Abstract
Under ideal circumstances the problem of tomographic reconstruction is well-posed, and measured data are sufficient to obtain accurate estimates of volume densities. In such cases segmentation and surface estimation from the reconstructed volume are justified. In other situations the reconstructed volumes are not suitable for subsequent segmentation. This can happen in the case of incomplete sinograms, noise in the measurement process, or misregistration of the views. This paper presents a direct approach to the segmentation of incomplete and noisy tomographic data. The strategy is to impose a fairly simple model on the data, and treat segmentation as a problem of estimating the interface between two substances of somewhat homogeneous density. The segmentation is achieved by simultaneously deforming a surface model and updating density parameters in order to achieve a best fit between the projected model and the input sinograms. The deformation is implemented with level-set surface models, calculated at the resolution of the input data. Several computational innovations make the approach feasible with state-of-the-art computers. The usefulness of the approach is demonstrated by reconstructing the shape of spiny dendrites from electron microscope tomographic data.
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Keywords
- Electron Microscope Tomography
- Tomographic Reconstruction
- Reconstructed Volume
- Tomographic Data
- Sinogram Data
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References
Battle, X.L., Cunningham, G.S., Hanson, K.M. (ed.): 3D tomographic reconstruction using geometrical models. Proc. SPIE Medical Imaging: Image Processing 3034 (1997) 346–357
Battle, X.L., Bizais, Y.J., Le Rest, C., Turzo, A., Hanson, K.M. (ed.): Tomographic reconstruction using free-form deformation models. Proc. SPIEMedical Imaging: Image Processing 3661 (1999) 356–367
Caselles, V., Kimmel, R., Sapiro, G.: Geodesic Active Contours. International Conference on Computer Vision, IEEE Computer Society Press (1995) 694–699
Chan, T.F., Vese, L.A.: A Level Set Algorithm for Minimizing theMumford-Shah Functional in Image Processing. UCLA, Department of Mathematics, Technical report, CAM 00-13 (2000)
Dorn, O., Miller, E.L., Rappaport, C.: A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets. Inverse Problems: Special issue on Electromagnetic Imaging and Inversion of the Earth’s Subsurface 16 (2000) 1119–1156
Dorn, O., Miller, E.L., Rappaport, C.: Shape reconstruction in 2D from limited-view multifrequency electromagnetic data. to appear AMS series contemporary mathematics (2001)
Frank, J.: Electron Tomography: Three-Dimensional Imaging with the Transmission Electron Microscope. New York Plenum Press (1992)
Herman, G.T.: Image Reconstruction from Projections: The Fundamentals of Computerized Tomography. Academic Press, New York (1980)
Inouye, T.: Image Reconstruction with Limited Angle Projection Data. IEEE Transactions on Nuclear Science NS-26 (1979) 2666–2684
Malladi, R., Sethian, J.A., Vemuri, B.C.: Shape Modeling with Front Propagation: A Level Set Approach. IEEE PAMI 17(2) (1995) 158–175
Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics (1988) 12–49.
Prince, J.L., Willsky, A.S.: Hierarchical Reconstruction Using Geometry and Sinogram Restoration. IEEE Transactions on Image Processing 2(3) (1993) 401–416
Roerdink, J.B.T.M.: Computerized tomography and its applications: a guided tour. Nieuw Archief voor Wiskunde 10(3) (1992) 277–308
Santosa, F: A level set approach for inverse problems involving obstacles. European Series in Applied and Industrial Mathematics: Control Optimization and Calculus of Variations 1 (1996) 17–33
Sethian, J.A.: Level Set Methods: Evolving interfaces in Geometry, Fluid Mechanics, Computer Vision, and Material Sciences. Cambridge University Press (1996)
Tsai, A., Yezzi, A.,Jr., Willsky, A.: A Curve Evolution Approach to Smoothing and Segmentation Using the Mumford-Shah Functional. IEEE Computer Society Conference on Computer Vision and Pattern Recognition (2000) 119–124
Whitaker, R.T., Robb, R.A. (ed.): Volumetric Deformable Models: Active Blobs. SPIE Visualization In Biomedical Computing (1994) 122–134
Whitaker R.T.: A Level-Set Approach to 3D Reconstruction From Range Data. International Journal of Computer Vision 29(3) (1998) 203–231
Whitaker, R.T., Breen, D.E., Museth, K., Soni, N.: A Framework for Level Set Segmentation of Volume Datasets. to appear ACM Volume Graphics Workshop (2001)
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Elangovan, V., Whitaker, R.T. (2001). From Sinograms to Surfaces: A Direct Approach to the Segmentation of Tomographic Data. In: Niessen, W.J., Viergever, M.A. (eds) Medical Image Computing and Computer-Assisted Intervention – MICCAI 2001. MICCAI 2001. Lecture Notes in Computer Science, vol 2208. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45468-3_26
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DOI: https://doi.org/10.1007/3-540-45468-3_26
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