| Abstract: |
| Traditional variational segmentation models are typically solved by deriving the corresponding gradient flow, which evolves the level set function along the steepest descent direction toward a stationary point. While such first-order flows often suffer from slow convergence and sensitivity to initialization, frequently becoming trapped in local minima. In recent years, damped second-order gradient flows have gained attention for their ability to accelerate convergence through inertial dynamics. In this paper, we investigate a damped second-order gradient flow for a class of high-order variational segmentation models. By incorporating a damping mechanism, the proposed flow achieves significantly accelerated convergence to stationary points compared to standard first-order methods. To address numerical challenges arising from nonlinearity and high-order derivatives, we develop efficient, unconditionally energy-stable schemes based on the scalar auxiliary variable method and its variants, ensuring long-time stability without restrictive time step constraints. Extensive experiments demonstrate that the proposed method not only accelerates convergence substantially but also exhibits improved robustness against initialization, effectively alleviating the local minima issue inherent in traditional level set approaches. |
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