Acta Geotechnica

, Volume 14, Issue 1, pp 1–18 | Cite as

Reconstructing granular particles from X-ray computed tomography using the TWS machine learning tool and the level set method

  • Zhengshou Lai
  • Qiushi ChenEmail author
Research Paper


X-ray computed tomography (CT) has emerged as the most prevalent technique to obtain three-dimensional morphological information of granular geomaterials. A key challenge in using the X-ray CT technique is to faithfully reconstruct particle morphology based on the discretized pixel information of CT images. In this work, a novel framework based on the machine learning technique and the level set method is proposed to segment CT images and reconstruct particles of granular geomaterials. Within this framework, a feature-based machine learning technique termed Trainable Weka Segmentation is utilized for CT image segmentation, i.e., to classify material phases and to segregate particles in contact. This is a fundamentally different approach in that it predicts segmentation results based on a trained classifier model that implicitly includes image features and regression functions. Subsequently, an edge-based level set method is applied to approach an accurate characterization of the particle shape. The proposed framework is applied to reconstruct three-dimensional realistic particle shapes of the Mojave Mars Simulant. Quantitative accuracy analysis shows that the proposed framework exhibits superior performance over the conventional watershed-based method in terms of both the pixel-based classification accuracy and the particle-based segmentation accuracy. Using the reconstructed realistic particles, the particle-size distribution is obtained and validated against experiment sieve analysis. Quantitative morphology analysis is also performed, showing promising potentials of the proposed framework in characterizing granular geomaterials.


3D particle morphology Level set Machine learning Shape reconstruction X-ray computed tomography 



The authors would like to acknowledge the financial support provided by the NASA SC Space Consortium Grant (No. NNX15AL49H).


  1. 1.
    Al-Kofahi Y, Lassoued W, Lee W, Roysam B (2010) Improved automatic detection and segmentation of cell nuclei in histopathology images. IEEE Trans Biomed Eng 57(4):841–852Google Scholar
  2. 2.
    Andò E, Viggiani G, Hall S, Desrues J (2013) Experimental micro-mechanics of granular media studied by X-ray tomography: recent results and challenges. Géotech Lett 3(3):142–146Google Scholar
  3. 3.
    Andrade J, Vlahinić I, Lim K, Jerves A (2012) Multiscale ‘tomography-to-simulation’ framework for granular matter: the road ahead. Géotech Lett 2(3):135–139Google Scholar
  4. 4.
    Arganda-Carreras I, Kaynig V, Rueden C, Eliceiri K, Schindelin J, Cardona A, Sebastian Seung H (2017) Trainable Weka Segmentation: a machine learning tool for microscopy pixel classification. Bioinformatics 33(15):2424–2426Google Scholar
  5. 5.
    Arganda-Carreras I, Turaga S, Berger D, Cireşan D, Giusti A, Gambardella L, Schmidhuber J, Laptev D, Dwivedi S, Buhmann J et al (2015) Crowdsourcing the creation of image segmentation algorithms for connectomics. Front Neuroanat 9(14):1–13Google Scholar
  6. 6.
    Aubert G, Kornprobst P (2006) Mathematical problems in image processing: partial differential equations and the calculus of variations, vol 147, 2nd edn. Springer, BerlinzbMATHGoogle Scholar
  7. 7.
    Avendi M, Kheradvar A, Jafarkhani H (2016) A combined deep-learning and deformable-model approach to fully automatic segmentation of the left ventricle in cardiac MRI. Med Image Anal 30:108–119Google Scholar
  8. 8.
    Blott S, Pye K (2008) Particle shape: a review and new methods of characterization and classification. Sedimentology 55(1):31–63Google Scholar
  9. 9.
    Bruchon J, Pereira J, Vandamme M, Lenoir N, Delage P, Bornert M (2013) Full 3D investigation and characterisation of capillary collapse of a loose unsaturated sand using X-ray CT. Granul Matter 15(6):783–800Google Scholar
  10. 10.
    Cheng L, Cord-Ruwisch R, Shahin M (2013) Cementation of sand soil by microbially induced calcite precipitation at various degrees of saturation. Can Geotech J 50(1):81–90Google Scholar
  11. 11.
    Colombo A, Cusano C, Schettini R (2006) 3d face detection using curvature analysis. Pattern Recognit 39(3):444–455zbMATHGoogle Scholar
  12. 12.
    Cox M, Budhu M (2008) A practical approach to grain shape quantification. Eng Geol 96(1):1–16Google Scholar
  13. 13.
    Cundall P, Strack O (1979) A discrete numerical model for granular assemblies. Géotechnique 29(1):47–65Google Scholar
  14. 14.
    Dadda A, Geindreau C, Emeriault F, du Roscoat S, Garandet A, Sapin L, Filet A (2017) Characterization of microstructural and physical properties changes in biocemented sand using 3D X-ray microtomography. Acta Geotech 12(5):955–970Google Scholar
  15. 15.
    DeJong J, Soga K, Kavazanjian E, Burns S, Van Paassen L, Al Qabany A, Aydilek A, Bang S, Burbank M, Caslake L et al (2013) Biogeochemical processes and geotechnical applications: progress, opportunities and challenges. Géotechnique 63(4):287–301Google Scholar
  16. 16.
    Desrues J, Viggiani G, Besuelle P (2010) Advances in X-ray tomography for geomaterials, vol 118. Wiley, LondonGoogle Scholar
  17. 17.
    Ersoy A, Waller M (1995) Textural characterisation of rocks. Eng Geol 39(3–4):123–136Google Scholar
  18. 18.
    Fernández-Delgado M, Cernadas E, Barro S, Amorim D (2014) Do we need hundreds of classifiers to solve real world classification problems. J Mach Learn Res 15(1):3133–3181MathSciNetzbMATHGoogle Scholar
  19. 19.
    Gao H, Chae O (2010) Individual tooth segmentation from CT images using level set method with shape and intensity prior. Pattern Recognit 43(7):2406–2417Google Scholar
  20. 20.
    Garboczi E (2011) Three dimensional shape analysis of JSC-1A simulated Lunar regolith particles. Powder Technol 207(1):96–103Google Scholar
  21. 21.
    Gibson S (1998) Constrained elastic surface nets: generating smooth surfaces from binary segmented data. In: Wells W, Colchester A, Delp S (eds) Medical image computing and computer-assisted intervention-MICCAI’98, vol 1496. Springer, Berlin, pp 888–898Google Scholar
  22. 22.
    Gilkes R, Suddhiprakarn A (1979) Biotite alteration in deeply weathered granite. I. Morphological, mineralogical, and chemical properties. Clays Clay Miner 27(5):349–360Google Scholar
  23. 23.
    Gleaton J, Xiao R, Lai Z, McDaniel N, Johnstone C, Burden B, Chen Q, Zheng Y (2018) Biocementation of martian regolith simulant with in-situ resources. In: Proceedings of the 2018 ASCE Earth and Space: engineering for extreme environments conference. ASCEGoogle Scholar
  24. 24.
    Guo P, Su X (2007) Shear strength, interparticle locking, and dilatancy of granular materials. Can Geotech J 44(5):579–591Google Scholar
  25. 25.
    Hall M, Frank E, Holmes G, Pfahringer B, Reutemann P, Witten IH (2009) The weka data mining software: an update. ACM SIGKDD Explor Newsl 11(1):10–18Google Scholar
  26. 26.
    Hashemi M, Khaddour G, François B, Massart T, Salager S (2014) A tomographic imagery segmentation methodology for three-phase geomaterials based on simultaneous region growing. Acta Geotech 9(5):831–846Google Scholar
  27. 27.
    Hentschel M, Page N (2003) Selection of descriptors for particle shape characterization. Particle Particle Syst Charact 20(1):25–38Google Scholar
  28. 28.
    Hobson D, Carter R, Yan Y (2009) Rule based concave curvature segmentation for touching rice grains in binary digital images. In: 2009 IEEE instrumentation and measurement technology conference, pp 1685–1689. IEEEGoogle Scholar
  29. 29.
    Jaccard N (2015) Development of an image processing method for automated, non-invasive and scale-independent monitoring of adherent cell cultures. PhD thesis, University College LondonGoogle Scholar
  30. 30.
    Ketcham R, Carlson W (2001) Acquisition, optimization and interpretation of X-ray computed tomographic imagery: applications to the geosciences. Comput Geosci 27(4):381–400Google Scholar
  31. 31.
    Lai Z, Chen Q (2017) Characterization and discrete element simulation of grading and shape-dependent behavior of JSC-1A Martian regolith simulant. Granul Matter 19(4):69Google Scholar
  32. 32.
    Li C, Xu C, Gui C, Fox M (2010) Distance regularized level set evolution and its application to image segmentation. IEEE Trans Image Process 19(12):3243–3254MathSciNetzbMATHGoogle Scholar
  33. 33.
    Li C, Xu C, Gui C, Fox MD (2005) Level set evolution without re-initialization: a new variational formulation. In: IEEE Computer Society conference on computer vision and pattern recognition, 2005. CVPR 2005, vol 1, pp. 430–436. IEEEGoogle Scholar
  34. 34.
    Liu Y, Captur G, Moon J, Guo S, Yang X, Zhang S, Li C (2016) Distance regularized two level sets for segmentation of left and right ventricles from cine-MRI. Magn Reson Imaging 34(5):699–706Google Scholar
  35. 35.
    Lombardot B (2017) Interactive H-Watershed. Accessed 30 Apr 2018
  36. 36.
    Lorensen W, Cline H (1987) Marching cubes: a high resolution 3D surface construction algorithm. In: Proceedings of the 14th annual conference on computer graphics and interactive techniques, SIGGRAPH ’87, New York, USA. ACM, pp 163–169Google Scholar
  37. 37.
    Luerkens D, Beddow J, Vetter A (1982) Morphological fourier descriptors. Powder Technol 31(2):209–215Google Scholar
  38. 38.
    Madra A, El Hajj N, Benzeggagh M (2014) X-ray microtomography applications for quantitative and qualitative analysis of porosity in woven glass fiber reinforced thermoplastic. Compos Sci Technol 95:50–58Google Scholar
  39. 39.
    Matsushima T, Katagiri J, Uesugi K, Tsuchiyama A, Nakano T (2009) 3D shape characterization and image-based DEM simulation of the lunar soil simulant FJS-1. J Aerosp Eng 22(1):15–23Google Scholar
  40. 40.
    Meijering E (2012) Cell segmentation: 50 years down the road [life sciences]. IEEE Signal Process Mag 29(5):140–145Google Scholar
  41. 41.
    Mollon G, Zhao J (2013) Generating realistic 3D sand particles using Fourier descriptors. Granul Matter 15(1):95–108Google Scholar
  42. 42.
    Osher S, Sethian J (1988) Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations. J Comput Phys 79(1):12–49MathSciNetzbMATHGoogle Scholar
  43. 43.
    Papoulis D, Tsolis-Katagas P, Katagas C (2004) Progressive stages in the formation of kaolin minerals of different morphologies in the weathering of plagioclase. Clays Clay Miner 52(3):275–286Google Scholar
  44. 44.
    Peters G, Abbey W, Bearman G, Mungas G, Smith J, Anderson R, Douglas S, Beegle L (2008) Mojave Mars simulant—characterization of a new geologic Mars analog. Icarus 197(2):470–479Google Scholar
  45. 45.
    Powers M (1953) A new roundness scale for sedimentary particles. J Sediment Res 23(2):117–119Google Scholar
  46. 46.
    Quinlan J (1986) Induction of decision trees. Mach Learn 1(1):81–106Google Scholar
  47. 47.
    Santamarina J, Cho G (2004) Soil behaviour: the role of particle shape. In: Advances in geotechnical engineering: the Skempton conference, vol 1. Thomas Telford, London, pp 604–617Google Scholar
  48. 48.
    Semnani SJ, Borja RI (2017) Quantifying the heterogeneity of shale through statistical combination of imaging across scales. Acta Geotech 12(6):1193–1205Google Scholar
  49. 49.
    Sezgin M, Sankur B (2004) Survey over image thresholding techniques and quantitative performance evaluation. J Electron Imaging 13(1):146–168Google Scholar
  50. 50.
    Sleutel S, Cnudde V, Masschaele B, Vlassenbroek J, Dierick M, Van Hoorebeke L, Jacobs P, De Neve S (2008) Comparison of different nano-and micro-focus X-ray computed tomography set-ups for the visualization of the soil microstructure and soil organic matter. Comput Geosci 34(8):931–938Google Scholar
  51. 51.
    Sommer C, Gerlich D (2013) Machine learning in cell biology-teaching computers to recognize phenotypes. J Cell Sci 126(24):5529–5539Google Scholar
  52. 52.
    Stark N, Hay A, Cheel R, Lake C (2014) The impact of particle shape on the angle of internal friction and the implications for sediment dynamics at a steep, mixed sand–gravel beach. Earth Surf Dyn 2(2):469–480Google Scholar
  53. 53.
    Sun W, Andrade JE, Rudnicki JW (2011a) Multiscale method for characterization of porous microstructures and their impact on macroscopic effective permeability. Int J Numer Methods Eng 88(12):1260–1279MathSciNetzbMATHGoogle Scholar
  54. 54.
    Sun W, Andrade JE, Rudnicki JW, Eichhubl P (2011b) Connecting microstructural attributes and permeability from 3d tomographic images of in situ shear-enhanced compaction bands using multiscale computations. Geophys Res Lett. Google Scholar
  55. 55.
    Tagliaferri F, Waller J, Andò E, Hall S, Viggiani G, Bésuelle P, DeJong J (2011) Observing strain localisation processes in bio-cemented sand using X-ray imaging. Granul Matter 13(3):247–250Google Scholar
  56. 56.
    Tsomokos A, Georgiannou V (2010) Effect of grain shape and angularity on the undrained response of fine sands. Can Geotech J 47(5):539–551Google Scholar
  57. 57.
    Viggiani G, Andò E, Takano D, Santamarina J (2015) Laboratory X-ray tomography: a valuable experimental tool for revealing processes in soils. Geotech Test J 38(1):61–71Google Scholar
  58. 58.
    Vincent L, Soille P (1991) Watersheds in digital spaces: an efficient algorithm based on immersion simulations. IEEE Trans Pattern Anal Mach Intell 6:583–598Google Scholar
  59. 59.
    Vlahinić I, Andò E, Viggiani G, Andrade J (2014) Towards a more accurate characterization of granular media: extracting quantitative descriptors from tomographic images. Granul Matter 16(1):9–21Google Scholar
  60. 60.
    Wadell H (1933) Sphericity and roundness of rock particles. J Geol 41(3):310–331Google Scholar
  61. 61.
    Wang H, Zhang H, Ray N (2012) Clump splitting via bottleneck detection and shape classification. Pattern Recognit 45(7):2780–2787Google Scholar
  62. 62.
    Zhao B, Wang J (2016) 3D quantitative shape analysis on form, roundness, and compactness with \(\mu\)CT. Powder Technol 291:262–275Google Scholar
  63. 63.
    Zheng J, Hryciw R (2016) Segmentation of contacting soil particles in images by modified watershed analysis. Comput Geotech 73:142–152Google Scholar
  64. 64.
    Zheng J, Hryciw R (2017a) An image based clump library for DEM simulations. Granul Matter 2(19):26Google Scholar
  65. 65.
    Zheng J, Hryciw R (2017b) Soil particle size and shape distributions by stereophotography and image analysis. Geotech Test J 40(2):317–328Google Scholar
  66. 66.
    Zheng J, Hryciw R, Ventola A (2017) Compressibility of sands of various geologic origins at pre-crushing stress levels. Geotech Geol Eng 35(5):2037–2051Google Scholar
  67. 67.
    Zhou B, Wang J, Wang H (2018) Three-dimensional sphericity, roundness and fractal dimension of sand particles. Géotechnique 68(1):18–30Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Glenn Department of Civil EngineeringClemson UniversityClemsonUSA

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