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Applications of the mean curvature flow associated to anisotropic Generalized Lagrange metrics in image processing
Last modified: 2014-02-05
Abstract
The Geodesic Active Field (GAF) approach from image processing - whose mathematical background is the Riemannian theory of submanifolds, was recently extended by the authors to the Finslerian setting, for certain specific metrics of Randers type.
The present work studies the significantly more flexible Generalized Lagrange (GL) extension, which allows a versatile adapting of the GAF process to Finslerian, pseudo-Finslerian and Lagrangian structures.
The mathematically essential GAF mean curvature flow PDEs of three such GL structures (Randers-Ingarden, Synge-Beil and proper Generalized Lagrange) are explicitly obtained, discussed, implemented, and their corresponding feature evolution is compared with the classic results produced by the established original Riemannian GAF model.
The present work studies the significantly more flexible Generalized Lagrange (GL) extension, which allows a versatile adapting of the GAF process to Finslerian, pseudo-Finslerian and Lagrangian structures.
The mathematically essential GAF mean curvature flow PDEs of three such GL structures (Randers-Ingarden, Synge-Beil and proper Generalized Lagrange) are explicitly obtained, discussed, implemented, and their corresponding feature evolution is compared with the classic results produced by the established original Riemannian GAF model.