Anisotropic Scale Selection, Robust Gaussian Fitting, and Pulmonary Nodule Segmentation in Chest CT Scans

  • Kazunori OkadaEmail author


This chapter presents the theory and design principles used to derive semiautomatic algorithms for pulmonary nodule segmentation toward realizing a reliable and reproducible clinical application for nodule volumetry. The proposed algorithms are designed to be robust against the variabilities due to (1) user-interactions for algorithm initialization, (2) attached or adjacent nontarget structures, and (3) nonstandard shape and appearance. The proposed theory offers an elegant framework to introduce the robust data analysis techniques into a solution for nodule segmentation in chest X-ray computed tomography (CT) scans. The theory combines two distinct concepts for generic data analysis: automatic scale selection and robust Gaussian model fitting. The unification is achieved by (1) relating Lindeberg’s scale selection theory in Gaussian scale-space (Int J Comput Vis 30(2):79–116, 1998; Scale-space theory in computer vision Kluwer Academic Publishers, 1994) to Comaniciu’s robust feature space analyses with mean shift in Gaussian kernel density estimation (KDE) (IEEE Trans Pattern Anal Mach Intell 25(2):281–288, 2003; IEEE Trans Pattern Anal Mach Intell 24(5):603–619, 2002) and (2) extending both approaches to consider anisotropic scale from their original isotropic formulations. This chapter demonstrates how the resulting novel concept of anisotropic scale selection gives a useful and robust solution to the Gaussian fitting problem used as a part of our robust nodule segmentation solutions.


Segmentation Pulmonary nodules Chest CT Automatic scale selection Anisotropic scale-space Gaussian scale-space Gaussian fitting Robust estimation Mean shift Scale-space mean shift 



The author wishes to thank Dorin Comaniciu, Visvanathan Ramesh, and Arun Krishnan for their support and stimulating discussions.


  1. 1.
    Almansa A, Lindeberg T (2000) Fingerprint enhancement by shape adaptation of scale-space operators with automatic scale selection. IEEE Trans Image Process 9:2027–2042PubMedCrossRefGoogle Scholar
  2. 2.
    Armato SG III, Li F, Giger ML, MacMahon H, Sone S, Doi K (2002) Lung cancer: performance of automated lung nodule detection applied to cancers missed in a CT screening program. Radiology 225:685–693PubMedCrossRefGoogle Scholar
  3. 3.
    Ashraf H, de Hoop B, Shaker SB, Dirksen A, Back KS, Hansen H, Prokop M, Pedersen JH (2010) Lung nodule volumetry: segmentation algorithms within the same software package cannot be used interchangeably. Eur Radiol 20:1878–1885PubMedCrossRefGoogle Scholar
  4. 4.
    Bhalerao A, Wilson R (2001) Estimating local and global structure using a Gaussian intensity model. Presented at the Medical Image Understanding and Analysis, Birmingham, U.K.Google Scholar
  5. 5.
    Bi J, Periaswamy S, Okada K, Kubota T, Fung G, Salganicoff M, Rao RB (2006) Computer aided detection via asymmetric cascade of sparse hyperplane classifiers. ACM SIGKDD, pp 837–844Google Scholar
  6. 6.
    Bigun J, Granlund GH, Wiklund J (1991) Multidimensional orientation estimation with applications to texture analysis and optical flow. IEEE Trans Pattern Anal Mach Intell 13:775–790CrossRefGoogle Scholar
  7. 7.
    Black MJ, Sapiro G, Marimont D, Heeger D (1998) Robust anisotropic diffusion. IEEE Trans Image Process 7:421–432PubMedCrossRefGoogle Scholar
  8. 8.
    Brown MS, McNitt-Gray MF, Goldin JG, Suh RD, Sayre JW, Aberle DR (2001) Patient-specific models for lung nodule detection and surveillance in CT images. IEEE Trans Med Imaging 20:1242–1250PubMedCrossRefGoogle Scholar
  9. 9.
    Cardinale L, Ardissone F, Novello S, Busso M, Solitro F, Longo M, Sardo D, Giors M, Fava C (2009) The pulmonary nodule: clinical and radiological characteristics affecting a diagnosis of malignancy. Radiol Med 114:871–889PubMedCrossRefGoogle Scholar
  10. 10.
    Chen Y, McInroy JE (2002) Estimating symmetric, positive definite matrices in robotic control. IEEE International Conference on Robotics and Automation, Washington, D.C., pp 4269–4274Google Scholar
  11. 11.
    Cheng Y (1995) Mean shift, mode seeking, and clustering. IEEE Trans Pattern Anal Mach Intell 17(8):790–799CrossRefGoogle Scholar
  12. 12.
    Collins RT (2003) Mean-shift blob tracking through scale space. IEEE Conference on Computer Vision and Pattern Recognition, vol II, pp 234–240Google Scholar
  13. 13.
    Comaniciu D (2003) An algorithm for data-driven bandwidth selection. IEEE Trans Pattern Anal Mach Intell 25(2):281–288CrossRefGoogle Scholar
  14. 14.
    Comaniciu D, Meer P (1999) Mean shift analysis and applications. Proceedings of the IEEE international conference on computer vision, pp 1197–1203Google Scholar
  15. 15.
    Comaniciu D, Meer P (2002) Mean shift: a robust approach toward feature space analysis. IEEE Trans Pattern Anal Mach Intell 24(5):603–619CrossRefGoogle Scholar
  16. 16.
    Comaniciu D, Ramesh V, Meer P (2000) Real-time tracking of non-rigid objects using mean shift. Proceedings of the IEEE conference on computer vision and pattern recognition, pp 142–149Google Scholar
  17. 17.
    Dehmeshki J, Amin H, Valdivieso M, Ye X (2008) Segmentation of pulmonary nodules in thoracic CT scans: a region growing approach. IEEE Trans Med Imaging 27:467–480PubMedCrossRefGoogle Scholar
  18. 18.
    Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc Ser B 39:1–38Google Scholar
  19. 19.
    Diciotti S, Lombardo S, Coppini G, Grassi L, Falchini M, Mascalchi M (2010) The LoG characteristic scale: a consistent measurement of lung nodule size in CT imaging. IEEE Trans Med Imaging 29:397–409PubMedCrossRefGoogle Scholar
  20. 20.
    Diciotti S, Picozzi G, Falchini M, Mascalchi M, Villari N, Valli G (2008) 3-D segmentation algorithm of small lung nodules in spiral CT images. IEEE Trans Inf Tech Biomed 12:7–19CrossRefGoogle Scholar
  21. 21.
    El-Baz A, Farag A, Gimel’farb G, Falk R, El-Ghar MA, Eldiasty TA (2006) Framework for automatic segmentation of lung nodules from low dose chest CT scans. Proceedings of the IARP international conference on pattern recognitionGoogle Scholar
  22. 22.
    Faas FG, van Vliet LJ (2003) 3D-Orientation space; filters and sampling. Scandinavian conference on image analysisGoogle Scholar
  23. 23.
    Farag A, El-Baz A, Gimel’farb G, Falk R, El-Ghar MA, Eldiasty T (2006) Appearance models for robust segmentation of pulmonary nodules in 3D LDCT chest images. Proceedings of the international conference on medical imaging computing and computer-assisted interventionGoogle Scholar
  24. 24.
    Florack LMJ, Ter Haar Romey BM, Koenderink JJ, Viergever MA (1993) Cartesian differential invariants in scale-space. J Math Imaging Vis 3:327–348CrossRefGoogle Scholar
  25. 25.
    Freeman WT, Adelson EH (1991) The design and use of steerable filters. IEEE Trans Pattern Anal Mach Intell 13:891–906CrossRefGoogle Scholar
  26. 26.
    Fukunaga K, Hostetler L (1975) The estimation of the gradient of a density function, with applications in pattern recognition. IEEE Trans Inf Theory 21(1):32–40CrossRefGoogle Scholar
  27. 27.
    Gavrielides MA, Kinnard LM, Myers KJ, Petrick N (2009) Noncalcified lung nodules: volumetric assessment with thoracic CT. Radiology 251:26–37PubMedCrossRefGoogle Scholar
  28. 28.
    Godoy MCB, Naidich DP (2009) Subsolid pulmonary nodules and the spectrum of peripheral adenocarcinomas of the lung: recommended interim guidelines for assessment and management. Radiology 253:606–622PubMedCrossRefGoogle Scholar
  29. 29.
    Goldin JG, Brown MS, Petkovska I (2008) Computer-aided diagnosis in lung nodule assessment. J Thorac Imaging 23:97–104PubMedCrossRefGoogle Scholar
  30. 30.
    Goo JM, Tongdee T, Tongdee R, Yeo K, Hildebolt CF, Bae KT (2005) Volumetric measurement of synthetic lung nodules with multi-detector row CT: effect of various image reconstruction parameters and segmentation thresholds on measurement accuracy. Radiology 235:850–856PubMedCrossRefGoogle Scholar
  31. 31.
    Henschke CI, Yankelevitz DF, Mirtcheva R, McGuinness G, McCauley D, Miettinen OS (2002) CT screening for lung cancer: frequency and significance of part-solid and nonsolid nodules. AJR Am J Roentgenol 178(5):1053–1057PubMedGoogle Scholar
  32. 32.
    van Huffel S, Vandewalle J (1991) The total least squares problem computational aspects and analysis. SIAM, PhiladelphiaGoogle Scholar
  33. 33.
    Jaffe CC (2006) Measures of response: RECIST, WHO, and new alternatives. J Clin Oncol 24:3245–3251PubMedCrossRefGoogle Scholar
  34. 34.
    Jirapatnakul AC, Fotin SV, Reeves AP, Biancardi AM, Yankelevitz DF, Henschke CI (2009) Automated nodule location and size estimation using a multi-scale Laplacian of gaussian filtering approach. Proceedings of the IEEE engineering in medicine and biology societyGoogle Scholar
  35. 35.
    Kanazawa Y, Kanatani K (2001) Do we really have to consider covariance matrices for image features? Proceedings of the IEEE international conference on computer vision, pp 586–591, VancouverGoogle Scholar
  36. 36.
    Kawata Y, Niki N, Ohmatsu H, Kakimuma R, Eguchi K, Kaneko M, Moriyama N (1997) Classification of pulmonary nodules in thin-section CT images based on shape characterization. Proceedings of the IEEE international conference on image processingGoogle Scholar
  37. 37.
    Kawata Y, Niki N, Ohmatsu H, Kakinuma R, Eguchi K, Kaneko M, Moriyama N (1998) Quantitative surface characterization of pulmonary nodules based on thin-section CT images. IEEE Trans Nucl Sci 45:2132–2138CrossRefGoogle Scholar
  38. 38.
    Kim S, Yoon KJ, Kweon IS (2008) Object recognition using a generalized robust invariant feature and Gestalt’s law of proximity and similarity. PR 41:726–741Google Scholar
  39. 39.
    Ko JP (2005) Lung nodule detection and characterization with multi-slice CT. J Thorac Imaging 20:196–209PubMedCrossRefGoogle Scholar
  40. 40.
    Ko JP, Rusinek H, Jacobs EL, Babb JS, Betke M, McGuinness G, Naidich DP (2003) Small pulmonary nodules: volume measurement at chest CT – phantom study. Radiology 228:864–870PubMedCrossRefGoogle Scholar
  41. 41.
    Koenderink JJ (1984) The structure of images. Biol Cybern 50:363–370PubMedCrossRefGoogle Scholar
  42. 42.
    Kostis WJ, Reeves AP, Yankelevitz DF, Henschke CI (2003) Three-dimensional segmentation and growth-rate estimation of small pulmonary nodules in helical CT images. IEEE Trans Med Imaging 22:1259–1274PubMedCrossRefGoogle Scholar
  43. 43.
    Kostis WJ, Yankelevitz DF, Reeves AP, Fluture SC, Henschke CI (2004) Small pulmonary nodules: reproducibility of Three-dimensional volumetric measurement and estimation of time to follow-up CT. Radiology 231:446–452PubMedCrossRefGoogle Scholar
  44. 44.
    Kubota T, Jerebko A,Salganicoff M, Dewan M, Krishnan A (2008) Robust segmentation of pulmonary nodules of various densities: from ground-glass opacities to solid nodules. International workshop on pulmonary image processingGoogle Scholar
  45. 45.
    Kuhnigk JM, Dicken V, Bornemann L, Bakai A, Wormanns D, Krass S, Peitgen HO (2006) Morphological segmentation and partial volume analysis for volumetry of solid pulmonary lesions in thoracic CT scans. IEEE Trans Med Imaging 25:417–434PubMedCrossRefGoogle Scholar
  46. 46.
    Lampert CH, Wirjadi O (2006) An optimal non-orthogonal separation of the anisotropic Gaussian convolution filter. IEEE Trans Image Process 15:3501–3513PubMedCrossRefGoogle Scholar
  47. 47.
    Lee MC, Wiemker R, Boroczky L, Sungur-Stasik K, Cann AD, Borczuk AC, Kawut SM, Powell CA (2008) Impact of segmentation uncertainties on computer-aided diagnosis of pulmonary nodules. Int J Comput Assist Radiol Surg 3:551–558CrossRefGoogle Scholar
  48. 48.
    Lee Y, Hara T, Fujita H, Itoh S, Ishigaki T (2001) Automated detection of pulmonary nodules in helical ct images based on an improved template-matching technique. IEEE Trans Med Imaging 20:595–604PubMedCrossRefGoogle Scholar
  49. 49.
    Li Q (2007) Recent progress in computer-aided diagnosis of lung nodules on thin-section CT. Comput Med Imaging Graph 31:248–257PubMedCrossRefGoogle Scholar
  50. 50.
    Li Q, Li F, Suzuki K, Shiraishi J, Abe H, Engelmann R, Nie Y, MacMahon H, Doi K (2005) Computer-aided diagnosis in thoracic CT. Semin Ultrasound CT MR 26:357–363PubMedCrossRefGoogle Scholar
  51. 51.
    Lin J (1991) Divergence measures based on the Shannon entropy. IEEE Trans Inf Theory 37(1):145–151CrossRefGoogle Scholar
  52. 52.
    Lindeberg T (1998) Feature detection with automatic scale selection. Int J Comput Vis 30(2):79–116CrossRefGoogle Scholar
  53. 53.
    Lindeberg T (1994) Scale-space theory in computer vision. Kluwer Academic Publishers, Norwell, MAGoogle Scholar
  54. 54.
    Lindeberg T, Garding J (1997) Shape-adapted smoothing in estimation of 3-D shape cues from affine distortions of local 2-D brightness structure. Image Vis Comp 15:415–434CrossRefGoogle Scholar
  55. 55.
    Lowe D (2004) Distinctive image features from scale-invariant keypoints. Int J Comput Vis 60:91–110CrossRefGoogle Scholar
  56. 56.
    Malladi R, Sethian JA, Vemuri BC (1995) Shape modeling with front propagation: a level set approach. IEEE Trans Pattern Anal Mach Intell 17:158–175CrossRefGoogle Scholar
  57. 57.
    Manmatha R, Srimal N (1999) Scale space technique for word segmentation in handwritten documents. International conference on scale-space theories in computer visionGoogle Scholar
  58. 58.
    Messay T, Hardie RC, Rogers SK (2010) A new computationally efficient CAD system for pulmonary nodule detection in CT imagery. Med Imag Anal 14:390–406CrossRefGoogle Scholar
  59. 59.
    Mikolajczyk K, Schmid C (2004) Scale & affine invariant interest point detectors. Int J Comput Vis 60:63–86CrossRefGoogle Scholar
  60. 60.
    Min JH, Lee HY, Lee KS, Han J, Park K, Ahn MJ, Lee SJ (2010) Stepwise evolution from a focal pure pulmonary ground-glass opacity nodule into an invasive lung adenocarcinoma: An observation for more than 10 years. Lung Cancer 69:123–126PubMedCrossRefGoogle Scholar
  61. 61.
    Mullally W, Betke M, Wang J, Ko JP (2004) Segmentation of nodules on chest computed tomography for growth assessment. Med Phys 31:839–848PubMedCrossRefGoogle Scholar
  62. 62.
    Nielsen M, Florack L, Deriche R (1997) Regularization, scale space, and edge detection filters. J Math Imaging Vis 7(4):291–307CrossRefGoogle Scholar
  63. 63.
    Ohtsuka T, Nomori H, Horio H, Naruke T, Suemasu K (2003) Radiological examination for peripheral lung cancers and benign nodules less than 10 mm. Lung Cancer 42:291–296PubMedCrossRefGoogle Scholar
  64. 64.
    Okada K, Akdemir U, Krishnan A (2005) Blob segmentation using joint space-intensity likelihood ratio test: application to volumetric tumor characterization. IEEE Conference on Computer Vision and Pattern Recognition, vol II, pp 437–444Google Scholar
  65. 65.
    Okada K, Comaniciu D, Dalal N, Krishnan A (2004) A robust algorithm for characterizing anisotropic local structures. Proceedings of the European conference on computer vision, vol I, pp 549–561Google Scholar
  66. 66.
    Okada K, Comaniciu D, Krishnan A (2004) Robust 3D segmentation of pulmonary nodules in multislice CT images. Proceedings of the international conference on medical imaging computing and computer-assisted intervention, vol II, 881–889Google Scholar
  67. 67.
    Okada K, Comaniciu D, Krishnan A (2005) Robust anisotropic gaussian fitting for volumetric characterization of pulmonary nodules in multislice CT. IEEE Trans Med Imaging 24(3):409–423PubMedCrossRefGoogle Scholar
  68. 68.
    Okada K, Comaniciu D, Krishnan, A (2004) Scale selection for anisotropic scale-space: application to volumetric tumor characterization. Proceedings of the IEEE conference on computer vision and pattern recognition, vol I, pp 594–601Google Scholar
  69. 69.
    Hein PA, Romano VC, Rogalla P, Klessen C, Lembcke A, Bomemann L, Dicken V, Hamm B, Bauknecht HC (2010) Variability of semiautomated lung nodule volumetry on ultralow-dose CT: comparison with nodule volumetry on standard-dose CT. J Digit Imaging 23:8–17PubMedCrossRefGoogle Scholar
  70. 70.
    Perona P, Malik J (1990) Scale-space and edge detection using anisotropic diffusion. IEEE Trans Pattern Anal Mach Intell 12(7):629–639CrossRefGoogle Scholar
  71. 71.
    Reeves AP, Biancardi AM, Apanasovich TV, Meyer CR, MacMahon H, van Beek EJR, Kazerooni EA, Yankelevitz D, McNitt-Gray MF, McLennan G, Armato SG III, Henschke CI, Aberle DR, Croft BY, Clarke LP (2007) The Lung Image Database Consortium (LIDC): a comparison of different size metrics for pulmonary nodule measurements. Acad Radiol 14:1475–1485PubMedCrossRefGoogle Scholar
  72. 72.
    Reeves AP, Chan AB, Yankelevitz DF, Henschke CI, Kressler B, Kostis WJ (2006) On measuring the change in size of pulmonary nodules. IEEE Trans Med Imaging 25:435–450PubMedCrossRefGoogle Scholar
  73. 73.
    Rinaldi MF, Bartalena T, Braccaioli L, Sverzellati N, Mattioli S, Rimondi E, Rossi G, Zompatori M, Battista G, Canini R (2010) Three-dimensional analysis of pulmonary nodules: variability of semiautomated volume measurements between different versions of the same software. Radiol Med 115:403–412PubMedCrossRefGoogle Scholar
  74. 74.
    Rousseeuw PJ, Leroy AM (1987) Robust regression and outlier detection. Wiley, New YorkCrossRefGoogle Scholar
  75. 75.
    Sluimer I, Schilham A, Prokop M, van Ginneken B (2006) Computer analysis of computed tomography scans of the lung: a survey. IEEE Trans Med Imaging 25:385–405PubMedCrossRefGoogle Scholar
  76. 76.
    American Cancer Society (2009) Cancer facts & figures 2009. American Cancer Society, AtlantaGoogle Scholar
  77. 77.
    Sone S, Tsushima K, Yoshida K, Hamanaka K, Hanaoka T, Kondo R (2010) Pulmonary nodules: preliminary experience with semiautomated volumetric evaluation by CT stratum. Acad Radiol 17:900–911PubMedCrossRefGoogle Scholar
  78. 78.
    Sporring J, Nielsen M, Florack LMJ, Johansen P (1997) Gaussian scale-space theory. SpringerGoogle Scholar
  79. 79.
    Suzuki K, Li F, Sone S, Doi K (2005) Computer-aided diagnostic scheme for distinction between benign and malignant nodules in thoracic low-dose ct by use of massive training artificial neural network. IEEE Trans Med Imaging 24:1138–1150PubMedCrossRefGoogle Scholar
  80. 80.
    Wand MP, Jones MC (1995) Kernel smoothing. Chapman & Hall, LondonGoogle Scholar
  81. 81.
    Wang J, Engelmann R, Li Q (2007) Segmentation of pulmonary nodules in three-dimensional CT images by use of a spiral-scanning technique. Med Phys 34:4678–4689PubMedCrossRefGoogle Scholar
  82. 82.
    Witkin A (1983) Scale-space filtering. International joint conference on artificial intelligence, pp 1019–1021, KarlsruheGoogle Scholar
  83. 83.
    Wormanns D, Kohl G, Klotz E, Marheine A, Beyer F, Heindel W, Diederich S (2004) Volumetric measurements of pulmonary nodules at multi-row detector CT: in vivo reproducibility. Chest 14:86–92Google Scholar
  84. 84.
    Yankelevitz DF, Reeves AP, Kostis WJ, Zhao B, Henschke CI (2000) Small pulmonary nodules: volumetrically determined growth rates based on CT evaluation. Radiology 217:251–256PubMedGoogle Scholar
  85. 85.
    Zhao B, Reeves AP, Yankelevitz DF, Henschke CI (1999) Three-dimensional multicriterion automatic segmentation of pulmonary nodules of helical computed tomography images. Opt Eng 38:1340–1347CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Computer ScienceSan Francisco State UniversitySan FranciscoUSA

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