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[其它] Global Parametrization of Range Image Sets

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发表于 2011-12-28 09:12:50 |只看该作者 |倒序浏览

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

can be aligned to geometric features.

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