Boundary estimation in ultrasound images

  • W J Lin
  • S M Pizer
  • V E Johnson
5. Segmentation: Multi-Scale, Surfaces And Topology
Part of the Lecture Notes in Computer Science book series (LNCS, volume 511)


Surface definition, a process of defining three dimensional surface from volume data, is essential in three dimensional volume data rendering. The traditional method applies a three dimensional gradient operator to the volume data to estimate the strength and orientation of surface present. Applying this method to ultrasound volume data does not produce satisfactory results due to noisy nature of the images and the sensitivity of certain signals to the direction of insonation. We propose a Bayesian approach to the surface definition problem of ultrasound images, and study this approach in two dimensions. We formulate the problem as the estimation of posterior means and standard deviations of Gibbs distributions for boundary believability and normal direction. A set of filters of directional derivatives of Gaussians are used to measure the edge strength and orientation at multiple scales. The likelihood function is based on the measurement at the smallest scale. The prior distribution reflects shape properties at multiple scales. It uses a pyramid algorithm for contour analysis where the lengths of contours are computed and contour gaps are closed at multiple scales. The outcome of the pyramid algorithm is the length and weight global attributes for each pixel. These attribute values are incorporated into the Gibbs prior using a data augmentation scheme. The design and implementation of such an approach are the subject of this paper.


Volume rendering surface estimation Bayesian likelihood function prior posterior Markov random field Gibbs distribution data augmentation 


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  1. Canny J (1986). A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence. PAMI-8(6):679–698.Google Scholar
  2. Dempster AP, Laird NM and Rubin DB (1977). Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical Society. Ser. B(39):1–38.Google Scholar
  3. Geman S and Geman D (1984). Stochastic relaxation, gibbs distributions, and the bayesian restoration of images. IEEE transactions on Pattern Analysis and Machine Intelligence. PAMI-6(6):721–741.Google Scholar
  4. Gelfand AE and Smith AFM (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association. 85(410):398–409.Google Scholar
  5. Hykes D, Hedrick WR and Starchman DE (1985). Ultrasound Physics and Instrumentation. Churchhill Livingstone, New York, N.Y., 1985.Google Scholar
  6. Kass M, Witkin A and Terzopoulos D (1988). Snake: Active Contour Models. International Journal of Computer Vision. 1:321–331.Google Scholar
  7. Korn AF (1988). Toward a symbolic representation of intensity changes in images. IEEE Transactions on Pattern Analysis and Machine Intelligence. PAMI-10(5):610–625.Google Scholar
  8. Levoy M (1988). Display of surfaces from volume data. IEEE Computer Graphics and Applications. 8(3):29–37.Google Scholar
  9. Lin WJ (1991). Boundary Estimation in Ultrasound Images. PhD thesis, U. of North Carolina, Chapel Hill, NC, 1991. To appear.Google Scholar
  10. Meer P, Sher CA and Rosenfeld A (1990). The chain pyramid: Hierarchical contour processing. IEEE Transactions on Pattern Analysis and Machine Intelligence. PAMI-12:363–376.Google Scholar
  11. Nassiri DK and Hill CR (1986). The use of angular acoustic scattering measurements to eliminate structural parameters of human and animal tissues. The Journal of the Acoustical Society of America. 79(6):2048–2054.Google Scholar
  12. Shneier M (1981). Two hierarchical linear feature representations: Edge pyramids and edge quadtrees. Computer Graphics and Image Processing. 17:211–224.Google Scholar
  13. Shattuck DP, Weinshenker MD, Smith SW and von Ramm OT (1984). Explososcan: A parallel processing technique for high speed ultrasound imaging with linear phased arrays. Journal of Acoustic Society of America. 75(4):1273–1282.Google Scholar
  14. Tanner MA and Wong WH (1987). The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association. 82(398):528–541.Google Scholar
  15. von Ramm OT, Smith SW, Sheikh KH, and Kisslo J (1988). Real-time, three-dimensional echocardiography. Circulation. 78. Supplement II.Google Scholar
  16. Wagg RC, Dalecki D and Christopher PE (1989). Spectral power determinations of compressibility and density variations in model media and calf liver using ultrasound. The Journal of the Acoustical Society of Americ. 85(1):423–431.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • W J Lin
    • 1
  • S M Pizer
    • 1
    • 2
    • 3
  • V E Johnson
    • 4
  1. 1.Department of Computer ScienceUniversity of North CarolinaChapel Hill
  2. 2.Department of RadiologyUniversity of North CarolinaChapel Hill
  3. 3.Department of Radiation OncologyUniversity of North CarolinaChapel Hill
  4. 4.Institute of Decision Science and StatisticsDuke UniversityDurham

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