Advertisement

Development, Implementation and Validation of an Automatic Centerline Extraction Algorithm for Complex 3D Objects

  • Sohail Younas
  • Chase R. Figley
Original Article

Abstract

Although centerlines (aka ‘skeletons’ or ‘medial axes’) are among the most efficient ways to represent items in digital images, and obtaining these from 2D shapes is relatively straight forward, extracting centerlines from 3D objects has remained a challenge—particularly if they are not smooth or uniform. Therefore, we have developed a novel 3D centerline extraction method for discrete binary objects using a ‘divide and conquer’ approach, in which any 3D object is sliced into a series of 2D images (in the X, Y and Z directions), a geometric (Voronoi) algorithm is applied to each planar image to extract the 2D centerlines, and the information is recombined (using an intersection technique) to obtain the centerline of the original 3D object. Validation of this approach was performed using a ground truth benchmark, standard 3D database objects, and more complex anatomical structures (segmented from medical imaging data). The algorithm consistently performed well for objects of moderate complexity, but occasionally left discontinuities in the extracted 3D skeletons of the most complex objects. Therefore, in order to deal with such cases, an optional 3D interpolation step—based on Delaunay triangles and a spherical search to establish the nearest neighboring points in 3D space—was developed to allow continuous centerlines to be extracted from even the most complex anatomical structures tested. As a result, we anticipate that this approach could have wide-ranging applications, including data reduction for large microscopy and other 3D imaging datasets, automatic quantification of medical imaging data along anatomical structures, and others.

Keywords

Centerline Medial axis Skeletonization 2D images 3D object Voronoi Diagram Delaunay triangle Interpolation White matter 

Notes

Acknowledgements

This work was supported by a Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant, Brain Canada Platform Support Grant, Winnipeg Health Sciences Centre Foundation Operating Grant, and University of Manitoba Startup Grant to CRF, as well as a Manitoba Graduate Fellowship to SY. We would also like to thank Drs. Melanie Martin, Jennifer Kornelsen and Sherif Sherif for helpful input and discussions regarding the project, and Dr. Nasir Uddin, Teresa Figley, Anwar Shatil and Kevin Solar for commenting on earlier versions of the manuscript.

Supplementary material

40846_2018_402_MOESM1_ESM.tif (6.4 mb)
Supplementary material 1 (TIFF 6550 kb)
40846_2018_402_MOESM2_ESM.tif (5.8 mb)
Supplementary material 2 (TIFF 5967 kb)
40846_2018_402_MOESM3_ESM.tif (6.1 mb)
Supplementary material 3 (TIFF 6250 kb)
40846_2018_402_MOESM4_ESM.tif (6.6 mb)
Supplementary material 4 (TIFF 6799 kb)
40846_2018_402_MOESM5_ESM.tif (7 mb)
Supplementary material 5 (TIFF 7141 kb)
40846_2018_402_MOESM6_ESM.tif (5.8 mb)
Supplementary material 6 (TIFF 5937 kb)
40846_2018_402_MOESM7_ESM.tif (7.2 mb)
Supplementary material 7 (TIFF 7353 kb)

References

  1. 1.
    Blum, H., & Nagel, R. N. (1978). Symmetric axis features. Pattern Recognition, 10, 167–180.CrossRefzbMATHGoogle Scholar
  2. 2.
    Sudhalkar, A., Gursijzt, L., & Prinzt, F. (1966). Box-skeletons of discrete solids. Computer-Aided Design, 26, 507–517.Google Scholar
  3. 3.
    Sheehy, D. J., Armstrong, C. G., & Robinson, D. J. (1996). Shape description by medial surface construction. IEEE Transactions on Visualization and Computer Graphics, 2(1), 62–72.CrossRefGoogle Scholar
  4. 4.
    Tian, S., Shivakumara, P., Phan, T. Q., & Tan, C. L. (2013). Scene character reconstruction through medial axis. In: Proceedings of the International Conference on Document Analysis and Recognition, ICDAR, pp. 1360–1364.Google Scholar
  5. 5.
    Tian, S., Shivakumara, P., Phan, T. Q., Lu, T., & Tan, C. L. (2015). Character shape restoration system through medial axis points in video. Neurocomputing, 161, 183–198.CrossRefGoogle Scholar
  6. 6.
    Pizer, S., Siddiqi, K., & Yushkevich, P. (2008). Medial representations (Vol. 37). Berlin: Springer.zbMATHGoogle Scholar
  7. 7.
    Maragos, P. A., & Schafer, R. W. (1986). Morphological skeleton representation and coding of binary images. IEEE Transactions on Acoustics, Speech, and Signal Processing, 34(5), 1228–1244.CrossRefGoogle Scholar
  8. 8.
    Jang, B. K., & Chin, R. T. (1992). One-pass parallel thinning analysis, properties, and quantitative evaluation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, 1129–1140.CrossRefGoogle Scholar
  9. 9.
    Lam, L., & Suen, C. Y. (1995). Evaluation of parallel thinning algorithms for character recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(9), 914–919.CrossRefGoogle Scholar
  10. 10.
    Lam, L., & Lee, S. W. (1992). Thinning methodologies—A comprehensive survey. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(9), 869–885.CrossRefGoogle Scholar
  11. 11.
    Hilitch, C. J. (1969). Linear skeletons from square cupboards. Machine Intelligence, 4, 403–420.Google Scholar
  12. 12.
    Xie, W., Thompson, R. P., & Perucchio, R. (2003). A topology-preserving parallel 3D thinning algorithm for extracting the curve skeleton. Pattern Recognition, 36(7), 1529–1544.CrossRefzbMATHGoogle Scholar
  13. 13.
    Zhou, Y., & Toga, A. W. (1999). Efficient skeletonization of volumetric objects. IEEE Transactions on Visualization and Computer Graphics, 5(3), 196–209.CrossRefGoogle Scholar
  14. 14.
    Choi, W. P., Lam, K. M., & Siu, W. C. (2003). Extraction of the Euclidean skeleton based on a connectivity criterion. Pattern Recognition, 36(3), 721–729.CrossRefzbMATHGoogle Scholar
  15. 15.
    Leymarie, F., & Levine, M. D. (1992). Simulating the grassfire transform using an active contour model. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(1), 56–75.CrossRefGoogle Scholar
  16. 16.
    Ahuja, N., & Chuang, J. H. (1997). Shape representation using a generalized potential field model. IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(2), 169–176.CrossRefGoogle Scholar
  17. 17.
    Xia, H., & Tucker, P. G. (2011). Fast equal and biased distance fields for medial axis transform with meshing in mind. Applied Mathematical Modelling, 35(12), 5804–5819.MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Kimmel, R., & Maurer, R. (2003). Method of computing sub-pixel Euclidean distance maps.Google Scholar
  19. 19.
    Danielsson, P. E. (1980). Euclidean distance mapping. Computer Graphics and Image Processing, 14(3), 227–248.CrossRefGoogle Scholar
  20. 20.
    Arcelli, C., & Di Baja, G. S. (1985). A width-independent fast thinning algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence, 7(4), 463–474.CrossRefGoogle Scholar
  21. 21.
    Gauch, J. M., & Pizer, S. M. (1993). Multiresolution analysis of ridges and valleys in grey-scale images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(6), 635–646.CrossRefGoogle Scholar
  22. 22.
    Ogniewicz, R. L., & Kubler, O. (1995). Hierarchic Voronoi skeletons. Pattern Recognition, 28(3), 343–359.CrossRefGoogle Scholar
  23. 23.
    Mayya, N., & Rajan, V. T. (1994) Voronoi diagrams of polygons: A framework for shape representation. In Proceedings CVPR’94, 1994 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Vol. 378, pp. 1–32).Google Scholar
  24. 24.
    Mayya, N., & Rajan, V. T. (1995). An efficient shape representation scheme using Voronoi skeletons. Pattern Recognition Letters, 16(2), 147–160.CrossRefGoogle Scholar
  25. 25.
    Brandt, J. W., & Algazi, V. R. (1992). Continuous skeleton computation by Voronoi diagram. CVGIP: Image Understanding, 55(3), 329–338.CrossRefzbMATHGoogle Scholar
  26. 26.
    Saha, P. K., Borgefors, G., & Sanniti di Baja, G. (2016). A survey on skeletonization algorithms and their applications. Pattern Recognition Letters, 76, 3–12.CrossRefGoogle Scholar
  27. 27.
    Liu, H., Wu, Z.-H., Zhang, X., & Hsu, D. F. (2013). A skeleton pruning algorithm based on information fusion. Pattern Recognition Letters, 34(10), 1138–1145.CrossRefGoogle Scholar
  28. 28.
    Amenta, N., & Kolluri, R. K. (2001). The medial axis of a union of balls. Computational Geometry, 20(1–2), 25–37.MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Mokhtarian, F., & Mackworth, A. K. (1992). A theory of multiscale, curvature-based shape representation for planar curves.pdf. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(8), 789.CrossRefGoogle Scholar
  30. 30.
    Aurenhammer, F. (1991). Voronoi diagrams. ACM Computing Surveys, 23(3), 94.MathSciNetCrossRefGoogle Scholar
  31. 31.
    Aurenhammer, F. (1991). Voronoi diagrams—A survey of a fundamental data structure. ACM Computing Surveys, 23(3), 345–405.CrossRefGoogle Scholar
  32. 32.
    Guibas, L., & Stolfi, J. (1985). Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams. ACM Transactions on Graphics, 4(April), 74–123.CrossRefzbMATHGoogle Scholar
  33. 33.
    Muller, D. E., & Preparata, F. P. (1978). Finding the intersection of two convex polyhedra. Theoretical Computer Science, 7(2), 217–236.MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Green, P. J., & Sibson, R. (1978). Computing dirichlet tessellations in the plane. The Computer Journal, 21(2), 168–173.MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Ohya, T., Iri, M., & Murota, K. (1984). Improvements of the incremental method for the Voronoi diagram with computational comparison of various algorithms. Journal of the Operations Research Society of Japan, 27(4), 306–336.MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Sugihara, K., & Iri, M. (1992). Construction of the Voronoi diagram for ‘one million’ generators in single-precision arithmetic. Proceedings of the IEEE, 80(9), 1471–1484.CrossRefGoogle Scholar
  37. 37.
    Shamos, M. I., & Hoey, D. (1975). Closest-point problems. In 16th Annual Symposium on Foundations of Computer Science, 1975 (pp. 151–162).Google Scholar
  38. 38.
    Brown, K. Q. (1981). Algorithms for reporting and counting geometric intersections. IEEE Transactions on Computers, C-30(2), 147–148.CrossRefzbMATHGoogle Scholar
  39. 39.
    Spontón, H., & Cardelino, J. (2015). A review of classic edge detectors. Image Processing on Line, 5, 90–123.MathSciNetCrossRefGoogle Scholar
  40. 40.
    Telea, A., & van Wijk, J. J. (2002). An augmented fast marching method for computing skeletons and centerlines. In: Joint EUROGRAPHICS—IEEE TCVG Symposium on Visualization (pp. 251–260).Google Scholar
  41. 41.
    Maus, A., & Drange, J. (2010). All closest neighbors are proper Delaunay edges generalized, and its application to parallel algorithms. In Proceedings of Norwegian informatikkonferanse (pp. 1–12).Google Scholar
  42. 42.
    De Berg, M., Cheong, O., Van Kreveld, M., & Overmars, M. (2008). Computational geometry: Algorithms and applications (Vol. 17). Berlin: Springer.CrossRefzbMATHGoogle Scholar
  43. 43.
    Farin, G., Hoffman, D., & Johnson, C. R. (2006). Triangulations and applications. New York.Google Scholar
  44. 44.
    Lee, D. T., & Schachter, B. J. (1980). Two algorithms for constructing a Delaunay triangulation. International Journal of Computer & Information Sciences, 9(3), 219–242.MathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    Bai, X., Yang, X., Latecki, L. J., Liu, W., & Tu, Z. (2010). Learning context-sensitive shape similarity by graph transduction. IEEE Transactions on Pattern Analysis and Machine Intelligence, 32(5), 861–874.CrossRefGoogle Scholar
  46. 46.
    Siddiqi, K., Zhang, J., MacRini, D., Shokoufandeh, A., Bouix, S., & Dickinson, S. (2008). Retrieving articulated 3-D models using medial surfaces. Machine Vision and Applications, 19(4), 261–275.CrossRefzbMATHGoogle Scholar
  47. 47.
    Bouix, S., Siddiqi, K., & Tannenbaum, A. (2005). Flux driven automatic centerline extraction. Medical Image Analysis, 9, 209–221.CrossRefGoogle Scholar
  48. 48.
    Figley, T. D., Bhullar, N., Courtney, S. M., & Figley, C. R. (2015). Probabilistic atlases of default mode, executive control and salience network white matter tracts: an fMRI-guided diffusion tensor imaging and tractography study. Frontiers in Human Neuroscience, 9, 585.CrossRefGoogle Scholar
  49. 49.
    Figley, T. D., Mortazavi Moghadam, B., Bhullar, N., Kornelsen, J., Courtney, S. M., & Figley, C. R. (2017). Probabilistic white matter atlases of human Auditory, Basal Ganglia, Language, Precuneus, Sensorimotor, Visual and Visuospatial Networks. Frontiers in Human Neuroscience, 11, 306.CrossRefGoogle Scholar
  50. 50.
    Kasthuri, N., et al. (2015). Saturated reconstruction of a volume of neocortex. Cell, 162(3), 648–661.CrossRefGoogle Scholar
  51. 51.
    Lichtman, J. W., Pfister, H., & Shavit, N. (2014). The big data challenges of connectomics. Nature Neuroscience, 17(11), 1448–1454.CrossRefGoogle Scholar
  52. 52.
    Yeatman, J. D., Dougherty, R. F., Myall, N. J., Wandell, B. A., & Feldman, H. M. (2012). Tract profiles of white matter properties: Automating fiber-tract quantification. PLoS ONE, 7(11), e49790.CrossRefGoogle Scholar
  53. 53.
    Colby, J. B., Soderberg, L., Lebel, C., Dinov, I. D., Thompson, P. M., & Sowell, E. R. (2012). Along-tract statistics allow for enhanced tractography analysis. Neuroimage, 59(4), 3227–3242.CrossRefGoogle Scholar
  54. 54.
    Walsh, M., et al. (2011). Object working memory performance depends on microstructure of the frontal-occipital fasciculus. Brain Connectivity, 1(4), 317–329.CrossRefGoogle Scholar

Copyright information

© Taiwanese Society of Biomedical Engineering 2018

Authors and Affiliations

  1. 1.Biomedical Engineering Graduate ProgramUniversity of ManitobaWinnipegCanada
  2. 2.Neuroscience Research ProgramKleysen Institute for Advanced MedicineWinnipegCanada
  3. 3.Department of RadiologyUniversity of ManitobaWinnipegCanada
  4. 4.Division of Diagnostic ImagingWinnipeg Health Sciences CentreWinnipegCanada
  5. 5.Department of Psychological and Brain SciencesJohns Hopkins UniversityBaltimoreUSA

Personalised recommendations