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IPI

Registration methods could be roughly divided into two groups:
area-based methods and feature-based methods. In the literature, the
Monge-Kantorovich (MK) mass transport problem has been applied to
image registration as an area-based method. In this paper, we
propose to use Monge-Kantorovich (MK) mass transport
model as a feature-based method. This novel image matching
model is a coupling of the MK problem with
the well-known alpha divergence from the probability theory.
The optimal matching scheme is the one which minimizes the
weighted alpha divergence between two images.
A primal-dual
approach is employed to analyze the existence and
uniqueness/non-uniqueness of the optimal matching scheme. A block
coordinate method, analogous to the Sinkhorn matrix balancing
method, can be used to compute the optimal matching scheme.
We also derive a distance function for image morphing.
Similar to elastic distances proposed by Younes, the
geodesic under this distance function has an explicit expression.

CPAA

In this paper we consider a nonlocal differential equation,
which is a limiting equation of one dimensional Gierer-Meinhardt model. We
study the existence of spike steady states and their stability. We
also construct a single-spike quasi-equilibrium solution and investigate the dynamics of spike-like solutions.

CPAA

We study the uniqueness of minimizers for the Allen-Cahn energy
and the nonexistence of monotone stationary solutions for the
Allen-Cahn equation with double well potentials of different
depths.

DCDS

In this paper, we study the convexity, interior gradient estimate,
Liouville type theorem and asymptotic behavior at infinity of
translating solutions to mean curvature flow as well as the
nonlinear flow by powers of the mean curvature.

keywords:
asymptotic behavior
,
Elliptic equation
,
mean curvature flow
,
convex solution
,
gradient estimate.

## Year of publication

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