An Accurate and Practical Explicit Hybrid Method for the Chan–Vese Image Segmentation Model

Darae Jeong, Sangkwon Kim, Chaeyoung Lee and Junseok Kim
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Darae Jeong: Department of Mathematics, Kangwon National University, Gangwon-do 24341, Korea
Sangkwon Kim: Department of Mathematics, Korea University, Seoul 02841, Korea
Chaeyoung Lee: Department of Mathematics, Korea University, Seoul 02841, Korea
Junseok Kim: Department of Mathematics, Korea University, Seoul 02841, Korea

Mathematics, 2020, vol. 8, issue 7, 1-14

Abstract: In this paper, we propose a computationally fast and accurate explicit hybrid method for image segmentation. By using a gradient flow, the governing equation is derived from a phase-field model to minimize the Chan–Vese functional for image segmentation. The resulting governing equation is the Allen–Cahn equation with a nonlinear fidelity term. We numerically solve the equation by employing an operator splitting method. We use two closed-form solutions and one explicit Euler’s method, which has a mild time step constraint. However, the proposed scheme has the merits of simplicity and versatility for arbitrary computational domains. We present computational experiments demonstrating the efficiency of the proposed method on real and synthetic images.

Keywords: image processing; Allen–Cahn equation; finite difference method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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