Images captured under water are often characterized by low contrast, color distortion, and
noise, hindering some visual tasks carried out on it. Despite remarkable breakthrough has …

In this paper, we consider a proximal linearized alternating direction method of multipliers, or
PL-ADMM, for solving linearly constrained nonconvex and possibly nonsmooth optimization …

In this study, our goal is to integrate classical mathematical models with deep neural
networks by introducing two novel deep neural network models for image segmentation …

Euler's elastica model has a wide range of applications in image processing and computer
vision. However, the nonconvexity, the nonsmoothness, and the nonlinearity of the …

We consider curvature depending variational models for image regularization, such as
Euler's elastica. These models are known to provide strong priors for the continuity of edges …

The curvature regularities are well-known for providing strong priors in the continuity of
edges, which have been applied to a wide range of applications in image processing and …

Gaussian curvature is an important geometric property of surfaces, which has been used
broadly in mathematical modeling. Due to the full nonlinearity of the Gaussian curvature …

We propose a variational functional with a curvature constraint to reconstruct implicit
surfaces from point cloud data. In the point cloud data, only locations are assumed to be …

Deep neural network is a powerful tool for many tasks. Understanding why it is so successful
and providing a mathematical explanation is an important problem and has been one …

Due to the influence of light absorption and scattering in the water medium, underwater
images often appear with different degrees of blur, color distortion, and so on. The physical …