29 July 1993 Finite-element-based deformable model for 3D biomedical image segmentation
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This paper presents a physics-based approach to 3D image segmentation using a 3D elastically deformable surface model. This deformable 'balloon' is a dynamic model and its deformation is governed by the laws of nonrigid motion. The formulation of the motion equations includes a strain energy, simulated forces, and other physical quantities. The strain energy stems from a thin-plate under tension spline and the deformation results from the action of internal forces (which describe continuity constraints) and external forces (which describe data compatibility constraints). We employ the finite element method to discretize the deformable balloon model into a set of connected element domains. The finite element method provides an analytic surface representation. Furthermore, we use a finite element with nodal variables which reflect the derivative terms found in the thin-plate under tension energy expression. That is, the nodal variables include not only the nodal positions, but all of the first and second order partial derivatives of the surface as well. This information can be used to compute the volume, shape, and motion properties of the reconstructed biological structures. To demonstrate the usefulness of our 3D segmentation technique and demonstrate the dynamic properties of our model, we apply it to dynamic 3D CT images of a canine heart to reconstruct the left ventricle and track its motion over time.
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Tim J. McInerney, Tim J. McInerney, Demetri Terzopoulos, Demetri Terzopoulos, } "Finite-element-based deformable model for 3D biomedical image segmentation", Proc. SPIE 1905, Biomedical Image Processing and Biomedical Visualization, (29 July 1993); doi: 10.1117/12.148638; https://doi.org/10.1117/12.148638

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