Abstract
We evaluate an image model for simultaneous reconstruction and segmentation of piecewise continuous images. The model assumes that the intensities of the piecewise continuous image are relatively constant within contiguous regions and that the intensity levels of these regions can be determined either empirically or theoretically before reconstruction. The assumptions might be valid, for example, in cardiac blood-pool imaging or in transmission tomography of the thorax for non-uniform attenuation correction of emission tomography. In the former imaging situation, the intensities or radionuclide activities within the regions of myocardium, blood-pool and background may be relatively constant and the three activity levels can be distinct. For the latter case, the attenuation coefficients of bone, lungs and soft tissues can be determined prior to reconstructing the attenuation map. The contiguous image regions are expected to be simultaneously segmented during image reconstruction. We tested the image model with experimental phantom studies. The phantom consisted of a plastic cylinder having an elliptical cross section and containing five contiguous regions. There were three distinct activity levels within the phantom. Projection data were acquired using a SPECT system. Reconstructions were performed using an iterative maximum a posteriori probability procedure. As expected, the reconstructed image consisted of contiguous regions and the acitivities within the regions were relatively constant. Compared with maximum likelihood and a Bayesian approach using a Gibbs prior, the results obtained using the image model demonstrated the improvement in identifying the contiguous regions and the associated activities.
Preview
Unable to display preview. Download preview PDF.
References
Akaike H (1974). A New Look at the Statistical Model Identification. IEEE Trans. Auto. Control, vol.19, pp.716–723.
Akaike H (1978). A Bayesian Analysis of the Minimum AIC Procedure. Ann. Inst. Statist. Math., vol.30, pp.9–14.
Baxter L (1990). Futures of Statistics. The Amer. Statistician, vol.44, pp.128–129.
Besag J (1974). Spatial Interation and the Statistical Analysis of Lattice Systems. J.R. Stat. Soc., series B, vol.26, pp.192–236.
Budinger T and Gullberg G (1974). Three-Dimensional Reconstruction in Nuclear Medicine Emission Imaging. IEEE Trans. Nucl. Sci., vol.21, pp.2–20.
Dempster A, Laird N and Rubin D (1977). Maximum Likelihood from Incomplete Data via the EM Algorithm. J. R. Stat. Soc., vol.39, series B, pp.1–38.
Derin H and Elliott H (1987). Modeling and Segmentation of Noisy and Textured Images Using Gibbs Random Fields. IEEE Trans. Pattern Anal. Machine Intell., vol.9, pp.39–55.
Efron B (1986). How Biased is the Apparent Error Rate of a Prediction Rule. J. Am. Stat. Assoc., vol.81, pp.461–470.
Gilland D, Jaszczak R, Greer K. Coleman R (1991). Quantitative SPECT Reconstruction of Iodine-123 Data. J. Nucl. Medicine, to appear.
Goris M and Briandet P (1983). A Clinical and Mathematical Introduction to Computer Processing of Scintigraphic Images. Raven Press, New York.
Hall E (1979). Computer Image Processing and Recognition. Academic Press, New York.
Herman G (1980). Image Reconstruction from Projections: the fundamentals of computerized tomography. Academic Press, New York.
Johnson V (1989). Bayesian Restoration of PET Images Using Gibbs Priors. In: Information Processing in Medical Imaging, vol.11, Berkerley, CA.
Kullback S (1959). Information Theory and Statistics. John Wiley & Sons, Inc., New York.
Lei T and Sewchand W (1988). A New Stochastic Model-Based Image Segmentation Technique for X-ray CT Images. In: SPIE, Visual Communication and Image Processing 3, Boston, MA.
Lei T and Sewchand W (1989). Image Segmentation by Using Finite Normal Mixture Model and EM Algorithm. In: IEEE Intern. Conf. on Image Processing, Singapore.
Liang Z and Hart H (1987). Bayesian Image Processing of Data from Constrained Source Distributions: fuzzy pattern constraints. Phys. Med. Biol., vol.32, pp.1481–1494.
Liang Z and Hart H (1988a). Source Continuity and Boundary Discontinuity Considerations in Bayesian Image Processing. Med. Physics, vol.15, pp.754–756.
Liang Z and Hart H (1988b). Bayesian Reconstruction in Emission Computerized Tomography. IEEE Trans. Nucl. Sci., vol.35, pp.877–885.
Liang Z, Jaszczak R, Coleman R and Johnson V (1991a). Simultaneous Reconstruction, Segmentation, and Edge Enhancement of Relatively Piecewise Continuous Images with Intensity-Level Information. Med. Physics, vol.18, in press.
Liang Z, Gilland, Jaszczak R and Coleman R (1991b). Implementation of Non-Linear Filters for Iterative Penalized Maximum Likelihood Image Reconstruction. In: IEEE Conf. Med. Imaging, Arlington, VA.
Luenberger D (1973). Introduction to Linear and Non-Linear Programming. Addison-Wesley, Reading, MA.
Margulis A and Gooding C (1989). Diagnostic Radiology. J. B. Lippincott Comp., Philadelphia.
Pohost G, Higgins C, Morganroth J, Ritchie J and Schelbert H (1989). New Concepts in Cardiac Imaging. Year Book Med. Publish., Inc., Chicago.
Redner R and Walker H (1984). Mixture Densities, Maximum Likelihood and the EM Algorithm. SIAM Review, vol.26, pp.195–239.
Rissanen J (1978). Modeling by Shortest Data Description. Automatica, vol.14, pp.465–471.
Schwarz G (1978). Estimating the Dimension of a Model. Annal. Stat., vol.6, pp.461–464.
Shepp L and Vardi Y (1982). Maximum Likelihood Reconstruction for Emission Tomography. IEEE Trans. Med. Imaging, vol.1, pp.113–122.
Stone M (1979). Comments on Model Selection Criteria of Akaike and Schwarz. J. Royal Statist. Soc., vol.41, pp.276–278.
Titterington T, Smith A and Makov V (1985). Statistical Analysis of Finite Mixture Distributions. John Wiley & Sons, Inc., New York.
Young T and Fu K (1986). Handbook of Pattern Recognition and Image Processing. Academic Press, New York.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Liang, Z., Jaszczak, R., Coleman, R. (1991). On reconstruction and segmentation of piecewise continuous images. In: Colchester, A.C.F., Hawkes, D.J. (eds) Information Processing in Medical Imaging. IPMI 1991. Lecture Notes in Computer Science, vol 511. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0033745
Download citation
DOI: https://doi.org/10.1007/BFb0033745
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54246-9
Online ISBN: 978-3-540-47521-7
eBook Packages: Springer Book Archive