The evolution of immersed locally convex plane curves driven by anisotropic curvature flow

Article Mathematics, Applied

NUMERICAL ANALYSIS OF AN ODE AND A LEVEL SET METHODS FOR EVOLVING SPIRALS BY CRYSTALLINE EIKONAL-CURVATURE FLOW

Tetsuya Ishiwata et al.

Summary: This paper considers the evolution of a polygonal spiral curve under crystalline curvature flow with a pinned center from two viewpoints - a discrete model and one using the level set method. The differences between these models are investigated numerically by calculating the area of the interposed region by their spiral curves. It is found that the numerical results exhibit small differences, despite slight variations in the model equations around the center and the farthest facet.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S (2021)

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Article Mathematics, Applied

AN APPLICATION OF INTERPOLATION INEQUALITIES BETWEEN THE DEVIATION OF CURVATURE AND THE ISOPERIMETRIC RATIO TO THE LENGTH-PRESERVING FLOW

Kohei Nakamura

Summary: In this study, new interpolation inequalities between the deviation of curvature and the isoperimetric ratio are applied to investigate the large-time behavior of the length-preserving flow of closed plane curves without a convexity assumption, building on previous work by Nagasawa and the author.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S (2021)

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Article Mathematics, Applied

SEGMENTATION OF COLOR IMAGES USING MEAN CURVATURE FLOW AND PARAMETRIC CURVES

Petr Paus et al.

Summary: An algorithm for automatic object detection in photos and images using the parametric mean curvature flow equation and CIE94 color distance function is proposed in this study. The parametric method is enriched with an enhanced algorithm for topological changes by computing the intersection of curves instead of relying on unreliable curve distances. The result is a set of parametric curves enclosing the object, demonstrated on a test image and real photos.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S (2021)

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Article Mathematics, Applied