I, Herlin I, Rocquencourt I (1996) Optical flow and phase portrait methods for environmental satellite image sequences. In: Proceedings of the 4th European conference on computer vision 2, pp. 141–150.

  109. Li J, Yau WY, Wang H (2008) Combining singular points and orientation image information for fingerprint classification. Pattern Recognit 41:353–366

    Article  MATH  Google Scholar 

  110. Li J, Yau WY, Wang H (2006) Constrained nonlinear models of fingerprint orientations with prediction. Pattern Recognit 39:102–114

    Article  Google Scholar 

  111. Shu CF, Jain RC (1994) Vector field analysis for oriented patterns. IEEE Trans Pattern Anal Mach Intell 16:946–950

    Article  Google Scholar 

  112. Tian X, Samarasinghe S, Murphy G (1999) An integrated algorithm for detecting position and size of knots on logs using texture analysis. In: Proceedings of conference on image and visions computing, pp. 121–132

  113. Yau WY, Li J, Wang H (2004) Nonlinear phase portrait modeling of fingerprint orientation. In: Proceedings of international conference on control, automation, robotics and vision (ICARCV2004 8th), pp. 1262–1267.

  114. Rangayyan R, Ayres F (2006) Gabor filters and phase portraits for the detection of architectural distortion in mammograms. Med Biol Eng Comput 44:883–894

    Article  Google Scholar 

  115. Jordan D, Smith P (2007) Nonlinear ordinary differential equations: An introduction for scientists and engineers, 4th edn. Oxford University Press, Oxford

    MATH  Google Scholar 

  116. Chucherd S, Rodtook A, Makhanov SS (2010) Phase portrait analysis for multiresolution generalized gradient vector flow. IEICE Trans Inf Syst E93-D:2822–2835

    Article  Google Scholar 

  117. Ngoi KP, Jia JC (1999) An active contour model for colour region extraction in natural scenes. Image Vis Comput 17(13):955–966

    Article  Google Scholar 

  118. Choi W, Lam K, Siu W (2001) An adaptive active contour model for highly irregular boundaries. Pattern Recognit 34:323–331

    Article  MATH  Google Scholar 

  119. Nakaguro Y, Dailey MN, Marukatat S, Makhanov SS (2013) Defeating line-noise CAPTCHAs with multiple quadratic snakes. Comput Secur 37:91–110

    Article  Google Scholar 

  120. Jain AK, Zhong Y, Lakshmanan S (1996) Object matching using deformable templates. IEEE Trans Pattern Anal Mach Intell 18:267–278

    Article  Google Scholar 

Download references

Acknowledgments

This research is sponsored by Thailand Research Fund grant BRG5780012.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Stanislav S. Makhanov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kirimasthong, K., Rodtook, A., Chaumrattanakul, U. et al. Phase portrait analysis for automatic initialization of multiple snakes for segmentation of the ultrasound images of breast cancer. Pattern Anal Applic 20, 239–251 (2017). https://doi.org/10.1007/s10044-016-0556-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10044-016-0556-9

Keywords

Navigation