Curvature-based interface restoration algorithm using phase-field equations

• Published in: PloS one Vol. 18; no. 12; p. e0295527
• Main Authors: Lee, Seunggyu, Choi, Yongho
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 14.12.2023; Public Library of Science (PLoS)
• Subjects: Algorithms; Analysis; Biology and Life Sciences; Boundary conditions; Chemical potential; Circles (geometry); Curvature; Dirichlet problem; Equilibrium flow; Form Perception; Health aspects; Image restoration; Interfaces; Medicine and Health Sciences; Motion; Numerical analysis; Order parameters; Physical Sciences; Research and Analysis Methods; Restoration ecology; South Korea
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0295527

In this study, we propose a restoration algorithm for distorted objects using a curvature-driven flow. First, we capture the convex-hull shaped contour of the distorted object using the mean curvature flow. With the supplemented mass on the captured feature, we evolve the constraint mean curvature flow to a steady state, preserving the non-distorted region. With respect to the mass, we select a restorative shape by considering the square of the curvature derivative. The Allen-Cahn and Cahn-Hilliard equations are applied to the generated restored image from the implicit curvature motions represented by the order parameter. We impose the Dirichlet boundary condition for the order parameter and the Neumann boundary for the chemical potential to fix the feature and to inherit the mass conservation, respectively. We provided examples of the restoration of half-circle and parentheses-shaped objects to reconstruct a circle shape.