Geodesic
Segmentation of MRI data by means of nonlinear diffusion
Kybernetika, Tome 49 (2013) no. 2, pp. 301-318.

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The article focuses on the application of the segmentation algorithm based on the numerical solution of the Allen-Cahn non-linear diffusion partial differential equation. This equation is related to the motion of curves by mean curvature. It exhibits several suitable mathematical properties including stable solution profile. This allows the user to follow accurately the position of the segmentation curve by bringing it quickly to the vicinity of the segmented object and by approaching the details of the segmentation curve. The purpose of the article is to indicate how the algorithm parameters are set up and to show how the algorithm behaves when applied to the particular class of medical data. In detail we describe the algorithm parameters influencing the segmentation procedure. The left ventricle volume estimated by the segmentation of scanned slices is evaluated through the cardiac cycle. Consequently, the ejection fraction is evaluated. The described approach allows the user to process cardiac cine MR images in an automated way and represents, therefore, an alternative to other commonly used methods. Based on the physical and mathematical background, the presented algorithm exhibits the stable behavior in the segmentation of MRI test data, it is computationally efficient and allows the user to perform various implementation improvements.
Classification : 35A40, 35K20, 35K55, 68U10, 80A22, 82C26, 92C55, 94A08
Keywords: degenerate diffusion; Allen–Cahn equation; image segmentation; magnetic resonance imaging 
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     author = {Chabiniok, Radom{\'\i}r and M\'aca, Radek and Bene\v{s}, Michal and Tint\v{e}ra, Jaroslav},
     title = {Segmentation of {MRI} data by means of nonlinear diffusion},
     journal = {Kybernetika},
     pages = {301--318},
     publisher = {mathdoc},
     volume = {49},
     number = {2},
     year = {2013},
     mrnumber = {3085398},
     zbl = {1266.94004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2013__49_2_a6/}
}
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Chabiniok, Radomír; Máca, Radek; Beneš, Michal; Tintěra, Jaroslav. Segmentation of MRI data by means of nonlinear diffusion. Kybernetika, Tome 49 (2013) no. 2, pp. 301-318. http://geodesic.mathdoc.fr/item/KYB_2013__49_2_a6/