A Survey of Content Based 3D Shape Retrieval Methods
Johan W.H. Tangelder and Remco C. Veltkamp
Institute of Information and Computing Sciences, Utrecht University
hanst@cs.uu.nl, Remco.Veltkamp@cs.uu.nl
Abstract
Recent developments in techniques for modeling, digitiz-
ing and visualizing 3D shapes has led to an explosion in
the number of available 3D models on the Internet and in
domain-specific databases. This has led to the development
of 3D shape retrieval systems that, given a query object,
retrieve similar 3D objects. For visualization, 3D shapes
are often represented as a surface, in particular polygo-
nal meshes, for example in VRML format. Often these mod-
els contain holes, intersecting polygons, are not manifold,
and do not enclose a volume unambiguously. On the con-
trary, 3D volume models, such as solid models produced
by CAD systems, or voxels models, enclose a volume prop-
erly. This paper surveys the literature on methods for con-
tent based 3D retrieval, taking into account the applicabil-
ity to surface models as well as to volume models. The meth-
ods are evaluated with respect to several requirements of
content based 3D shape retrieval, such as: (1) shape repre-
sentation requirements, (2) properties of dissimilarity mea-
sures, (3) efficiency, (4) discrimination abilities, (5) ability
to perform partial matching, (6) robustness, and (7) neces-
sity of pose normalization. Finally, the advantages and lim-
its of the several approaches in content based 3D shape re-
trieval are discussed.
1. Introduction
The advancementof modeling, digitizing and visualizing
techniques for 3D shapes has led to an increasing amount
of 3D models, both on the Internet and in domain-specific
databases. This has led to the development of the first exper-
imental search engines for 3D shapes, such as the 3D model
search engine at Princeton university [2, 57], the 3D model
retrieval system at the National Taiwan University [1, 17],
the Ogden IV system at the National Institute of Multimedia
Education, Japan [62, 77], the 3D retrieval engine at Utrecht
University [4, 78], and the 3D model similarity search en-
gine at the University of Konstanz [3, 84].
Laser scanning has been applied to obtain archives
recording cultural heritage like the Digital Michelan-
gelo Project [25, 48], and the Stanford Digital Formae
Urbis Romae Project [75]. Furthermore, archives contain-
ing domain-specific shape models are now accessible by
the Internet. Examples are the National Design Repos-
itory, an online repository of CAD models [59, 68],
and the Protein Data Bank, an online archive of struc-
tural data of biological macromolecules [10, 80].
Unlike text documents, 3D models are not easily re-
trieved. Attempting to find a 3D model using textual an-
notation and a conventional text-based search engine would
not work in many cases. The annotations added by human
beings depend on language, culture, age, sex, and other fac-
tors. They may be too limited or ambiguous. In contrast,
content based 3D shape retrieval methods, that use shape
properties of the 3D models to search for similar models,
work better than text based methods [58].
Matching is the process of determining how similar two
shapes are. This is often done by computing a distance. A
complementary process is indexing. In this paper, indexing
is understood as the process of building a datastructure to
speed up the search. Note that the term indexing is also of-
ten used for the identification of features in models, or mul-
timedia documents in general. Retrieval is the process of
searching and delivering the query results. Matching and in-
dexing are often part of the retrieval process.
Recently, a lot of researchers have investigated the spe-
cific problem of content based 3D shape retrieval. Also, an
extensive amount of literature can be found in the related
fields of computer vision, object recognition and geomet-
ric modelling. Survey papers to this literature have been
provided by Besl and Jain [11], Loncaric [50] and Camp-
bell and Flynn [16]. For an overview of 2D shape match-
ing methods we refer the reader to the paper by Veltkamp
[82]. Unfortunately, most 2D methods do not generalize di-
rectly to 3D model matching. Work in progress by Iyer et
al. [40] provides an extensive overview of 3D shape search-
ing techniques. Atmosukarto and Naval [6] describe a num-
ber of 3D model retrieval systems and methods, but do not
provide a categorization and evaluation.
In contrast, this paper evaluates 3D shape retrieval meth-
ods with respect to several requirements on content based
3D shape retrieval, such as: (1) shape representation re-
quirements, (2) properties of dissimilarity measures, (3) ef-
ficiency, (4) discrimination abilities, (5) ability to perform
partial matching, (6) robustness, and (7) necessity of pose
3Dmodel
database
descriptors
index
structure
query
sketch
result
query
descriptor
fetching
descriptor
extraction
descriptor
extraction
matching
index
construction
visualization
query
formulation
browsing
queryby
example
directquery
model
id’s
offline
online
Figure 1. Conceptual framework for shape retrieval.
normalization. In section 2 we discuss several aspects of 3D
shape retrieval. The literature on 3D shape matching meth-
ods is discussed in section 3 and evaluated in section 4.
2. 3D shape retrieval aspects
In this section we discuss several issues related to 3D
shape retrieval.
2.1. 3D shape retrieval framework
At a conceptual level, a typical 3D shape retrieval frame-
work as illustrated by fig. 1 consists of a database with an
index structure created
offline
and an
online
query engine.
Each 3D model has to be identified with a shape descrip-
tor, providing a compact overall description of the shape.
To efficiently search a large collection online, an indexing
data structure and searching algorithm should be available.
The
online
query engine computes the query descriptor, and
models similar to the query model are retrieved by match-
ing descriptors to the query descriptor from the index struc-
ture of the database. The similarity between two descriptors
is quantified by a dissimilarity measure. Three approaches
can be distinguished to provide a query object: (1) browsing
to select a new query object from the obtained results, (2)
a direct query by providing a query descriptor, (3) query by
example by providing an existing 3D model or by creating
a 3D shape query from scratch using a 3D tool or sketch-
ing 2D projections of the 3D model. Finally, the retrieved
models can be visualized.
2.2. Shape representations
An important issue is the type of shape representation(s)
that a shape retrievalsystem accepts. Most of the 3D models
found on the World Wide Web are meshes defined in a file
format supporting visual appearance. Currently, the most
common format used for this purpose is the Virtual Real-
ity Modeling Language (VRML) format. Since these mod-
els have been designed for visualization, they often contain
only geometry and appearance attributes. In particular, they
are represented by “polygon soups”, consisting of unorga-
nized sets of polygons. Also, in general these models are
not “watertight” meshes, i.e. they do not enclose a volume.
By contrast, for volume models retrieval methods depend-
ing on a properly defined volume can be applied.
2.3. Measuring similarity
In order to measure how similar two objects are, it is nec-
essary to compute distances between pairs of descriptors us-
ing a dissimilarity measure. Although the term similarity is
often used, dissimilarity corresponds to the notion of dis-
tance: small distances means small dissimilarity, and large
similarity.
A dissimilarity measure can be formalized by a func-
tion defined on pairs of descriptors indicating the degree
of their resemblance. Formally speaking, a dissimilarity
measure d on a set S is a non-negative valued function
d : S × S → R
+
∪ {0}. Function d may have some of
the following properties:
i. Identity: For all x ∈ S, d(x, x) = 0.
ii. Positivity: For all x 6= y in S, d(x, y) > 0.
iii. Symmetry: For all x, y ∈ S, d(x, y) = d(y, x).
iv. Triangle inequality:
For all x, y, z ∈ S, d(x, z) ≤ d(x, y) + d(y, z).
v. Transformation invariance: For a chosen transforma-
tion group G, for all x, y ∈ S, g ∈ G, d(g(x), g(y)) =
d(x, y).
The identity property says that a shape is completely
similar to itself, while the positivity property claims that dif-
ferent shapes are never completely similar. This property is
very strong for a high-level shape descriptor, and is often
not satisfied. However, this is not a severe drawback, if the
loss of uniqueness depends on negligible details.
Symmetry is not always wanted. Indeed, human percep-
tion does not always find that shape x is equally similar to
shape y, as y is to x. In particular, a variant x of prototype
y, is often found more similar to y then vice versa [81].
Dissimilarity measures for partial matching, giving a
small distance d(x, y) if a part of x matches a part of y,
do not obey the triangle inequality.
Transformation invariance has to be satisfied, if the com-
parison and the extraction process of shape descriptors have
to be independent of the place, orientation and scale of the
object in its Cartesian coordinate system. If we want that
a dissimilarity measure is not affected by any transforma-
tion on x, then we may use as alternative formulation for
(v): Transformation invariance: For a chosen transforma-
tion group G, for all x, y ∈ S, g ∈ G, d(g(x), y) = d(x, y).
When all the properties (i)-(iv) hold, the dissimilarity
measure is called a
metric
. Other combinations are possi-
ble: a pseudo-metric is a dissimilarity measure that obeys
(i), (iii) and (iv) while a semi-metric obeys only (i), (ii) and
(iii). If a dissimilarity measure is a pseudo-metric, the tri-
angle inequality can be applied to make retrieval more effi-
cient [7, 83].
2.4. Efficiency
For large shape collections, it is inefficient to sequen-
tially match all objects in the database with the query object.
Because retrieval should be fast, efficient indexing search
structures are needed to support efficient retrieval. Since for
query by example the shape descriptor is computed online,
it is reasonable to require that the shape descriptor compu-
tation is fast enough for interactive querying.
2.5. Discriminative power
A shape descriptor should capture properties that dis-
criminate objects well. However, the judgement of the sim-
ilarity of the shapes of two 3D objects is somewhat sub-
jective, depending on the user preference or the application
at hand. E.g. for solid modeling applications often topol-
ogy properties such as the numbers of holes in a model are
more important than minor differences in shapes. On the
contrary, if a user searches for models looking visually sim-
ilar the existence of a small hole in the model, may be of no
importance to the user.
2.6. Partial matching
In contrast to global shape matching, partial matching
finds a shape of which a part is similar to a part of another
shape. Partial matching can be applied if 3D shape mod-
els are not complete, e.g. for objects obtained by laser scan-
ning from one or two directions only. Another application
is the search for “3D scenes” containing an instance of the
query object. Also, this feature can potentially give the user
flexibility towards the matching problem, if parts of inter-
est of an object can be selected or weighted by the user.
2.7. Robustness
It is often desirable that a shape descriptor is insensitive
to noise and small extra features, and robust against arbi-
trary topological degeneracies, e.g. if it is obtained by laser
scanning. Also, if a model is given in multiple levels-of-
detail, representations of different levels should not differ
significantly from the original model.
2.8. Pose normalization
In the absence of prior knowledge, 3D models have ar-
bitrary scale, orientation and position in the 3D space. Be-
cause not all dissimilarity measures are invariant under ro-
tation and translation, it may be necessary to place the 3D
models into a canonical coordinate system. This should be
the same for a translated, rotated or scaled copy of the
model.
A natural choice is to first translate the center to the ori-
gin. For volume models it is natural to translate the cen-
ter of mass to the origin. But for meshes this is in gen-
Figure 2. Similar mugs oriented by principal axes in dif-
ferent ways [30].
eral not possible, because they have not to enclose a vol-
ume. For meshes it is an alternative to translate the cen-
ter of mass of all the faces to the origin. For example
the Principal Component Analysis (PCA) method computes
for each model the principal axes of inertia e
1
, e
2
and e
3
and their eigenvalues λ
1
, λ
2
and λ
3
, and make the nec-
essary conditions to get right-handed coordinate systems.
These principal axes define an orthogonal coordinate sys-
tem (e
1
, e
2
, e
3
), with λ
1
≥ λ
2
≥ λ
3
. Next, the polyhe-
dral model is rotated around the origin such that the co-
ordinate system (e
x
, e
y
, e
z
) coincides with the coordinate
system(e
1
, e
2
, e
3
).
The PCA algorithm for pose estimation is fairly simple
and efficient. However, if the eigenvalues are equal, prin-
cipal axes may switch, without affecting the eigenvalues.
Similar eigenvalues may imply an almost symmetrical mass
distribution around an axis (e.g. nearly cylindrical shapes)
or around the center of mass (e.g. nearly spherical shapes).
Fig. 2 illustrates the problem.
3. Shape matching methods
In this section we discuss 3D shape matching methods.
We divide shape matching methods in three broad cate-
gories: (1) feature based methods, (2) graph based meth-
ods and (3) other methods. Fig. 3 illustrates a more detailed
categorization of shape matching methods. Note, that the
classes of these methods are not completely disjoined. For
instance, a graph-based shape descriptor, in some way, de-
scribes also the global feature distribution. By this point of
view the taxonomy should be a graph.
3.1. Feature based methods
In the context of 3D shape matching, features denote ge-
ometric and topological properties of 3D shapes. So 3D
shapes can be discriminated by measuring and comparing
their features. Feature based methods can be divided into
four categories according to the type of shape features used:
(1) global features, (2) global feature distributions, (3) spa-
tial maps, and (4) local features. Feature based methods
from the first three categories represent features of a shape
using a single descriptor consisting of a d-dimensional vec-
tor of values, where the dimension d is fixed for all shapes.
Featurebased
Graphbased
Other
Globalfeatures
Spatialmap
Localfeatures
Globalfeature
distribution
Modelgraph
Skeleton
Reebgraph
Viewbased
Volumetricerrorbased
Weightedpointsetbased
Deformationbased
Figure 3. Taxonomy of shape matching methods.
The value of d can easily be a few hundred. The descriptor
of a shape is a point in a high dimensional space, and two
shapes are considered to be similar if they are close in this
space. Retrieving the k best matches for a 3D query model is
equivalent to solving the k nearest neighbors problem. Us-
ing the Euclidean distance, matching feature descriptors can
be done efficiently in practice by searching in multiple 1D
spaces to solve the approximate k nearest neighbor prob-
lem as shown by Indyk and Motwani [36]. In contrast with
the feature based methods from the first three categories, lo-
cal feature based methods describe for a number of surface
points the 3D shape around the point. For this purpose, for
each surface point a descriptor is used instead of a single de-
scriptor.
3.1.1. Global feature based similarity
Global features characterize the global shape of a 3D model.
Examples of these features are the statistical moments of the
boundary or the volume of the model, volume-to-surface ra-
tio, or the Fourier transform of the volume or the boundary
of the shape.
Zhang and Chen [88] describe methods to com-
pute global features such as volume, area, statistical mo-
ments, and Fourier transform coefficients efficiently.
Paquet et al. [67] apply bounding boxes, cords-based,
moments-based and wavelets-based descriptors for 3D
shape matching.
Corney et al. [21] introduce convex-hull based indices
like hull crumpliness (the ratio of the object surface area
and the surface area of its convex hull), hull packing (the
percentage of the convex hull volume not occupied by the
object), and hull compactness (the ratio of the cubed sur-
face area of the hull and the squared volume of the convex
hull).
Kazhdan et al. [42] describe a reflective symmetry de-
scriptor as a 2D function associating a measure of reflec-
tive symmetry to every plane (specified by 2 parameters)
through the model’s centroid. Every function value provides
a measure of global shape, where peaks correspond to the
planes near reflective symmetry, and valleys correspond to
the planes of near anti-symmetry. Their experimental results
show that the combination of the reflective symmetry de-
scriptor with existing methods provides better results.
Since only global features are used to characterize the
overall shape of the objects, these methods are not very dis-
criminative about object details, but their implementation is
straightforward. Therefore, these methods can be used as an
active filter, after which more detailed comparisons can be
made, or they can be used in combination with other meth-
ods to improve results.
Global feature methods are able to support user feed-
back as illustrated by the following research. Zhang and
Chen [89] applied features such as volume-surface ratio,
moment invariants and Fourier transform coefficients for
3D shape retrieval. They improve the retrieval performance
by an active learning phase in which a human annotator as-
signs attributes such as airplane, car, body, and so on to a
number of sample models. Elad et al. [28] use a moments-
based classifier and a weighted Euclidean distance measure.
Their method supports iterative and interactive database
searching where the user can improve the weights of the
distance measure by marking relevant search results.
3.1.2. Global feature distribution based similarity
The concept of global feature based similarity has been re-
fined recently by comparing distributions of global features
instead of the global features directly.
Osada et al. [66] introduce and compare shape distribu-
tions, which measure properties based on distance, angle,
area and volume measurements between random surface
points. They evaluate the similarity between the objects us-
ing a pseudo-metric that measures distances between distri-
butions. In their experiments the D2 shape distribution mea-
suring distances between random surface points is most ef-
fective.
Ohbuchi et al. [64] investigate shape histograms that are
discretely parameterized along the principal axes of inertia
of the model. The shape descriptor consists of three shape
histograms: (1) the moment of inertia about the axis, (2)
the average distance from the surface to the axis, and (3)
the variance of the distance from the surface to the axis.
Their experiments show that the axis-parameterized shape
features work only well for shapes having some form of ro-
tational symmetry.
Ip et al. [37] investigate the application of shape distri-
butions in the context of CAD and solid modeling. They re-
fined Osada’s D2 shape distribution function by classifying
2 random points as 1) IN distances if the line segment con-
necting the points lies complete inside the model, 2) OUT
distances if the line segment connecting the points lies com-
plete outside the model, 3) MIXED distances if the line seg-
ment connecting the points lies passes both inside and out-
side the model. Their dissimilarity measure is a weighted
distance measure comparing D2, IN, OUT and MIXED dis-
tributions. Since their method requires that a line segment
can be classified as lying inside or outside the model it is
required that the model defines a volume properly. There-
fore it can be applied to volume models, but not to polyg-
onal soups. Recently, Ip et al. [38] extend this approach
with a technique to automatically categorize a large model
database, given a categorization on a number of training ex-
amples from the database.
Ohbuchi et al. [63], investigate another extension of the
D2 shape distribution function, called the Absolute Angle-
Distance histogram, parameterized by a parameter denot-
ing the distance between two random points and by a pa-
rameter denoting the angle between the surfaces on which
two random points are located. The latter parameter is ac-
tually computed as an inner product of the surface normal
vectors. In their evaluation experiment this shape distribu-
tion function outperformed the D2 distribution function at
about 1.5 times higher computational costs. Ohbuchi et al.
[65] improved this method further by a multi-resolution ap-
proach computing a number of alpha-shapes at different
scales, and computing for each alpha-shape their Absolute
Angle-Distance descriptor. Their experimental results show
that this approach outperforms the Angle-Distance descrip-
tor at the cost of high processing time needed to compute
the alpha-shapes.
Shape distributions distinguish models in broad cate-
gories very well: aircraft, boats, people, animals, etc. How-
ever, they perform often poorly when having to discrimi-
nate between shapes that have similar gross shape proper-
ties but vastly different detailed shape properties.
3.1.3. Spatial map based similarity
Spatial maps are representations that capture the spatial lo-
cation of an object. The map entries correspond to physi-
cal locations or sections of the object, and are arranged in a
manner that preserves the relative positions of the features
in an object. Spatial maps are in general not invariant to ro-
tations, except for specially designed maps. Therefore, typ-
ically a pose normalization is done first.
Ankerst et al. [5] use shape histograms as a means of an-
alyzing the similarity of 3D molecular surfaces. The his-
tograms are not built from volume elements but from uni-
formly distributed surface points taken from the molecular
surfaces. The shape histograms are defined on concentric
shells and sectors around a model’s centroid and compare
shapes using a quadratic form distance measure to compare
the histograms taking into account the distances between
the shape histogram bins.
Vrani´c et al. [85] describe a surface by associating to
each ray from the origin, the value equal to the distance to
the last point of intersection of the model with the ray and
compute spherical harmonics for this spherical extent func-
tion. Spherical harmonics form a Fourier basis on a sphere
much like the familiar sine and cosine do on a line or a cir-
cle. Their method requires pose normalization to provide
rotational invariance. Also, Yu et al. [86] propose a descrip-
tor similar to a spherical extent function and a descriptor
counting the number of intersections of a ray from the ori-
gin with the model. In both cases the dissimilarity between
two shapes is computed by the Euclidean distance of the
Fourier transforms of the descriptors of the shapes. Their
method requirespose normalization to provide rotational in-
variance.
Kazhdan et al. [43] present a general approach based on
spherical harmonics to transform rotation dependent shape
descriptors into rotation independent ones. Their method is
applicable to a shape descriptor which is defined as either a
collection of spherical functions or as a function on a voxel
grid. In the latter case a collection of spherical functions is
obtained from the function on the voxel grid by restricting
the grid to concentric spheres. From the collection of spher-
ical functions they compute a rotation invariant descriptor
by (1) decomposing the function into its spherical harmon-
ics, (2) summing the harmonics within each frequency, and
computing the L
2
-norm for each frequency component. The
resulting shape descriptor is a 2D histogram indexed by ra-
dius and frequency, which is invariant to rotations about the
center of the mass. This approach offers an alternative for
pose normalization, because their method obtains rotation
invariant shape descriptors. Their experimental results show
indeed that in general the performance of the obtained ro-
tation independent shape descriptors is better than the cor-
responding normalized descriptors. Their experiments in-
clude the ray-based spherical harmonic descriptor proposed
by Vrani´c et al. [85]. Finally, note that their approach gen-
eralizes the method to compute voxel-based spherical har-
monics shape descriptor, described by Funkhouser et al.
[30], which is defined as a binary function on the voxel grid,
where the value at each voxel is given by the negatively ex-
ponentiated Euclidean Distance Transform of the surface of
a 3D model.
Novotni and Klein [61] present a method to compute
3D Zernike descriptors from voxelized models as natural
extensions of spherical harmonics based descriptors. 3D
Zernike descriptors capture object coherence in the radial
direction as well as in the direction along a sphere. Both
3D Zernike descriptors and spherical harmonics based de-
scriptors achieve rotation invariance. However, by sampling
the space only in radial direction the latter descriptors do