标题: Global Parametrization of Range Image Sets [打印本页] 作者: 晃晃 时间: 2011-12-28 09:12 标题: Global Parametrization of Range Image Sets Global Parametrization of Range Image Sets
Nico Pietroni1 Marco Tarini 1;2 Olga Sorkine3;4 Denis Zorin4
Abstract
We present a method to globally parameterize a surface represented
by height maps over a set of planes (range images). In contrast
to other parametrization techniques, we do not start with a man-
ifold mesh. The parametrization we compute defines a manifold
s***cture, it is seamless and globally smooth, can be aligned to ge-
ometric features and shows good quality in terms of angle and area
preservation, comparable to current parametrization techniques for
meshes. Computing such global seamless parametrization makes it
possible to perform quad remeshing, texture mapping and texture
synthesis and many other types of geometry processing operations.
Our approach is based on a formulation of the Poisson equation on
a manifold s***cture defined for the surface by the range images.
Cons***ction of such global parametrization requires only a way to
project surface data onto a set of planes, and can be applied directly
to implicit surfaces, nonmanifold surfaces, very large meshes, and
collections of range scans. We demonstrate application of our tech-
nique to all these geometry types.
CR Categories: I.3.5 [Computational Geometry and Object Mod-
eling]: Geometric algorithms, languages, and systems
Keywords: geometry processing, parametrization, range scans
1 Introduction
A high-quality global parametrization greatly simplifies many oper-
ations on surfaces. Recent techniques made substantial progress in
improving the quality and robustness of global parametrization. At
the same time, the work on parametrization, with few notable ex-
ceptions, focuses on manifold meshes, rather than on other forms of
geometric data. In this paper, we describe how global parametriza-
tion techniques based on solving the Poisson equation (or another
PDE) on the surface can be extended to a surface represented by a
set of projections to planes. In some cases (e.g., range scanning)
raw surface data is directly given in this format. In many other
cases, it can be easily computed from a given arbitrary geometry
representation: for example, if a geometry description can be ren-
dered with depth values, it can serve as the input to our algorithm.
Range image sets occupy an intermediate place between point
clouds or triangle soups, and manifold meshes. On one hand, they
exhibit a regular connectivity and implicitly define a global man-
ifold s***cture for the object, with transition maps determined by
reprojection. On the other hand, each point on the surface may be
represented by multiple positions inside different range images, and
the connectivities of different range images, while highly regular,
are inconsistent with each other.
Our method directly recovers a global parametrization from a range
image set, entirely avoiding the need to cons***ct a consistent mani-
fold mesh first; this parametrization itself can be used to create high
quality regular meshes. This considerably reduces the complexity
of the meshing pipeline, replacing a more difficult step of manifold
mesh recons***ction by simple and robust projections, followed di-
rectly by parametrization and quadrangulation.
Our method is based on a novel discretization of the seamless global
parametrization equations and constraints on a collection of over-
lapping triangles, in contrast to conventional discretization on a sin-
gle mesh. Our parametrization is globally consistent (images of a
point in each range image are assigned the same parametric coordi-
nates), seamless and globally smooth. It has comparable area and
angle preservation quality to similar approaches for meshes, and
