Xiao-Ping Wang

Variational models are widely used in image segmentation, with various models designed to address different types of images by optimizing specific objective functionals. However, traditional segmentation models primarily focus on the visual attributes of the image, often neglecting the topological properties of the target objects. This limitation can lead to segmentation results that deviate from the ground truth, particularly in images with complex topological structures. In this paper, we introduce a connected-component preserving constraint into the iterative convolution-thresholding method (ICTM), resulting in the connected-component preserving ICTM (CP-ICTM). Extensive experiments demonstrate that, by explicitly preserving the topological properties of target objects—such as connectivity—the proposed algorithm achieves enhanced accuracy and robustness, particularly in images with intricate structures or noise.

In this paper, we propose a simple energy decaying iterative thresholding algorithm to solve the two-phase minimum compliance problem. The material domain is implicitly represented by its characteristic function, and the problem is formulated into a minimization problem by the principle of minimum complementary energy. We prove that the energy is decreasing in each iteration. Two effective continuation schemes are proposed to avoid trapping into the local minimum. Numerical results on 2D isotropic linear material demonstrate the effectiveness of the proposed methods. Minimum compliance, convolution, thresholding, linear elasticity. 65K10, 74B05, 74P15, 35K08 COPYRIGHT: © Global Science Press

We propose an efficient iterative convolution thresholding method for the formulation of flow networks where the fluid is modeled by the Darcy–Stokes flow with the presence of volume sources. The method is based on the minimization of the dissipation power in the fluid region with a Darcy term. The flow network is represented by its characteristic function and the energy is approximated under this representation. The minimization problem can then be approximately solved by alternating: 1) solving a Brinkman equation to model the Darcy–Stokes flow and 2) updating the characteristic function by a simple convolution and thresholding step. The proposed method is simple and easy to implement. We prove mathematically that the iterative method has the total energy decaying property. Numerical experiments demonstrate the performance and robustness of the proposed method and interesting structures are observed.