Abstract
This paper describes an approach to elastic modelling of human tissue based on the use of 3D solid active models — active cubes [2] — and a shape description based on the metric tensor in a solid. Active cubes are used because they provide a natural parameterization of the surface and the interior of the given object when deformed to match the object’s shape. Using the metric tensor to store the shape of the deformed active cube the elastic behaviour of the object in response to applied forces or subject to constraints is modelled by minimizing an energy based on the metric tensor. The application of this approach to modelling the elastic deformation of human tissue in response to movement of bones is demonstrated.
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References
K.A. Bartels, A.C. Bovik and C.E. Griffin: Spatio-temporal tracking of material shape change via multi-dimensional splines, Proc. IEEE Workshop Biomedical Image Analysis, Seattle, USA, pp. 110–116, June 1994
M. Bro-Nielsen: Active nets and cubes, submitted to CVGIP: Image Understanding, 1994
L. Caponetti and A.M. Fanelli: Computer-aided simulation for bone surgery, IEEE Computer Graphics & Applications, November, pp. 86–92, 1993
L. D. Cohen and I. Cohen: Finite-element methods for active contour models and balloons for 2-D and g-D images, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 15, no. 11, pp. 1131–1147, 1989
H. Delingette, G. Subsol, S. Cotin and J. Pignon: A craniofacial surgery simulation testbed, INRIA Tech. Rep. 2199, 1994
M.P. Do Carmo: Differential geometry of curves and surfaces, USA, Prentice-Hall, 1976
M. Kass, A. Witkin and D. Terzopoulos: Snakes: Active contour models, Int. J. of Computer Vision, vol. 2, pp. 321–331, 1988
J. Satoh, H. Ciyokura, M. Kobayashi and T. Fujino: Simulation of surgical operations based on solid modelling, in T. L. Kunii: Visual computing, Integrating computer graphics with computer vision, Tokyo, Springer Verlag, pp. 907–916, 1992
R.H. Taylor: An overview of computer assisted surgery research at IBM T.J. Watson research center, in Innovation et technologie en biologie et medecine, 1992
D. Terzopoulos: Deformable models, The Visual Computer, vol. 4, pp. 306–331, 1988
D. J. Williams and M. Shah: A fast algorithm for active contours and curvature estimation, CVGIP: Image Understanding, vol. 55, no. 1, pp. 14–26, 1992
T. Yasuda, Y. Hashimoto, S. Yokoi and J-I. Toriwaki: Computer system for craniofacial surgical planning based on CT images, IEEE Trans. Medical Imaging, vol. 9, no. 3, pp. 270–280, 1990
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© 1995 Springer-Verlag Berlin Heidelberg
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Bro-Nielsen, M. (1995). Modelling Elasticity in Solids Using Active Cubes — Application to Simulated Operations. In: Ayache, N. (eds) Computer Vision, Virtual Reality and Robotics in Medicine. CVRMed 1995. Lecture Notes in Computer Science, vol 905. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-49197-2_70
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DOI: https://doi.org/10.1007/978-3-540-49197-2_70
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-59120-7
Online ISBN: 978-3-540-49197-2
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