A Locally Gradient-Preserving Reinitialization for Level Set Functions

Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups

We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...

Differential equation based constrained reinitialization for level set methods

A partial differential-equation based reinitialization method is presented in the framework of a localized level set method. Two formulations of the new reinitialization scheme are derived. These formulations are modifications of the partial differential equation introduced by Sussman et al. [J. Comp. Phys. 114 (1994), 146-159] and, in particular, improvements of the second-order accurate modif...

Conformal mappings preserving the Einstein tensor of Weyl manifolds

In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...

An effective optimization algorithm for locally nonconvex Lipschitz functions based on mollifier subgradients

An efficient, scalable, and adaptable framework for solving generic systems of level-set PDEs

In the last decade, level-set methods have been actively developed for applications in image registration, segmentation, tracking, and reconstruction. However, the development of a wide variety of level-set PDEs and their numerical discretization schemes, coupled with hybrid combinations of PDE terms, stopping criteria, and reinitialization strategies, has created a software logistics problem. ...