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COMPUTER ANIMATION AND VIRTUAL WORLDS

Comp. Anim. Virtual Worlds

2012; 23:407–416

Published online 24 May 2012 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/cav.1464

SPECIAL ISSUE PAPER

Detail-feature-preserving surface reconstruction

Xu Zhao

, Zhong Zhou

*,YeDuan

and Wei Wu

State Key Laboratory of Virtual Reality Technology and Systems, School of Computer Science and Engineering, Beihang

University, Beijing, China

Computer Graphics and Image Understanding Lab, Department of Computer Science, University of Missouri – Columbia,

Columbia, MO, USA

ABSTRACT

In this paper, we propose a feature-preserving surface reconstruction method from sparse noisy 3D measurements such

as range scanning or passive multiview stereo. In contrast to earlier methods, we deﬁne a novel type of explicit 3D

ﬁlter—regularized weighted least squares ﬁlter—to characterize the detail features such as surface wrinkles and sharp

features. To account for noise, we rasterize input-oriented points into a probabilistic volume (base volume) and then create

a guidance volume by Gaussian ﬁltering. Both the base volume and the guidance volume are further ﬁltered by regularized

weighted least squares ﬁlter to detect and recover detail features. After the two-stage ﬁltering, a global minimal surface is

computed by graph cut and meshed as a geometric model. Experimental results on various datasets show that our method

is robust to noise, outliers, and missing parts, which makes it more suitable to ﬁt indoor/outdoor multiview stereo data.

Unlike other methods, our method can completely recover scene structures and preserve detail features from noisy point

KEYWORDS

surface reconstruction; computational geometry; computer graphics

*Correspondence

Zhong Zhou, State Key Laboratory of Virtual Reality Technology and Systems, School of Computer Science and Engineering,

Beihang University, Beijing, China.

E-mail: zz@vrlab.buaa.edu.cn

1. INTRODUCTION

Reconstructing 3D surfaces from point samples is well

studied in many areas of computer graphics, including laser

scanning, reconstructing image-based surfaces, and repair-

ing of noisy meshes [1]. It focuses on approximately ﬁtting

a surface to point samples, ﬁlling holes, or remeshing exist-

ing models with the use of information about the sampling

process, for example, bounds on the noise magnitude or the

sampling density.

There are many approaches for acquiring 3D shapes

from real-world objects, which can be basically classiﬁed

into two categories: active lighting systems and passive

stereo systems. Active lighting systems, such as laser-

based scanners, structured light scanners, and infrared

light devices, can produce more stable and accurate point

samples than passive stereo systems. Recently, however,

the passive stereo systems have become increasingly

popular for their low-cost acquiring devices and attrac-

tive indoor/outdoor applications [2,3]. Unfortunately, most

surface reconstruction algorithms cannot be directly used

for passive stereo systems. For example, in passive mul-

tiview stereo, reconstructed point samples are seriously

affected by insufﬁcient images, illumination changes,

calibration errors, poor photo-consistent matches, and the

structure and appearance of the scene to be reconstructed.

Until recently, it has been a challenge to perform surface

ﬁtting from such poor point samples.

The latest surface reconstruction algorithms, such as

Poisson surface [4] and touch expand [5], alleviate the poor

data ﬁtting problem to some extent and are widely used in

image-based modeling systems. The key objective of these

two methods is to deﬁne a s urface-ﬁt quality function from

oriented points and then solve this optimization function. It

is important to note that they all implicitly use a Gaussian

ﬁlter in their algorithms to avoid the inﬂuence of noise and

outliers and to achieve a smooth mesh model. They per-

form well in many cases especially when the surface of the

reconstructed object is inherently smooth. But the smooth

shape prior assumption also ignores some important detail

features such as surface wrinkles as well as sharp edges and

corners that occur widely in natural and artiﬁcial objects.

Meanwhile, when considering points obtained using multi-

view stereo, detail features are difﬁcult to distinguish from

the noisy or incomplete point samples because both details

and noise are high-frequency s ignals.

Detail-feature-preserving surface reconstruction X. Zhao

et al.

To solve these problems, we present a novel feature-

preserving ﬁlter called regularized weighted least squares

(RWLS) ﬁlter. The key idea is to deﬁne the detail

features as the covariances between the input and a

Gaussian-smoothed intermediate result. Also, a regulariza-

tion parameter is added into the kernel function to balance

the two. To account for noise, we ﬁrst rasterize oriented

points into a probabilistic volume (also called base volume)

and create a guidance volume by Gaussian ﬁltering. This

ﬁltering is completed using a large ﬁlter radius to ensure

the reconstruction completeness and suppress noise as well

as details. Only the signiﬁcant high-frequency features that

are deﬁned as detail features are detected and recovered

during RWLS ﬁltering. Finally, meshes are generated from

the ﬁltered volume by graph cut.

The advantages of our method include the following: (1)

the method has the ability to recover both sharp features as

well as surface wrinkle features, and the level of detail can

be easily controlled by adjusting ﬁlter parameters; and (2)

the method is robust to noise, outliers, and missing parts,

which cannot only be used for range scan data ﬁtting but is

also suitable for indoor/outdoor multiview data.

2. RELATED WORK

The earliest surface reconstruction methods are primar-

ily designed for ﬁtting 3D laser scanner data. They can

be roughly classiﬁed into two major categories: implicit

surface methods and Delaunay-based methods.

The goal of implicit surface methods is to implicitly

deﬁne a level-set surface function such as signed distance

function [6], radial basis function [7], or moving least

squares (MLS) [8]. Among them, the MLS scheme can

approximate the local surface from the point set with a

moderate amount of noise, and various methods are fur-

ther developed to improve its stability [9] or preserve sharp

features [10]. However, they always fail when the points

are irregularly sampled (e.g., incomplete) or too noisy. The

idea behind MLS is to perform a local polynomial ﬁtting

in weighted least squares (WLS) sense, which can also be

seen as an optimization-based ﬁlter kernel. Similarly, we

deﬁne an RWLS ﬁlter for surface reconstruction. However,

there are two differences in our method: (1) the ﬁltering

process is computed in 3D probabilistic space; (2) a guid-

ance volume is generated by Gaussian ﬁltering to suppress

more noise and ensure the reconstruction completeness.

Note that the 2D RWLS ﬁlter has been recently proposed in

an image processing area [11]. Its applications include haze

removal, image matting, high dynamic range (HDR) com-

pression, noise reduction, and others [12]. An extensive

literature search led to the conclusion that our method is

the ﬁrst attempt to extend the ﬁlter to 3D digital geometry

processing, which led to its successful application in

detail-feature-preserving surface reconstruction.

Delaunay-based methods typically interpolate all or

most of the points on the basis of combinatorial structures,

such as Delaunay triangulations [13], alpha shapes [14],

or Voronoi diagrams [15]. More recent work focuses

on combining with other techniques such as partition-

ing strategy [16], variation method [17], or energy opti-

mization framework [18] to improve the robustness to

noise, outliers, and irregular sampling. Most notably,

Salman et al. [19] addressed the problem of generating

surface meshes from 3D point samples while preserving

sharp features. They explicitly extract sharp features on

the basis of the covariance matrices of Voronoi cells and

then perform a feature-preserving variant of a Delaunay

reﬁnement process. However, most of these methods are

not designed for the passive stereo system.

For the problem of surface reconstruction from multi-

view stereo (MVS) point sets to be solved, shape priors

and probabilistic optimization framework are often used.

The basic shape prior assumes that the surface to be

reconstructed is smooth, which yields to a regularized

optimization problem [5,20]. Poisson surface [4] and

touch expand [5] are two typical surface reconstruction

algorithms and are widely applied in MVS reconstruction

for their robustness. Kazhdan et al. [4] aligned the gradient

of the indicator function with a vector ﬁeld from the

input-oriented points and compute it as a Poisson problem.

Lempitsky and Boykov’s global optimization approach [5]

is based on the minimal surface framework with graph cuts

in [21] and expresses the generic surface-to-data ﬁt quality

measurement as a ﬂux-based function. Both methods

implicitly use the Gaussian ﬁlter to handle sample noise,

which is equivalent to the smoothness shape priors.

Nevertheless, in practice, we found that if the ﬁlter radius

is large, both implicit model and globalization methods

will obtain a complete but oversmooth model. However, if

the ﬁlter radius is small, a detailed but incorrect geometric

model is produced. In many cases, both the completeness

(scene structure) and surface details are crucial to the

perception of 3D models. However, it is hard to make a

trade off between them. Unlike these methods, our method

ﬁrst creates a guidance volume by Gaussian ﬁltering

and then recovers detail features by RWLS ﬁltering. The

two-stage ﬁltering ensures that the resulting model can

contain both complete structures and detail features.

Moreover, the RWLS ﬁlter parameters can be easily

adjusted to control the level of detail features to be

preserved. Recently, more shape priors such as planar

plane [22] and basic geometric shape primitives [23] are

introduced. However, these assumptions are more suitable

for urban scenes, whereas the local shape priors in RWLS

ﬁlter are adaptively determined within a given neighbor-

hood and have no limitation of scene types.

3. METHOD OVERVIEW

The overall goal of our method is to reconstruct a mesh

surface from well/poor-sampled oriented points, to ensure

the completeness and to recover detail features as much

as possible. Figure 1 illustrates the basic step-by-step pro-

cess of our surface reconstruction method, which consists

408

Comp. Anim. Virtual Worlds

DOI: 10.1002/cav

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