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Volume 21 (2002), number 2 pp. 149–172

COMPUTER GRAPHICS

for um

The 3D Model Acquisition Pipeline

Fausto Bernardini and Holly Rushmeier

IBM Thomas J. Watson Research Center, Yorktown Heights, New York, USA

Abstract
Three-dimensional (3D) image acquisition systems are rapidly becoming more affordable, especially systems
based on commodity electronic cameras. At the same time, personal computers with graphics hardware capable
of displaying complex 3D models are also becoming inexpensive enough to be available to a large population.
As a result, there is potentially an opportunity to consider new virtual reality applications as diverse as cultural
heritage and retail sales that will allow people to view realistic 3D objects on home computers.
Although there are many physical techniques for acquiring 3D data—including laser scanners, structured light
and time-of-flight—there is a basic pipeline of operations for taking the acquired data and producing a usable
numerical model. We look at the fundamental problems of range image registration, line-of-sight errors, mesh
integration, surface detail and color, and texture mapping. In the area of registration we consider both the
problems of finding an initial global alignment using manual and automatic means, and refining this alignment
with variations of the Iterative Closest Point methods. To account for scanner line-of-sight errors we compare
several averaging approaches. In the area of mesh integration, that is finding a single mesh joining the data from
all scans, we compare various methods for computing interpolating and approximating surfaces. We then look
at various ways in which surface properties such as color (more properly, spectral reflectance) can be extracted
from acquired imagery. Finally, we examine techniques for producing a final model representation that can be
efficiently rendered using graphics hardware.

Keywords: 3D scanning, range images, reflectance models, mesh generation, texture maps sensor fusion

ACM CSS: I.2.10 Vision and Scene Understanding—Modeling and recovery of physical attributes, shape,
texture; I.3.5 Computational Geometry and Object Modeling—Geometric algorithms, languages and systems;
I.3.7 Three-Dimensional Graphics and Realism—Color, shading, shadowing, and texture; I.4.1 Digitization and
Image Capture—Reflectance, sampling, scanning

1. Introduction

The past few years have seen dramatic decreases in the cost
of three-dimensional (3D) scanning equipment, as well as in
the cost of commodity computers with hardware graphics
display capability. These trends, coupled with increasing
Internet bandwidth, are making the use of complex 3D
models accessible to a much larger audience. The potential
exists to expand the use of 3D models beyond the well
established games market to new applications ranging from
virtual museums to e-commerce. To realize this potential,
the pipeline from data capture to usable 3D model must be
further developed. In this report we examine the state of the
art of the processing of the output of range scanners into
efficient numerical representations of objects for computer
graphics applications.

Three-dimensional scanning has been widely used for

many years for reverse engineering and part inspection [1].
Here we focus on acquiring 3D models for computer
graphics applications. By 3D model, we refer to a numerical
description of an object that can be used to render images
of the object from arbitrary viewpoints and under arbitrary
lighting conditions. We consider models that can be used
to simulate the appearance of an object in novel synthetic
environments. Furthermore, the models should be editable
to provide the capability of using existing physical objects as
the starting point for the design of new objects in computer
modeling systems. The geometry should be editable—i.e.
holes can be cut, the object can be stretched, or appended
to other objects. The surface appearance properties should
also be editable—i.e. surfaces can be changed from shiny to
dull, or the colors of the surface can be changed.

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To achieve this flexibility in the use of scanned objects, we

consider systems which output shape in the form of clouds of
points that can be connected to form triangle meshes, and/or
fitted with NURBS or subdivision surfaces. The 3D points
are augmented by additional data to specify surface finish
and color. With the exception of surfaces with relatively
uniform spatial properties, fine scale surface properties such
as finish and color are ultimately stored as image maps
covering the geometry.

The shape of 3D objects may be acquired by a variety

of techniques, with a wide range in the cost of the acqui-
sition hardware and in the accuracy and detail of the ge-
ometry obtained. On the high cost end, an object can be
CAT scanned [2], and a detailed object surface can be ob-
tained with isosurface extraction techniques. On the low cost
end, models with relatively sparse 3D spatial sampling can
be constructed from simple passive systems such as video
streams by exploiting structure from motion [3], or by ob-
serving silhouettes and using space carving techniques [4].

In this report we focus on scanning systems that capture

range images—that is an array of depth values for points on
the object from a particular viewpoint. While these scanners
span a wide range of cost, they are generally less expensive
and more flexible than full 3D imaging systems such as
CAT scanners, while obtaining much more densely sampled
shapes than completely passive systems. We briefly review
various types of range image scanners, and the principles
they work on. However, for this report we consider a range
scanner as a generic component, and consider the model
building process given range images as input.

The process of building models from a range scanning

system is shown in Figure 1. There are fundamentally two
streams of processing—one for the geometry, and one for the
fine scale surface appearance properties. As indicated by the
dotted lines, geometric and surface appearance information
can be exchanged between the two processing streams to
improve both the quality and efficiency of the processing of
each type of data. In the end, the geometry and fine scale
surface appearance properties are combined into a single
compact numerical description of the object.

2. Scanning Hardware

Many different devices are commercially available to obtain
range images. Extensive lists of vendors are maintained at
various web sites. To build a model, a range scanner can be
treated as a “black box” that produces a cloud of 3D points. It
is useful however to understand the basic physical principles
used in scanners. Characteristics of the scanner should be
exploited to generate models accurately and efficiently.

The most common range scanners are triangulation

systems, shown generically in Figure 2. A lighting system
projects a pattern of light onto the object to be scanned—
possibly a spot or line produced by a laser, or a detailed

Postprocessing and

Textured Model

Integration of scans

into a single mesh

illumination invariants

Computation of

registration

Texture-to-geometry

Range

images

Intensity

compensation

Line-of-sight error

Texture map

parameterization

Registration

reconstruction

Figure 1: The sequence of steps required for the reconstruc-
tion of a model from multiple overlapping scans.

pattern formed by an ordinary light source passing through
a mask or slide. A sensor, frequently a CCD camera, senses
the reflected light from the object. Software provided with
the scanner computes an array of depth values, which can
be converted to 3D point positions in the scanner coordinate
systems, using the calibrated position and orientation of the
light source and sensor. The depth calculation may be made
robust by the use of novel optics, such as the laser scanning
systems developed at the National Research Council of
Canada [5]. Alternatively, calculations may be made robust
by using multiple sensors [6]. A fundamental limitation of
what can be scanned with a triangulation system is having
an adequate clear view for both the source and sensor
to see the surface point currently being scanned. Surface
reflectance properties affect the quality of data that can be
obtained. Triangulation scanners may perform poorly on
materials that are shiny, have low surface albedo, or that
have significant subsurface scattering.

An alternative class of range scanners are time-of-flight

systems. These systems send out a short pulse of light, and
estimate distance by the time it takes the reflected light
to return. These systems have been developed with near
real time rates, and can be used over large (e.g. 100 m)
distances. Time-of-flight systems require high precision in
time measurements, and so errors in time measurement
fundamentally limit how accurately depths are measured.

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Laser projector

CCD sensor

Figure 2: Principles of a laser triangulation system. A laser
projector shines a thin sheet of light onto the object. The
CCD sensor detects, on each scan line, the peak of reflected
laser light. 3D point positions are computed by intersecting
the line through the pixel with the known plane of laser light.

Basic characteristics to know about a range scanner are

its scanning resolution, and its accuracy. Accuracy is a
statement of how close the measured value is to the true
value. The absolute accuracy of any given measurement is
unknown, but a precision that is a value for the standard
deviation that typifies the distribution of distances of
the measured point to true point can be provided by the
manufacturer. The tests used by manufacturers to determine
precision are based on standard tests for length measurement
developed for coordinate measurement machines or survey-
ing applications, depending on the scale of the application.
The absolute value of error increases with distance between
the scanner and object. The deviation of measurements is
a thin ellipsoid rather than a sphere—the error is greatest
along the line-of-sight of the sensor. The precision of the
measurements may vary across a range image. There are
some effects that produce random errors of comparable
magnitude at each point. Other effects may be systematic,
increasing the error towards the edges of the scan. Because
models are built from points acquired from many different
range images, it is important to understand the relative
reliability of each point to correctly combine them.

Resolution is the smallest distance between two points

that the instrument measures. The accuracy of measured 3D
points may be different than the resolution. For example, a
system that projects stripes on an object may be able to find
the depth at a particular point with submillimeter accuracy.
However, because the stripes have some width, the device

may only be able to acquire data for points spaced millime-
ters apart on the surface. Resolution provides a fundamen-
tal bound on the dimensions of the reconstructed surface
elements, and dictates the construction of intermediate data
structures used in forming the integrated representation.

Range scanners do not simply provide clouds of 3D

points [7], but implicitly provide additional information.
Simply knowing a ray from each 3D point to the scanning
sensor indicates that there are no occluding surfaces along
that ray, and provides an indicator of which side of the
point is outside the object. Since range images are organized
as two-dimensional (2D) arrays, an estimate of the surface
normal at each point can be obtained by computing vector
cross products for vectors from each point to its immediate
neighbors. These indicators of orientation can be used to
more efficiently reconstruct a full surface from multiple
range images.

3. Registration

For all but the simplest objects, multiple range scans must be
acquired to cover the whole object’s surface. The individual
range images must be aligned, or registered, into a common
coordinate system so that they can be integrated into a single
3D model.

In high-end systems registration may be performed by

accurate tracking. For instance, the scanner may be attached
to a coordinate measurement machine that tracks its position
and orientation with a high degree of accuracy. Passive
mechanical arms as well as robots have been used. Optical
tracking can also be used, both of features present in the
scene or of special fiducial markers attached to the model or
scanning area.

In less expensive systems an initial registration is found by

scanning on a turntable, a simple solution that limits the size
and geometric complexity of scanable objects (they must fit
on the turntable and the system provides only a cylindrical
scan which cannot re-construct self-occluding objects), and
that leaves unsolved the problem of registration for scans
of the top and bottom of the object. Many systems rely on
interactive alignment: a human operator is shown side-by-
side views of two overlapping scans, and must identify three
or more matching feature points on the two images which are
used to compute a rigid transformation that aligns the points.

Automatic feature matching for computing the initial

alignments is an active area of research (recent work
includes [8–12]). The most general formulation of the
problem, that makes no assumptions on type of features
(in the range and/or associated intensity images) and
initial approximate registration is extremely hard to solve.
Approximate position and orientation of the scanner can be
tracked with fairly inexpensive hardware in most situations,
and can be used as a starting point to avoid searching a large
parameter space.

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F. Bernardini and H. Rushmeier / 3D Model Acquisition

3.1. Registration of two views

Neither the controlled motion nor the feature matching
techniques can usually achieve the same degree of accuracy
as the range measurements. The initial alignment must
therefore be refined by a different technique. The most
successful approach to solve this problem has been the
Iterative Closest Point (ICP) algorithm, originally proposed
by Besl and McKay [13], Chen and Medioni [14], and
Zhang [15].

The ICP algorithm consists of two steps: in the first step,

pairs of candidate corresponding points are identified in
the area of overlap of two range scans. Subsequently, an
optimization procedure computes a rigid transformation that
reduces the distance (in the least-squares sense) between
the two sets of points. The process is iterated until some
convergence criterion is satisfied. The general idea is that at
each iteration the distance between the two scans is reduced,
allowing for a better identification of true matching pairs,
and therefore an increased chance of a better alignment at
the next iteration. It has been proved [13] that the process
converges to a local minimum, and in good implementations
it does so in few steps. However, the algorithm may or may
not converge to a global minimum, depending on the initial
configuration. One obvious problem arises with surfaces that
have few geometric features: two aligned partial scans of a
cylindrical surface can slide relative to each other while the
distance between corresponding points remains zero. When
available, features in co-acquired texture images can help
solve this underconstrained problems (see Section 3.3).

Variations of the algorithm differ in how the candidate

matching pairs are identified, which pairs are used in
computing the rigid transformation, and in the type of
optimization procedure used. Besl and McKay [13] use the
Euclidean closest point as the matching candidate to a given
point. Chen and Medioni [14] find the intersection between
a line normal to the first surface at the given point and
the second surface, then minimize the distance between the
given point and the tangent plane to the second surface at the
intersection point. This technique has two advantages: it is
less sensitive to non-uniform sampling, and poses no penalty
for two smooth surfaces sliding tangentially one with respect
to the other, a desirable behavior because in flat areas false
matches can easily occur. See Figures 3 and 4.

Points from the first surface (control points) can be

selected using uniform subsampling, or by identifying
surface features. The set of candidate pairs can be weighted
and/or pruned based on estimates of the likelihood of
an actual match, and confidence in the data. Zhang [15]
introduces a maximum tolerable distance and an orientation
consistency check to filter out spurious pairings. Dorai
et al. [16] model sensor noise and study the effect of
measurement errors on the computation of surface normals.
They employ a minimum variance estimator to formulate the

Figure 3: One step of the ICP algorithm. Point matches
are defined based on shortest Euclidean distance. Scan P is
then transformed to minimize the length of the displacement
vectors, in the least-squares sense.

Figure 4: In Chen and Medioni’s method, a matching pair is
created between a control point p on scan P and the closest
point q on the tangent plane to Q at q

. q

is the sample point

on Q closest to the intersection with the line

perpendicular

to P in p.

error function to be minimized. They report more accurate
registration results than Chen and Medioni’s original method
in controlled experiments. In related work, Dorai et al. [17]
check distance constraints (given points p

and p

on the

first surface, and corresponding points q

, q

on the second

surface,

−

< ε

must hold) to prune

incompatible matches, also leading to improved registration
results. Many researchers have proposed incorporating other
features for validating matches: for example thresholding
the maximum distance, discarding matches along surface
discontinuities, evaluating visibility, and comparing surface
normals, curvature or surface color information (see for
example the good review in [18]). Use of the texture images
as an aid to registration is further discussed in Section 3.3.

Given the two sets of matching points P

= {

, . . . ,

}

= {

, . . . ,

}

, the next problem is computing a rotation

matrix R and translation vector T such that the sum of
squares of pair wise distances

−

(

)

is minimized. This problem can be solved in closed form by
expressing the rotation as a quaternion [19], by linearizing
the small rotations [14], or by using the Singular Value
Decomposition. More statistically robust approaches have

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153

been investigated to avoid having to preprocess the data to
eliminate outliers [20,21].

3.2. Registration of multiple views

When pair wise registration is used sequentially to align
multiple views errors accumulate, and the global registration
is far from optimal. Turk and Levoy [22] use a cylindrical
scan that covers most of the surface of the object, and then
incrementally register other scans to it. In their variation of
ICP, they compute partial triangle meshes from the range
scans, then consider the distance from each vertex of one
mesh to the triangulated surface representing the other scan.

Bergevin et al. [23] extend the incremental approach to

handle multiple views. One of the views is selected as
the central (or reference) view. All the other views are
transformed into the reference frame of the central view.
At each iteration, each view is registered with respect to all
other views using a varation of Chen and Medioni’s method.
The process is repeated until all incremental registration
matrices are close to the identity matrix. Benjemaa and
Schmitt [24] use a similar approach, but accelerate finding
matching pairs by resampling the range images from a
common direction of projection, and then performing the
searches for the closest points on these images.

Pulli [25] describes another incremental multiview regis-

tration method that is particularly suited to the registration
of large datasets. Pulli’s method consists of two steps: in the
first step, range scans are registered pair wise using Chen and
Medioni’s method. Matching points are discarded if they lie
on scan’s boundaries, if the estimated normals differ by more
than a constant threshold, or when their distance is too large.
A dynamic fraction, that increases as the registration gradu-
ally improves, of the best remaining pairs (the shorter ones)
is then used for the alignment. After this initial registration,
the overlap areas of each pair of scans is uniformly sampled,
and the relative position of sample points stored and used in
the successive step: the algorithm will assume that the pair
wise registration is exact and will try to minimize relative
motion. The second step considers the scans one at a time,
and aligns each to the set of scans already considered. An
inner loop in the algorithm considers all the scans that over-
lap with the current scan, and recursively aligns each of these
scans until the relative change is smaller than a threshold,
diffusing error evenly among all scans. By using a small
number of pairs of points in the global registration phase,
the need to have all the scans in memory is eliminated.

Blais and Levine [26] search for a simultaneous solution

of all the rigid motions using a simulated annealing
algorithm. Execution times for even just a few views are
reportedly long. Neugebauer [27] uses the Levenberg–
Marquardt method to solve a linearized version of the
least-squares problem. A resolution hierarchy is used to

improve robustness and efficiency. Invalid matches are
detected and discarded at each iteration.

A different class of methods models the problem by

imagining a set of springs attached to point pairs, and
simulating the relaxation of the dynamic system. Stoddart
and Hilton [28] assume that point pairs are given and
remain fixed. Eggert et al. [18] link each data point to
the corresponding tangent plane in another view with a
spring. They use a hierarchical subsampling that employs
an increasing number of control points as the algorithm
progresses, and update correspondences at each iteration.
They report better global registration error and a larger
radius of convergence than other methods, at the expense of
longer computation times. Their method also assumes that
each portion of the object surface appears in at least two
views.

3.3. Using the textures to aid registration

Images that record the ambient light reflected from an object
(rather than a structured light pattern used for triangulation)
may also be captured coincidently with the range images.
Color or grayscale images are recorded to be used at texture
maps (see Section 7). Range and texture images in systems
that acquire both coincidently are registered to one another
by calibration. That is, the relative position and orientation
of the texture and range sensors are known, and so the
projective mapping of the texture image onto the range
image is known. When texture images registered to the
range images are available, they may be used in the scan
registration process. This is particularly advantageous when
the texture images have a higher spatial resolution than the
range images, and/or the object itself has features in the
surface texture in areas that have few geometric features.

Texture images may be used in the initial alignment

phase. Gagnon et al. [29] use texture data to assist a human
operator in the initial alignment. Pairs of range images are
aligned manually by marking three points on overlapping
texture images. The locations of the matching points are
refined by an algorithm that searches in their immediate
neighborhoods using image cross-correlation [30]. A
least-squares optimization follows to determine a general
3D transformation between the scans that minimizes the
distances between the point pairs.

Roth [9] used textures in an automatic initial alignment

procedure. “Interest” points in each texture image, such
as corners, are identified using any of a variety of image
processing techniques. A 3D Delaunay tetrahedralization is
computed for all interest points in each scan. All matching
triangles are found from pairs of potentially overlapping
scans, and the transformation that successfully registers the
most matching triangles is used. The advantage of using
the triangles is that it imposes a rigidity constraint that
helps insure that the matches found are valid. The method

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F. Bernardini and H. Rushmeier / 3D Model Acquisition

requires an adequate number of “interest” points in the
textures. However, a relatively sparse pattern of points can
be projected onto an object using laser light to guarantee
that such points are available. Projected points were added to
texture maps in the case study presented by Bernardini and
Rushmeier [31], however the number of points per scan were
not adequate for a completely automatic initial alignment.

Texture images may also be used in the refinement of the

initial alignment. In general, there are two major approaches
to using texture image data in the refinement phase. In one
approach, the color image values are used as additional
coordinates defining each point captured in the scan. In the
other approach, matching operations are performed using the
images directly.

Johnson and Kang [32,33] describe a method in which

they use color from a texture as an additional coordinate
for each point in an ICP optimization. Because the range
images they use are of lower spatial resolution than the
texture images, the range images are first supersampled
to the texture resolution, and a color triplet is associated
with each 3D point. The color triplets need to be adjusted
to be comparable in influence to the spatial coordinates.
They recommend scaling the color coordinates so that
the range of values matches the range of values in the
spatial coordinates. Further, to minimize image-to-image
illumination variations they recommend using color in terms
of Y I Q rather than RG B, and applying a scale factor to
the luminance, Y coordinate, that is much smaller than the
chrominance I Q coordinates. The closest point search now
becomes a search in 6D space, and a 6D k-d tree is used
to accelerate the search. For tests using scanned models
of rooms which have many planar areas with high texture
variation, they demonstrate order of magnitude reductions
in alignment errors. Sch¨utz et al. [34] present a similar
extended-coordinate ICP method, that uses scaled normals
data (with normals derived from the range data) as well as
color data.

The alternative approach to using texture image data is to

perform matching operations on image data directly. This
allows image structure to be exploited, and avoids search
in high dimensional coordinate space. To compare texture
images directly, these types of methods begin by using
the range scan and an initial estimate of registration to
project the texture images into a common view direction, as
illustrated in Figure 5.

Weik [35] projects both the texture image and the texture

gradient image of a source scan to be aligned with a sec-
ond destination scan. The difference in intensities in the two
images in the same view are then computed. The texture dif-
ference image and gradient image are then used to estimate
the locations of corresponding points in the two images. A
rigid transformation is then computed that minimizes the
sum of the 3D distances between the corresponding point

Figure 5: Registration methods that work with images begin
by projecting overlapping textures into the same view. Here
geometries S

and S

are used to project the corresponding

texture maps D

and D

into the same view as a third scan

pairs. Pulli [36] describes a method similar to Weik’s that
replaces the use of image gradient and differences with a full
image registration to find corresponding points. Pulli’s tech-
nique uses a version of planar perspective warping described
by Szeliski and Shum [37] for image registration. To make
the registration more robust, Pulli describes a hierarchical
implementation. Similar to Kang and Johnson, Pulli exam-
ines alternative color spaces to minimize the effects of illu-
mination variations. For the test cases used—small objects
with rich geometric and textural features—there appears to
be no advantage of using images in color spaces other than

RG B.

Both Weik’s and Pulli’s methods require operations on the

full high-resolution texture images. A high degree of overlap
is required, and scan-to-scan variability in illumination
introduces error. Fine scale geometry is matched only if
these details are revealed by lighting in the images. Both
methods can be effective if there are substantial albedo
variations in the scans that dominate illumination variations.

Bernardini et al. [38] present a registration method

that combines elements of several of the other texture-
based techniques. The initial alignment is first refined
with a purely geometric ICP. Similar to Weik and Pulli,
the texture images are projected into a common view.
Similar to Roth, feature points are located in the texture
images. However, unlike Roth the method does not attempt
to match feature points. Rather, similar to the approach
by Gagnon et al. the initial correspondences are refined
by doing a search in a small neighborhood around each
point, and finding corresponding pixels where an image
cross-correlation measure is minimized. A rigid rotation is
then found that minimizes the distance between the newly
identified corresponding points.

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3.4. Future directions

Successful

refinement

initial

registration

has

been demonstrated for a large class of objects. This
step does not appear to be a major obstacle to a fully
automatic model-building pipeline. Robust solutions for the
automatic alignment of totally uncalibrated views are not
available, although some progress is being made. Scanner
instrumentation with an approximate positioning device
seems a feasible solution in most cases. Very promising is
the use of improved feature-tracking algorithms from video
sequences as an inexpensive way of producing the initial
registration estimate.

4. Line-of-sight Error

After the scans have been aligned the individual points
would ideally lie exactly on the surface of the reconstructed
object. However, one still needs to account for residual error
due to noise in the measurements, inaccuracy of sensor
calibration, and imprecision in registration. The standard
approach to deal with the residual error is to define new
estimates of actual surface points by averaging samples from
overlapping scans. Often the specific technique used is cho-
sen to take advantage of the data structures used to integrate
the multiple views into one surface. Because of this, details
of the assumed error model and averaging method are often
lost or overlooked by authors. We believe that this problem
is important enough to deserve a separate discussion. In
addition, line-of-sight error compensation, together with
resampling and outlier filtering, is a necessary preprocessing
step for interpolatory mesh integration methods.

Among the first to recognize the need for a mathemat-

ical model of scanner inaccuracies and noise were H´ebert
et al. [40], in the context of data segmentation and poly-
nomial section fitting. Their error model incorporates the
effects of viewing angle and distance, and is expressed as
an uncertainty ellipsoid defined by a Gaussian distribution.
Other sources of non-Gaussian error, such as shadows, sur-
face specularities and depth discontinuities, which generally
produce outliers, are not included in the model. For a typical
triangulation scanner the error in estimating the x, y position
of each sample is much smaller than the error in estimat-
ing the depth z. Therefore the ellipsoid is narrow with its
longer axis aligned with the direction towards the sensor,
see Figure 6. Building on the work of H´ebert et al. [40],
Rutishauser et al. [39] define an optimal reconstruction of a
surface from two sets of estimates, in the sense of probability
theory. However, they have to resort to some approxima-
tions in their actual computations. For a measured point on
one scan, they find the best matching point (again, in the
probabilistic sense) on the triangle defined by the three clos-
est samples on the second scan. The optimal estimation of
point location is then computed using the modified Kalman
minimum-variance estimator.

Measurement 2

Real surface

Measurement 1

Figure 6: Probabilistic model of measurement error
(adapted from Rutishauser et al. [39]).

Soucy and Laurendeau [41] model error in a laser triangu-

lation system as proportional to the fraction of illuminance
received by the sensor, expressed by the cosine square of
the angle between the surface normal at the measured point
and the sensor viewing direction. Overlapping range data is
resampled on a common rectangular grid lying on a plane
perpendicular to the average of the viewing directions of
all contributing scans. Final depth values are computed as
weighted averages of the resampled values, where the weight
used is the same cosine square defined above. These points
are then connected into a triangle mesh.

Turk and Levoy [22] employ a similar method, but invert

the steps of creating a triangulated surface and finding better
surface position estimates. In their approach individual range
scans are first triangulated, then stitched together. In areas of
overlap, vertices of the resulting mesh are moved along the
surface normal to a position computed as the average of all
the intersection of a line through the point in the direction of
the normal and all the overlapping range scans.

Neugebauer [27] adjusts point positions along the scanner

line-of-sight. He uses a weighted average where each weight
is the product of three components: the first is the cosine
of the angle between surface normal and sensor viewing
direction (if the cosine is smaller than 0

1, the weight

is set to zero); the second contribution is a function that
approximates the square distance of a sample point to the
scan boundary, allowing a smooth transition between scans;
the third component is Tukey’s biweight function, used to
filter outliers. The weighting is applied iteratively.

In volumetric methods line-of-sight error compensation

is done by computing a scalar field that approximates the
signed distance to the true surface, based on a weighted
average of distances from sample points on individual range
scans. The details of the various methods will be discussed
in the next section.

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5. Scan Integration

For most applications, it is desirable to merge the aligned
multiple scans into a unified, non-redundant surface repre-
sentation. A significant amount of research in this direction
has been done in the past. In this section, we will try to clas-
sify this work based on the type of assumptions and approach
taken, and we will point to recent publications that are repre-
sentative of each category, without trying to exhaustively cite
the vast literature available on this subject. Previous reviews
of work in this field include [42–44].

The goal of scan integration is to reconstruct the geometry

and topology of the scanned object from the available data.
The problem is difficult because in general the data points
are noisy, they may contain outliers, parts of the surface may
not have been reached by the scanner, and in general there is
no guarantee that the sampling density is even sufficient for
a correct reconstruction.

Some progress is being made in characterizing the prob-

lem more rigorously, at least in restricted settings. A first
classification of methods can be made based on whether the
input data is assumed to be unorganized points (point cloud)
or a set of range scans. Techniques that deal with the first
kind of input are more general, but also usually less robust
in the presence of noise and outliers. The second category
uses information in addition to simple point position, such as
estimated surface normal, partial connectivity embedded in
the range scan, sensor position, to better estimate the actual
surface.

A second classification groups techniques based on the ap-

proach taken to reconstruct surface connectivity. A practical
consequence of this choice is the size of the problem that can
be solved using given computing resources. We will review
selected work based on this second categorization.

5.1. Delaunay-based methods

The Delaunay complex D

(

)

associated with a set of points

S in R

decomposes the convex hull of S and imposes a

connectivity structure. Delaunay-based methods reconstruct
a surface by extracting a subcomplex from D

(

)

, a process

sometime called sculpting. This class of algorithms usually
assumes only a point cloud as input. A recent review and
unified treatment of these methods appears in [45].

One technique to select an interesting subcomplex, in fact

a parameterized family of subcomplexes, is based on alpha-
shapes [46]. Bajaj et al. [44,47] use a binary search on
the parameter

to find a subcomplex that defines a closed

surface containing all the data points. Smaller concave
features not captured by the alpha-shape are found with the
use of heuristics. The surface is then used to define a signed
distance. A C

implicit piecewise-polynomial function is

then adaptively fit to the signed distance field.

A commercial software product by Geomagic is based on

a different technique to extract the subcomplex, called the
wrap complex [48]. The technique can handle non-uniform
samplings, but requires some interactive input.

Amenta et al. [49,50] introduce the concept of crust, the

subcomplex of the Delaunay complex of S

∪

P, where P

is the set of poles of the Voronoi cells of S, formed by only
those simplices whose vertices belong to S. The poles of
a sample point s

∈

S are the two farthest vertices of its

Voronoi cell. The algorithm automatically handles non-
uniform samplings, and its correctness, under somewhat
stringent sampling density conditions, has been proven, both
in the sense of a topologically correct reconstruction and of
convergence to the actual surface for increasing sampling
density. Experimental results prove that the algorithm
performs well in practice for much less dense samplings
than the theoretical bound. Based on a similar concept,
but leading to a more efficient and robust implementation
is the power crust algorithm [51,52]. The first step of the
power crust algorithm is to compute a piecewise-linear
approximation of the medial axis transform, interpolating
the poles P of the Voronoi cells of S, defined as above. The
poles are weighted with the associate (approximate) radius
of the maximal balls that do not intersect the surface. The
second step computes a piecewise-linear approximation of
the surface as a subset of the faces of the power diagram
of the set of weighted poles. One additional benefit of the
algorithm is that it produces a closed (“watertight”) surface
in the presence of uneven sampling density. Sampling
assumptions and theoretical guarantees are defined in [52].
Practical extensions to deal with sharp features, holes and
noise are discussed in [51]. Experimental results for datasets
containing several hundred thousand points are shown.

Also using the concept of poles to define a local surface

approximation is the cocones algorithm proposed by Amenta
et al. [53]. Here the poles of the Voronoi diagram of P are
used to define an approximate normal for each sample point.
The complement (restricted to the Voronoi cell of the point)
of a double cone centered at p, with axis aligned with the
sample point normal and an aperture of 3

π/

8, is defined

as the cocone of p. It is proved that the cocone constitutes
a good approximation for the surface in the neighborhood
of p. The local surface reconstrucion is then defined by
the collection of Delaunay triangles incident on p that are
dual to Voronoi edges contained in the cocone of p. The
union of all the local reconstruction constitutes a superset
of the final manifold triangulation, which is obtained with a
global prune and walk algorithm. These results are presented
in the context of a practical implementation by Dey et al.
[54]. The authors employ a divide and conquer method
based on an octree partition of the input points to avoid
a global Voronoi computation. The pointsets contained in
each octree node are padded with enough points from
neighboring nodes to enforce the computation of compatible
triangulations along common boundaries. Again, a global

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prune and walk algorithms selects a manifold subset of
the candidate triangles. The divide and conquer approach
leads to reduced computation times and memory usage,
allowing the treatment of datasets with millions of samples
on common workstations.

In the context of Delaunay-based methods it is possible

to study the sampling conditions the guarantee a correct
reconstruction. Attempts so far have been mostly restricted
to the 2D case [55–57], with the exception of [50] and [52].
The main shortcomings of these methods are their sensitivity
to noise and outliers (these algorithms interpolate the data
points, so outliers must be removed in preprocessing), and
their computational complexity. Robustly computing and
representing the connectivity of the 3D Delaunay complex
can be a costly task. Experimental results are usually limited
to “clean” datasets with less than a few hundred thousand
points (with the exception of [54]).

5.2. Surface-based methods

Surface-based methods create the surface by locally param-
eterizing (or implicitly assuming a local parameterization
of) the surface and connecting each points to its neighbors
by local operations. Some methods make use of the partial
connectivity implicit in the range images.

The zippering approach of Turk and Levoy [22] works by

first individually triangulating all the range scans. The partial
meshes are then eroded to remove redundant, overlapping
triangles. The intersecting regions are then locally retrian-
gulated and trimmed to create one seamless surface. Vertex
positions are then readjusted to reduce error, as described in
Section 4.

Soucy and Laurendeau [41] use canonical Venn diagrams

to partition the data into regions that can be easily parameter-
ized. Points in each region are resampled and averaged (see
Section 4), and locally triangulated. Patches are then stitched
together with a constrained Delaunay algorithm.

A recent paper by Bernardini et al. [58] describes an algo-

rithm to interpolate a point cloud that is not based on sculpt-
ing a Delaunay triangulation. Their method follows a region
growing approach, based on a ball-pivoting operation. A ball
of fixed radius (approximately the spacing between two sam-
ple points) is placed in contact with three points, which form
a seed triangle. The three edges initialize a queue of edges
on the active boundary of the region. Iteratively, an edge
is extracted from the queue, and the ball pivots around the
extracted edge until it touches a new point. A new triangle is
formed, the region boundary updated, and the process con-
tinues. The approach can easily be extended to restart with
a larger ball radius to triangulate regions with sparser data
points. This method was implemented to make efficient use
of memory by loading at any time only the data in the region
currently visited by the pivoting ball, rather than the entire

dataset. This allowed the triangulation of a large collection
of scans with millions of samples.

Gopi et al. [59] compute local 2D Delaunay triangulations

by projecting each point and its neighborhood on a tangent
plane, and then lift the triangulation to 3D.

Surface based methods can easily process large datasets,

and can handle (and compensate for) small-scale noise in
the data. Robustness issues arise when the noise makes it
difficult to locally detect the correct topology of the surface.

5.3. Volumetric methods

Volumetric methods [60–62] are based on computing
a signed distance field in a regular grid enclosing the
data (usually, only in proximity of the surface), and then
extracting the zero-set of the trivariate function using the
marching cube algorithm [63]. The various approaches
differ on the details of how the signed distance is estimated
from the available data.

Curless and Levoy [60] compute the signed distance from

each scan by casting a ray from the sensor through each
voxel near the scan. The length of the ray from the voxel to
the point in which it intersects the range surface is computed
and accumulated at the voxel with values computed from
other scans using weights dependent, as usual, on surface
normal and viewing direction. This approach may lead to a
biased estimate of surface location, as noted in [61]. Hilton
et al. [62] also blend signed distances from individual scans,
and use extra rules to handle correctly the case of of different
surfaces in close proximity, both with the same and opposite
orientation. Wheeler et al. [61] propose a solution that is
less sensitive to noise, outliers, and orientation ambiguities.
They assign to each voxel the signed distance to the closest
point on the consensus surface, a weighted average of
nearby measurements. Only measurements for which a user-
specified quorum of samples with similar position and
orientation is found are used.

Boissonnat and Cazals [64] use natural neighbor interpo-

lation to define a global signed distance function. The natural
neighbors of a point x are the neighbors of x in the Delau-
nay triangulation of P

{

}

. Using natural neighbors avoids

some of the pitfalls of other local surface approximations
(for example taking just the points within a given distance
from x, or its k closest neighbors). However, it requires the
computation of a global Delaunay triangulation, which lim-
its the size of the datasets that can be handled by the al-
gorithm in practice. Since the Delaunay triangulation of the
points must be computed, it can also be used as the starting
point for the construction of piecewise-linear approximation
of the surface that satisfies a user-specified tolerance. The
initial approximation is formed by all those Delaunay trian-
gles whose dual Voronoi edge is bipolar, that is such that
the global signed distance function has different signs at its

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two endpoints. This triangulation is then incrementally re-
fined until the tolerance condition is satisfied. Examples of
reconstruction from datasets of moderate size are shown in
the paper.

Volumetric methods are well suited for very large datasets.

Once the individual range scans have been processed
to accumulate signed distance values, storage and time
complexity are output sensitive: they mainly depend on the
chosen voxel size, or resolution of the output mesh. Memory
usage can be reduced by explicitly representing only voxels
in close proximity to the surface [60] and by processing
the data in slices. The choice of voxel size is usually left
to the user. Small voxels produce an unnecessarily large
number of output triangles and increase usage of time and
space. Large voxels lead to oversmoothing and loss of small
features. These problems can be alleviated by using an
adaptive sampling (e.g. octree rather than regular grid [65])
and/or by postprocessing the initial mesh with a data fitting
procedure [66–68].

Volumetric methods are also well suited to producing

water-tight models. By using the range images to carve out a
spatial volume, an object definition can be obtained without
holes in the surface. Reed and Allen [69] demonstrate the
evolution of a solid model from a series of range images,
with the data from each image carving away the solid that
lies between the scanner and each sample point. Rocchini et
al. [70] also describe a volumetric method that fills holes.

5.4. Deformable surfaces

Another class of algorithms is based on the idea of deform-
ing an initial approximation of a shape, under the effect of
external forces and internal reactions and constraints.

Terzopoulos et al. [71] use an elastically-deformable

model with intrinsic forces that induce a preference for
symmetric shapes, and apply them to the reconstruction
of shapes from images. The algorithm is also capable of
inferring non-rigid motion of an object from a sequence of
images.

Pentland and Sclaroff [72] adopted an approach based on

the finite element method and parametric surfaces. They start
with a simple solid model (like a sphere or cylinder) and
attach virtual “springs” between each data point and a point
on the surface. The equilibrium condition of this dynamic
system is the reconstructed shape. They also show how the
set of parameters that describe the recovered shape can be
used in object recognition.

Recently a number of methods based on the concept of

levels sets have been proposed. These methods combine
a robust statistical estimation of surface position in the
presence of noise and outliers with an efficient framework
for surface evolution. See e.g. [73,74].

6. Postprocessing

Postprocessing operations are often necessary to adapt the
model resulting from scan integration to the application
at hand. Very common is the use of mesh simplification
techniques to reduce mesh complexity [75].

To relate a texture map to the integrated mesh, the surface

must be parameterized with respect to a 2D coordinate
system. A simple parameterization is to treat each triangle
separately [32,76] and to pack all of the individual texture
maps into a larger texture image. However, the use of
mip-mapping in this case is limited since adjacent pixels
in the texture may not correspond to adjacent points on
the geometry. Another approach is to find patches of
geometry which are height fields that can be parameterized
by projecting the patch onto a plane. Stitching methods [2]
use this approach by simply considering sections of the
scanned height fields as patches.

Many parameterization methods have been developed

for the general problem of texture mapping. Several
methods seek to preserve the relative distance between 3D
points in their pairing to a 2D coordinate system [77,78].
Marschner [79] describes an example of applying a
relative distance preserving parameterization in a scanning
application. The surface is subdivided into individual
patches by starting with seed triangles distributed over the
object, and growing regions around each seed. Harmonic
maps are found to establish a 2D coordinate system for each
patch, so individual patches need not be height fields.

Sloan et al. [80] have observed that maintaining relative

distances may not produce optimal parameterizations
for texture mapping. They suggest that uniform texture
information, rather than distance preservation, should drive
the parameterization. They applied this idea to synthetic
textures only, but it may prove to be an effective approach
in some scanning applications as well.

Another important step for applications that involve edit-

ing and animating the acquired model is the conversion of
the mesh to a parametric, higher-order surface representa-
tion, for example using NURBS or a subdivision scheme.

The technique of Hoppe et al. [81] starts with a triangle

mesh and produces a smooth surface based on Loop’s sub-
division scheme [82]. Their method is based on minimizing
an energy function that trades off conciseness and accuracy-
of-fit to the data, and is capable of representing surfaces
containing sharp features, such as creases and corners.

More recently, Eck and Hoppe [83] proposed an alter-

native surface fitting approach based on tensor-product B-
spline patches. They start by using a signed-distance zero-
surface extraction method [84]. An initial parameterization
is built by projecting each data point onto the closest face.
The method continues with building from the initial mesh
a base complex (a quadrilateral-domain complex, with the

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159

same topology of the initial mesh) and a continuous param-
eterization from the base complex to the initial mesh, lever-
aging on the work of Eck et al. [78]. A tangent-plane con-
tinuous network of tensor-product B-spline patches, having
the base complex as parametric domain, is then fit to the
data points, based on the scheme of Peters [85]. The fitting
process is cast as an iterative minimization of a functional,
which is a weighted sum of the distance functional (the sum
of square Euclidean distances of the data points from the sur-
face) and a fairness functional (thin plate energy functional).

Another NURBS fitting technique is described by

Krishnamurthy and Levoy [86]. The user interactively
chooses how to partition the mesh into quadrilateral patches.
Each polygonal patch is parametrized and resampled,
using a spring model and a relaxation algorithm. Finally,
a B-spline surface is fit to each quadrilateral patch. In
addition, a displacement map is computed that captures the
fine geometric detail present in the data.

Commercial packages that allow a semi-automated

parametrization and fitting are available.

7. Texture

In addition to the overall shape of an object, the rendering
of high quality images requires the fine scale surface
appearance, which includes surface color and finish. We
will refer to such properties generically as the surface
texture. Beyond color and finish, texture may also include
descriptions of fine scale surface geometry, such as high
spatial-resolution maps of surface normals or bidirectional
textures.

Surface color and finish are informal terms. Color is ac-

tually a perceived quantity, depending on the illumination
of an object, human visual response, and the intrinsic spec-
tral reflectance of the object. Finish—such as smoothness
or gloss—is also not a directly acquired property, but is a
consequence of an object’s intrinsic reflectance properties.
The fundamental quantity that encodes the intrinsic proper-
ties of the surface is the Bidirectional Reflectance Distribu-
tion Function (BRDF). To fully render an accurate image,
the BRDF must be known for all points on a surface. The
BRDF f

(λ,

)

at a surface point

(

)

is the

ratio of radiance reflected in a direction

to an incident

energy flux density from direction

for wavelength

. The

BRDF can vary significantly with position, direction and
wavelength. Most scanning systems consider detailed po-
sitional variations only, with wavelength variations repre-
sented by an RG B triplet, and Lambertian (i.e. uniform for
all directions) behavior assumed. Furthermore, most scan-
ning systems acquire relative estimates of reflectance, rather
than attempting to acquire an absolute value.

Here we will consider how texture data is acquired, and

then how it is processed to provide various types of BRDF
estimates, and estimates of fine scale surface structure.

7.1. Texture-geometry registration

It is possible to capture the spectral reflectance of an
object as points are acquired with a polychromatic laser
scanner [87]. However, data for texture is typically acquired
by an electronic color camera or using conventional color
photographs that are subsequently scanned into electronic
form. The texture images need to be registered with the
acquired 3D points. The most straightforward system for
doing this is registration by calibration. That is, color images
corresponding to each range image are acquired at the same
time, using a camera with a known, measured position
and orientation relative to the sensor used for obtaining
geometry. As discussed in Section 3.3, an advantage of
this approach is that acquired texture can be used in the
geometric registration process.

When textures are acquired separately from geometry, the

texture-to-geometry registration is performed after the full
mesh integration phase. Finding the camera position and ori-
entation associated with a 2D image of a 3D object is the
well-known camera calibration problem. Numerous refer-
ences on solutions to this problem can be found in the Price’s
Computer Vision bibliography [88], Section 15.2, “Camera
Calibration Techniques.” Camera calibration involves esti-
mating both the extrinsic and intrinsic parameters. The ex-
trinsic parameters are the translation and rotation to place
the camera viewpoint correctly in the object coordinate sys-
tem. The intrinsic parameters include focal length and radial
distortion. For objects which have an adequate number of
unique geometric features, it is possible to manually identify
pairs of corresponding points in the 2D images and on the
numerical 3D object. Given such correspondences, classic
methods such as that described by Tsai [89], can be used to
register the captured color images to the 3D model [2].

For some objects it may not be possible for a user to

find a large number of accurate 2D–3D correspondences.
Neugebauer and Klein [90] describe a method for refining
the registration of a group of existing texture images
to an existing 3D geometric model. The method begins
with a rough estimate of the camera parameters for each
image in the set, based on correspondences that are not
required to be highly accurate. The parameters for all of the
texture images are improved simultaneously by assuming
the intrinsic camera parameters are the same for all images,
and enforcing criteria that attempt to match the object
silhouettes in the image with the silhouette of the 3D model,
and to match the image characteristics at locations in texture
images that correspond to the same 3D point.

Lensch et al. [91] present a method for finding the camera

position for texture images in terms of a geometric object co-
ordinate system using comparisons of binary images. First,
a binary version of each texture image is computed by seg-
menting the object from the background. This is compared to
a synthetic binary image generated by projecting the known

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geometry into a camera view based on an initial guess of
camera parameters. The values of the camera parameters are
refined by using a downhill simplex method to minimize the
difference between the binary texture image and the syn-
thetic image. In a subsequent step the camera parameters
for all views of an object are adjusted simultaneously to
minimize the error in overlapping textures from neighboring
views.

Nishino et al. [92] apply an alternative technique that

relies on image intensities rather than identifying features
or extracting contours. They employ the general approach
developed by Viola [93] that formulates the alignment as
the maximization of the mutual information between the 3D
model and the texture image.

Rather than using an ad hoc method for deciding the

positions for capturing texture images, Matsushita and
Kaneko [94] use the existing 3D geometric model to plan
the views for capturing texture. Methods to plan texture
image capture can draw on the numerous computer vision
techniques for view planning, e.g. see [88] Section 15.1.4.1,
“Planning Sensor Position.” Matsushita and Kaneko develop
a table of a set of candidate views, and the object facets
that are visible in each view. Views are selected from the
table to obtain the views that image the largest number
of yet to be imaged facets. After the view set is selected,
synthetic images which form the views are generated. For
each synthetic image the real camera then is guided around
the object to find the view that approximates the synthetic
image, and a texture image is captured. The texture image to
model registration is refined after capture using a variation
of Besl and McKay’s ICP algorithm [13] that acts on points
on the silhouettes of the real and synthetic images.

7.2. Illumination invariance

The goal of capturing texture is to obtain a surface
description that is illumination invariant—i.e. intrinsic to
the surface and independent of specific lighting conditions.
The pixel values in an image acquired by an electronic
camera depend on the environmental lighting and the
camera transfer parameters as well as the object properties.
Approximate illumination invariants can be obtained
directly by appropriate lighting and camera design. More
complete estimates require processing of the acquired
images. The variety of techniques can be understood by
examining the specific relationships between the physical
acquisition equipment and the end numerical value stored in
an image.

Figure 7 shows a generic simplified system for obtaining

a texture image. A light source with radiance L

(λ,

)

direction

from the normal of the source surface is at

distance r

from the object. Light incident from direction

is reflected with radiance L

(λ,

)

into the direction of

Figure 7: Generic geometry of texture map acquisition.

a pixel p. The radiance L

(λ)

is related to the object BRDF

by:

(λ)

(λ,

)

(λ,

)

d A

(1)

The energy per unit area and time E

(λ)

incident on the

pixel from direction

for an exposure time of

is:

(λ)

(2)

where

is the solid angle of the object area viewed by the

pixel, determined by the camera focal length and pixel size.
This is converted to a 0–255 value (for an 8-bit sensor) C
where C corresponds to the red (R), green (G) or blue (B)
channel by:

(λ)

(3)

where K is the system sensitivity, s

(λ)

is the normalized

sensor spectral response for channel C, C

is the response

for zero illumination, and

is the system non-linearity. Even

cameras with sensors that have an essentially linear response
to light may produce images that have values adjusted with
a value of

other than one for the efficient use of the 0–255

range.

7.3. Direct use of captured images

Most inexpensive systems attempt to capture a relative
estimate of Lambertian reflectance, expressed directly in
terms of RG B. A Lambertian reflector reflects the same
radiance in all directions for any incident energy flux density.

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161

The Lambertian reflectance

is the fraction of incident

energy reflected, and is related to the BRDF by:

(λ,

)

(λ,

)/π.

(4)

The radiance reflected for a Lambertian surface then is:

(λ)

(λ,

)

(λ,

)

d A

(5)

The reflected radiances measured at each pixel then are a
good estimate of the relative spatial variation for Lambertian
surfaces if n

and r

are approximately the

same for all points on the surface imaged at any given
time. Maintaining constant r

is relatively straightforward

for systems with a fixed scanner location and object placed
on a turntable. As long as the distance to the light source is
large relative to the size of the surface area being imaged,
the effect of varying r

will be small. One approach to

controlling the variation due to the changing incident angle
is to use a large diffuse light source, so that each point on
the surface is illuminated by nearly the entire hemisphere
above it. Relying on indirect illumination in a room can
achieve this effect. Alternatively, for systems that acquire
texture simultaneously with range images, a camera flash
can be used nearly collocated with the camera sensor (the
standard design for a commodity camera). Surfaces obtained
in each range image are oriented so that the surface normal
is nearly parallel in the direction of the camera sensor. The
captured points then will all be illuminated with a value of
n

close in value to 1

0. An additional advantage

of using the flash built into the camera is that it is designed
to be compatible with the spectral sensitivity of the camera
sensor to produce good color match.

Captured image data can represent rich appearance details

as can be seen by contrasting the model shown in Figure 8(b)
with a texture map with geometry alone Figure 8(a). The
details of the fur can be seen in the texture, that would
be essentially impossible to capture as geometry. However,
there are clearly shadows on the bunny’s coat that are fixed
in the texture. Figures 8(c) and (d) show the model relit from
novel directions. The texture looks flatter because the detail
shadows do not appear consistent with the overall lighting
direction.

7.4. Correcting captured images

While they produce approximations of the relative
reflectance, inexpensive camera systems leave the texture
pixels in the form given by (3). If data from such systems
are to be used in rendering systems that use true physical
parameters, a grayscale card should be used to estimate
the

of the color camera. A grayscale card image can

also be used to assess the effect of the light source and
camera spectral sensitivities on the RG B values. Absolute
reflectance values can be estimated by capturing a reference

(a)

(b)

(c)

(d)

Figure 8: An example of a texture-mapped model obtained
from an inexpensive scanner; (a) the captured geometry;
(b) texture displayed as-captured; (c) textured model relit
from above; and (d) textured model relit from the back.

white card with the object, or by obtaining separate spot
measurements of the spectral reflectance of the object.

High-end systems that capture very accurate, dense range

images, coupled with low noise high resolution color
cameras may also be used to capture texture images. In
these systems, images can be corrected using the geometric
information to adjust for variations in angle and distance.
Thresholding can be used to eliminate low values for
values in shadow, and high values in specular highlights.
Alternatively the geometry can be used to predict areas that
will be in shadow or potentially in narrow specular peaks.
Levoy et al. [95] describe the use of a CCD digital still
camera with a laser stripe laser scanner to acquire accurate
estimates of Lambertian reflectance.

7.5. Spatially uniform, directionally varying BRDF

An alternative to acquiring a spatially detailed map of BRDF
that has no directional variation, is to acquire details of
a directionally varying BRDF on objects with no spatial
variation of surface properties. Such methods have been

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Figure 9: Torrance–Sparrow inspired reflectance models
attempt to model the magnitude of Lambertian reflected
light a with a parameter

, the magnitude of directionally

reflected light b with a parameter

and the width of the

directional lobe c with a parameter

described by Ikeuchi and Sato [96] for a range and intensity
image pair, and Baribeau et al. [87] for polychromatic laser
data. These methods use systems in which the angle between
sensor and light source position is fixed. However, because
the scanner sees a uniform BRDF surface with a variety of
surface orientations, data are obtained for L

(λ,

)

for

a variety of values of

(

)

. The methods compensate for

not sampling the entire range of angles over the hemisphere
by using the observed data to fit a parametric reflectance
model. Each paper uses a version of the Torrance–Sparrow
model [97]. Torrance–Sparrow-inspired models of BRDF
are expressed generically as:

(λ,

)

(λ)/π

(λ)

(σ,

)

(6)

where

is the fraction of incident light reflected diffusely

(i.e. as a Lambertian reflector),

is the fraction of light

reflected near the specular direction in excess of the diffusely
reflected light in that direction, and g is a function that
depends on a parameter

characterizing surface roughness

as well as the angles of incidence and reflection. Methods
attempt to estimate the three parameters

and

give the shape of the reflectance function diagrammed in
Figure 9.

For example, Ikeuchi and Sato [96] begin by assuming all

pixels reflected diffusely, and estimate values of

and the

light source direction (assumed uniform across the surface).
This value is then refined by thresholding pixels which have
values well above that predicted by the product of

and

(which result either from specular reflections or

surface interreflections) and well below the predicted value

(which result from either attached or cast shadows). After
the estimates of

and

are made, an iterative process

over non-Lambertian pixels distinguishes specular versus
interreflection pixels based on observed angle relative to the
angle of reflection. From the values of radiance recorded
for specular pixel, values of the specular reflectance and
surface roughness parameter are estimated. Alternatively
Baribeau et al. [87] capture samples of BRDF for a variety of
incident/reflected angle pairs using the polychromatic range
sensor. These data are then fit to the parametric model using
a non-linear least-squares algorithm.

These spatially uniform techniques of course do not

require objects that are completely uniform, but objects with
surfaces that can be segmented into reasonably large uniform
areas.

7.6. Spatially and directionally varying BRDF

To capture both spatially and directionally varying BRDF,
methods based on photometric stereo are used. Photometric
stereo, introduced by Woodham [98] uses N images of an
object from a single viewpoint under N different lighting
conditions. Initially, photometric stereo was used to estimate
surface normals, and from the normals surface shape.
Assuming a Lambertian surface, and small light sources
of uniform strength an equation for the surface normal n

visible through each pixel p in each image m for each light
source in direction

is given by:

(7)

where G

is the image grayscale value after correction for

non-linear

values, and

is a scaling constant that includes

the light source radiance and subtended solid angle. Since
n

has unit length and thus represents only two independent

variables, we can solve three equations for n

and

Kay and Caelli [99] couple the idea of images from

a photometric stereo system with a range image obtained
from the same viewpoint to expand on the idea introduced
by Ikeuchi and Sato. Rather than sampling a variety of
directions by viewing many orientations across the surface,
multiple incident light directions are observed for each
surface point from the set of photometric images. Kay
and Caelli used high dynamic range images to be able
to capture specular objects by taking pairs of images for
each lighting condition with and without a grayscale filter.
Because the directional sampling is still sparse, the data are
fit to a Torrance–Sparrow-inspired reflectance model. The
fitting process proceeds in four passes. First, weights are
estimated to account for noise in the surface and image data.
Next, pixels are classified as to whether there is enough
data to estimate the model parameters. In the third pass
the parameters are estimated where data is adequate. In the
final pass parameters are estimated for the areas in which
there was insufficient data from the intensity maps. The only

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restriction on the technique is that interreflections are not
accounted for, so strictly the method applies only to convex
objects.

Sato et al. [100] presented a method for obtaining an

estimate of BRDF for a full object. Range and color images
are obtained for an object, with the object, sensor and light
source positions registered by calibration by moving the
object with a robot arm manipulator. After the full object is
reconstructed, the color images—showing the object from a
variety of views and illumination directions—are used to fit
a Torrance–Sparrow-inspired model. The parameter fitting
problem is simplified by separating diffusely and specularly
reflected light in each image by examining the color of each
point on the surface in various images. Assuming non-white,
dielectric materials, the diffuse component will be the color
of the object (i.e. the result of body reflection), while the
specular component will be the color of the light source (i.e.
the result of surface reflection) [101]. Because the specular
component is sampled sparsely along the surface (there is no
way to guarantee that a specular highlight will be obtained
for each point even with a large number of images) the
estimate of specular reflectance parameters are interpolated
over larger areas of the object.

Lensch et al. [102] take a “top-down” approach to

estimating spatially varying BRDF. High dynamic range
images are taken from multiple views of an object of known
shape. Initially, it is assumed that the pixel luminance all
represent samples from a single BRDF. After this global
BRDF is computed, two groups of luminances values are
formed based on their distance from the global BRDF
estimate, and two new BRDFs are computed. This splitting
process is repeated until the distance of samples in a group
from the BRDF computed from them falls to some threshold.
Point by point variations are computed by computing each
BRDF for each point on the final model as a linear
combination of the set of BRDFs formed from the groups.

7.7. Capturing reflectance and small scale structure

Methods for obtaining texture may not just estimate
reflectance, but may also capture small scale details at a
resolution finer than the underlying range image. Rushmeier
et al. [103] developed a photometric stereo system attached
to a range imaging system. The photometric system allowed
the calculation of normals maps on the surface at a higher
spatial resolution than the underlying range image. They
developed a method [104] to use the normals of the
underlying low spatial resolution range image to adjust the
images acquired by the photometric system to insure that
the fine detail normals that are computed are consistent with
the underlying mesh. Given the range images and detailed
normals, the acquired color images were then adjusted
to produce estimates of the Lambertian reflectance of the
surface. Figure 10 shows an example of an underlying low

(a)

(b)

Figure 10: An example of a normals map used to enhance
the display of geometric detail. (a) Shows the underlying
2 mm resolution geometry. (b) Shows the geometry displayed
with a 0.5 mm resolution normals map. The illumination is
from a novel direction—i.e. not the direction of any of the
illumination in any of the captured images.

resolution geometry sampled at approximately every 2 mm,
and the same geometry with a normals map added to show
detailed features every 0.5 mm.

Dana et al. [105] observed that even full BRDF and

normals maps are not adequate for capturing the change in
detail surface appearance with lighting and view for surfaces
with fine scale geometric complexity such as bread and
velvet. They developed the concept of bidirectional textures,
which are sets of images (rather than individual values) of
surfaces for varying light and viewpoint.

No scanning method has been developed to truly capture

bidirectional textures for complete objects. However, there
have been a number of techniques that use the concept of
view dependent texture maps. View dependent texture maps
were introduced by Debevec et al. [106] in the context
of building models from photogrammetry and generic
parameterized models. A different texture map, obtained
from points closest to the current view, is used for each
view of a model. View dependent texture maps can portray
the variation of surface appearance due to changes in
self-occlusion as well as BRDF. View dependent texture
maps as described in [106] are not varied for different
lighting conditions. Pulli et al. [107] applied the idea to
texturing range images. In an interactive viewer, only the
range and color images that would be visible from the
current view are used. Texture is synthesized on the fly
using a combination of the three acquired textures closest
to the current view. The effect is to render the effects of
BRDF, occlusion and shadowing for the lighting conditions
that existing during acquisition. Since the textures were
acquired with both lighting and view changing, the effect
is approximately the same as observing the object with a
headlight at the viewer position.

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Miller et al. [108] developed the idea of surface light fields

that represent the light leaving each point on a surface in
all directions. They applied this idea to synthetic models.
Nishino et al. [109] developed the Eigen-Texture system
to capture and represent surface light field data. In their
method, a light is fixed to the object coordinate system,
and M views of an object are obtained using a turntable.
The result is M small texture maps for each triangle on a
simplified version of the geometry obtained from the range
images. The series of M small texture maps are compressed
by performing an eigenstructure analysis on the series and
finding a small number of textures that can be used as an
approximate basis set to form textures in the view space
encompassed by the originally M textures. The textures then
represent the effects of BRDF, self-shadowing, and self-
occlusion effects for the single lighting condition. Eigen-
Textures obtained for many different lighting conditions can
be combined linearly to generate textures for novel lighting
conditions. Wood et al. [110] proposed an alternate method
for capturing and storing surface light fields using a different
approach for data compression. They also demonstrated how
small changes could be made in an object represented by
surface light fields while maintaining a plausible, if not
completely accurate, appearance.

8. Texture Map Reconstruction

Texture map reconstruction involves combining all the tex-
ture maps acquired for an object into a single non-redundant
map over the entire object. Texture map reconstruction may
start with meshes that store a color for each vertex point,
and form images. Other methods begin with acquired (and
possibly processed) images. Methods for texture map recon-
struction starting with images may either select one piece
from one acquired image to texture each surface area or they
may combine multiple maps that cover each surface area.

Soucy et al. [76] developed a method for generating a

texture map from color per vertex models. The dense triangle
mesh is simplified to reduce the triangle count. Barycentric
coordinates are saved for each color triplet for which the
vertex has been removed. Separate texture maps are created
for each triangle in the simplified mesh. The texture image
for each triangle is required to be a half-square triangle.
Appropriate colors are assigned to texture pixels using the
original vertex colors and their barycentric coordinates.
Continuity between the texture maps is insured by requiring
vertices to coincide with pixel centers in the texture map,
and by requiring the number of pixels along the edges of
maps for adjacent texture maps to be integer multiples of one
another. With this constraint, pixels representing the same
location on two different texture maps can be forced to have
identical values. All of the individual texture maps are then
packed into a single texture image.

Methods for reconstructing texture from sets of images

have in common that for each texture image, the triangles

Figure 11: In determining which parts of a captured texture
image A

can be used in a texture map A for a surface P,

occlusion effects must be accounted for. Here the captured
texture pixel a

should not appear in the final texture map

pixel a

because the point p

is occluded from the point of

view of camera C

visible in that image are identified. As shown in Figure 11,
simply checking that a surface is contained within the image
view frustum and is oriented toward the camera position is
not adequate. A full rendering of the model is required to
detect whether another surface occludes the surface being
mapped.

Methods for reconstructing non-redundant texture for in-

expensive scanner systems that use captured images directly
for building maps generally select a piece of a single im-
age for each triangle in the mesh. An example of this sort
of method is described by Matsumoto et al. [111]. There
are two desirable properties in selecting the image that con-
tributes the texture for a given triangle—it should be from
the viewpoint in which the triangle projects to the largest
area, and it should be from the same image as adjacent tri-
angles. Matsumoto et al. cast this as an energy minimization
problem, where the energy is defined as the difference be-
tween a penalty function expressing the distance between the
images used for adjacent triangles and the scaled projected
area of a triangle on an an image.

An example of a texture map produced by an inexpensive

scanning system that selects image segments as large as
possible and then packs them into a single texture map is
shown in Figure 12 for the model that was shown in Figure 8.

Individual textures may be selected for regions of the

surface encompassing multiple triangles. Rocchini et al.
[2] describe a method for selecting one source texture per
region, with regions covered by a single source map made

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Figure 12: An example of the texture image used to display
the model in Figure 8.

as large as possible. First, a list of images containing each
vertex is found. Then in an iterative procedure, regions are
grown so that large regions of the surface are mapped to
the same image. The problem remains then of adjusting the
boundaries between regions so seams are not visible. For the
triangles on boundaries between different source images, a
detailed local registration is performed so that details from
the two source texture images match.

Methods that use zippering for mesh integration use the

original texture map for each section of range image used in
the final mesh. Just as overlapping meshes are used to adjust
point positions to reduce line-of-sight errors, overlapping
textures are used to adjust texture values to eliminate
abrupt color changes in the texture. Texture in the overlap
region is the weighted average of the two overlapping
textures, with the weight of each texture decreasing with
distance to the edge of the corresponding range image.
Figures 13(a) and (b) show two overlapping scans to be
merged. Figure 13(c) shows the result after the geometries
have been zippered (or stitched) together, with the original
texture maps. Figure 13(d) shows the final result after the
texture in the overlap region has been adjusted.

Rather than just use multiple textures pair wise, other

methods use data from multiple textures that contain each
triangle. Such methods are successful and avoid ghosting
and blurring artifacts if they are preceded by registration
techniques that make use of texture image data. Johnson
and Kang [32] use all textures containing each triangle,
with a weighted average that uses the angle of the surface
normal to the direction to camera for each image as the
weight. In Pulli et al. ’s [107] view-dependent texturing uses

(a)

(b)

(c)

(d)

Figure 13: An example of the zippering approach to
combining texture maps: (a) and (b) show two input scans
to be merged; (c) shows the merged textures without
adjustment; (d) shows the final texture after adjustment.

three types of weights in combining three source textures.
First a weight representing the angle between the current
view and each source view is computed. Then, similar to
Johnson and Kang, the surface normal to view angle is used.
Finally, similar to the zippering methods, these weights are
combined with a weight that decreases with distance to the
texture edge. Neugebauer and Klein [90] combine multiple
textures using weights that account for the angle of the
surface normal and view direction, and the distance to the
edge of the region of a texture image that will be used in the
final model. Because they use images that may still contain
artifacts such as specular highlights, Neugebauer and Klein
use a third weight that eliminates outliers.

Bernardini et al. [38] describe a method that uses

all available maps representing reflectance and normals
at each triangle obtained using the system described
in [103]. To minimize color variations, before the maps
representing reflectance are combined, a global color
balance is performed [104]. A set of points are randomly

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sampled on the integrated surface mesh. All of the maps
representing reflectance are projected onto the integrated
mesh, and for each point all of the maps that contain the
point are identified. A set of linear equations is formed for a
scalar correction factor for each channel for each image that
sets the colors in each map representing a common point
equal. A least squares solution is performed to compute
the correction factors for this over determined system. The
normals maps were previously made consistent with one
another by the process used to make them consistent with
the underlying integrated mesh. The map values are then
combined using three weights. Similar to the other methods,
one is based on the area of the triangle in the image using
the dot product of normal to view direction, combined with
the distance from the camera sensor to the triangle. Another
is a weight which diminishes with distance to the edge of the
texture. Finally a third weight is used that indicates whether
it was possible to compute a normal from the photometric
images, or if the normal from the underlying integrated
mesh was used.

9. Scanning Systems and Projects

By combining different features from the various methods
for each step outlined in Figure 1, it is possible to compose
many different systems for producing a 3D model of an
existing object suitable for computer graphics modeling
and rendering. The design of the particular processing
pipeline depends on the requirements of the end application,
constrained by the budgetary limitations for acquiring the
data.

A number of scanning applications with emphasis on

graphic display as the end product have been documented.
Major application areas include scanning historical objects
for scholarly study and virtual museums, scanning of
humans and e-commerce.

The National Research Council of Canada has conducted

a series of projects over the past 15 years scanning historical
artifacts ranging from 3D representations of oil paintings
to archeological sites. Their experiences acquiring and
displaying geometry and color reflectance of a variety
of objects are described in various publications [112]. In
particular Beraldin et al. [113] present a detailed practical
discussion of using a portable scanner (i.e. suitcase-sized)
to scan a number of sculptural and architectural features
on site in Italy. As an example of current capabilities, they
describe the scanning of Pisano’s Madonna col Bambino in
the Cappella degli Scrovegni in Padova. The were able to
acquire 150 scans at 1 mm resolution of the approximately
1 m tall statue in a 7 h period. The range images were
registered and integrated using Polyworks

software.

Many other cultural heritage projects are ongoing or

recently completed. Zheng, of the Kyushu Institute of
Technology in collaboration with the Museum of Qin

Figure 14: (left) A photograph of Michelangelo’s Florentine
Piet`a. (right) A synthetic picture from the 3D computer
model.

Shihuang Terra Cotta Warriors and Horses is conducting an
extensive scanning project to build models of relics found
at the site [114]. A custom portable laser scanner coupled
with a digital video camera was designed for the project.
Besides presenting the models as they are, the project seeks
to facilitate piecing together damaged relics, and digitally
restoring full color to figures using pigment fragments that
have been found.

Ikeuchi et al. have developed many techniques for the

steps in the model acquisition pipeline. These techniques
are now being applied to building a model of the 13 m
tall Kamakura Buddha from color images and time-of-flight
range scanning data [115].

Levoy et al. recently used a combination of laser

triangulation range scanning and high-resolution digital
color imaging to acquire models of many of the major
works of Michelangelo [95]. The high-end equipment
employed produced large quantities of data. To make the
results usable, they developed a novel rendering system
that generates images directly from points rather than from
triangle primitives [116].

Bernardini et al. [117] used a lower resolution structured

light system coupled with a photometric lighting system
for higher resolution reflectance and normals maps to scan
Michelangelo’s Florentine Piet`a. A rendering of the model
is shown next to a photograph of the statue in Figure 14.

Several projects are addressing the scanning of human

shape, e.g. [118]. Many of these applications address purely
geometric issues such as fit and ergonomic design, rather
than preparing models for computer graphics display. For

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animation systems however, there has been a great deal of
interest in the scanning of human faces. Building a realistic
face model is one of the most demanding applications,
because of human familiarity with the smallest details of
the face. Yau [119] described a system for building a face
model from a range scan that used light striping and a
color image for texture mapping. Nahas et al. [120] describe
obtaining a realistic face model from a laser range scanner
that captures reflectance information as well. Marschner
et al. [121] described a method to obtain skin BRDF for
realistic faces using color images and a detailed model from
a range scanner, in a method similar to that used by Ikeuchi
and Sato [96]. This work was extended to spatially varying
skin reflectance [122].

Debevec et al. [123] designed a specialized rig for

obtaining hundreds of images of an individual face with
calibrated lighting. They use this data to compute spatially
varying BRDFs and normals that are mapped onto a lower
resolution model of the face that is obtained with a structured
light system. Haro et al. [124] describe a less rigorous, but
also much less expensive, method for obtaining detailed
facial geometry. Photometric stereo is used to capture
the geometry of small patches of skin impressions made
in a polymeric material. These patches are placed onto
appropriate areas of the face model, and grown using texture
synthesis techniques to cover the whole face.

The cultural heritage and human face applications dis-

cussed above have emphasized using relatively high-end sys-
tems. An emerging application for acquired 3D models is e-
commerce—using 3D models to allow shoppers to examine
and/or customize items for purchase over the internet. This
new application requires both inexpensive equipment, and
a much higher level of “ease-of-use.” Companies targeting
this application area are offering systems at relatively low
(

$10,000) price for scanning small objects.

10. Conclusions

The current state of the art allows the acquisition of a
large class of objects, but requires expert operators and
time consuming procedures for all but the simplest cases.
Research is needed to improve the acquisition pipeline in
several key aspects:

•

planning methods for data acquisition;

•

reliable capture and robust processing of data for a
larger class of objects, including large size objects,
environments, and objects with challenging surface
properties;

•

automation of all the steps, to minimize user input;

•

real-time feedback of the acquired surface;

•

improved capture and representation of surface appear-
ance;

•

methods for assessing global model accuracy after range
scan registration.

Scanning and reconstruction technology will enable a more
extensive use of 3D computer graphics in a wide range of
applications.

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