A geometric map** establishes a correspondence between two domains. Since no real
object has zero or negative volume, such a map** is required to be inversion-free …

This chapter reviews several Riemannian metrics and evolution equations in the context of
diffeomorphic shape analysis. After a short review of various approaches at building …

The problem of map** triangular meshes into the plane is fundamental in geometric
modeling, where planar deformations and surface parameterizations are two prominent …

We present a new approach to obtain diffeomorphic registrations with large deformations
using landmark and intensity information via quasi-conformal maps. The basic idea is to …

Registration, which aims to find an optimal 1-1 correspondence between shapes, is an
important process in different research areas. Landmark-based surface registration has …

Modal decomposition techniques have become important mathematical methodologies in
analysing complex flow physics. The data-driven methods, such as proper orthogonal …

Constructing a high-quality parameterization of a computational domain is a fundamental
research problem in isogeometric analysis, which has been extensively investigated so far …

With the advancement of computer technology, there is a surge of interest in effective
map** methods for objects in higher-dimensional spaces. To establish a one-to-one …

We propose a new method to obtain landmark-matching transformations between n-
dimensional Euclidean spaces with large deformations. Given a set of feature …

Surface parameterization is of fundamental importance for many tasks in computer vision
and imaging. In recent years, computational quasi-conformal geometry has become an …