Directional adaptive deformable models for segmentation

Nicolas F. Rougon; Francoise J. Preteux

doi:10.1117/1.482641

1 January 1998 Directional adaptive deformable models for segmentation

Nicolas F. Rougon, Francoise J. Preteux

Author Affiliations +

Journal of Electronic Imaging, Vol. 7, Issue 1, (January 1998). https://doi.org/10.1117/1.482641

We address the problem of adapting the functions controlling the material properties of 2-D snakes, and show how introducing oriented smoothness constraints results in a novel class of active contour models for segmentation, which extends standard isotropic inhomogeneous membrane/thin-plate stabilizers. These constraints, expressed as adaptive L² matrix norms, are defined by two second-order symmetric and positive definite tensors that are invariant with respect to rigid motions in the image plane. These tensors, equivalent to directional adaptive stretching and bending densities, are quadratic with respect to first- and second-order derivatives of the image luminance, respectively. A representation theorem specifying their canonical form is established and a geometrical interpretation of their effects is developed. Within this framework, it is shown that by achieving a directional control of regularization such nonisotropic constraints consistently relate the differential properties (metric and curvature) of the deformable model with those of the underlying luminance surface, yielding a satisfying preservation of image contour characteristics. In particular, this model adapts to nonstationary curvature variations along image contours to be segmented, thus providing a consistent solution to curvature underestimation problems encountered near highcurvature contour points by classical snakes evolving with constant material parameters. Optimization of the model within continuous and discrete frameworks is discussed in detail. Finally, accuracy and robustness of the model are established on synthetic images. Its efficacy is further demonstrated on 2-D MRI sequences for which comparisons with segmentations obtained using classical snakes are provided.

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Nicolas F. Rougon and Francoise J. Preteux "Directional adaptive deformable models for segmentation," Journal of Electronic Imaging 7(1), (1 January 1998). https://doi.org/10.1117/1.482641

Published: 1 January 1998

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