Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image selective smoothing and edge detection by nonlinear diffusion
SIAM Journal on Numerical Analysis
Unique Determination of Multiple Cracks by Two Measurements
SIAM Journal on Control and Optimization
Medical Image Analysis: Progress over Two Decades and the Challenges Ahead
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Topological Asymptotic Expansion for the Dirichlet Problem
SIAM Journal on Control and Optimization
The Topological Asymptotic for PDE Systems: The Elasticity Case
SIAM Journal on Control and Optimization
Medical image segmentation using topologically adaptable surfaces
CVRMed-MRCAS '97 Proceedings of the First Joint Conference on Computer Vision, Virtual Reality and Robotics in Medicine and Medial Robotics and Computer-Assisted Surgery
Stability and Uniqueness for the Crack Identification Problem
SIAM Journal on Control and Optimization
Journal of Biomedical Imaging - Special issue on Mathematical Methods for Images and Surfaces 2011
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The aim of this article is to present an application of the topological asymptotic expansion to the medical image segmentation problem. We first recall the classical variational of the image restoration problem, and its resolution by topological asymptotic analysis in which the identification of the diffusion coefficient can be seen as an inverse conductivity problem. The conductivity is set either to a small positive coefficient (on the edge set), or to its inverse (elsewhere). In this paper a technique based on a power series expansion of the solution to the image restoration problem with respect to this small coefficient is introduced. By considering the limit when this coefficient goes to zero, we obtain a segmented image, but some numerical issues do not allow a too small coefficient. The idea is to use the series expansion to approximate the asymptotic solution with several solutions corresponding to positive (larger than a threshold) conductivity coefficients via a quadrature formula. We illustrate this approach with some numerical results on medical images.