Shape-Based Autotagging of 3D Models
for Retrieval
Ryutarou Ohbuchi, Shun Kawamura
Graduate School of Medicine and Engineering, University of Yamanashi,
4-30 Takeda, Kofu-shi, Yamanashi-ken, 400-8511, Japan
ohbuchiAT yamanashi.ac.jp, g09mk007AT yamanashi.ac.jp

Abstract. This paper describes an automatic annotation, or autotagging,algorithm that attaches textual tags to 3D models based on their shape andsemantic classes. The proposed method employs Manifold Ranking by Zhou etal, an algorithm that takes into account both local and global distributions offeature points, for tag relevance computation. Using Manifold Ranking, ourmethod propagates multiple tags attached to a training subset of models in a
database to the other tag-less models. After the relevance values for multiple
tags are computed for tag-less points, the method selects, based on the
distribution of feature points for each tag, the threshold at which the tag isselected or discarded for the points. Experimental evaluation of the method
using a text-based 3D model retrieval setting showed that the proposed method
is effective in autotagging 3D shape models.
Keywords: 3D geometric modeling, content based retrieval, automatic
annotation, manifold ranking, text tags, semantic retrieval.

1

Introduction

Specification of a query is one of the most fundamental issues in retrieving
multimedia objects such as images and 3D geometric models. These data objects may
be searched either by example(s) or by text(s), each approach having its own
advantages and disadvantages. To retrieve 3D models, a query for the Query-ByExample (QBE) approach could be sketches in either 2D [12] or 3D of the desired
shape, an example 3D model, or a photograph of a real-world object having thedesired shape. Most of the published work on 3D model retrieval used the QBE
approach [2, 5, 6, 7, 9, 10, 12, 14]. While the QBE approach is quite powerful anduseful in many application scenarios, it does have drawbacks. For example, it is often
impractical to find a 3D model that have a shape similar enough to the desired one.
Or, a user may find sketching a complex shape difficult. Capturing semantic aspect ofthe desired shape is also difficult with the QBE approach. Previous work used either
single-class learning via relevance feedback [6, 7] or off-line multi-class learning [10]for semantics.
An alternative, Query-By-Text (QBT) approach, employs a text as a query, as intext-based search engines. While the QBT is disadvantageous in directly specifying a

2

Ryutarou Ohbuchi, Shun Kawamura

desired shape, it has an advantage in describing semantic content of the desired shape.
For example, a word “mammal” could be used to retrieve both dolphin and cat thathave very different geometric shapes. The issue in QBT of 3D models is that most of
the 3D models are not associated with text tags, and that adding consistent tags
manually to a large number of 3D models can be quite difficult. An automatic orsemi-automatic approach, e.g., propagation of tags from a set of tagged models to alarge number of tag-less models, is necessary.
The authors know of only two examples, one by Zhang et al [16] and the other byGoldfeder et al [3] that studied autotagging of 3D models. The method by Zhang et al[16] associates a list of attributes, not text tags, with a 3D model. The method
employs biased kernel regression to propagate probabilities of the attributes from themanually tagged source models to the tag-less models. For retrieval, the method treats
the list of probabilities as a feature vector, and computes distances among feature
vectors. Thus, it is not strictly a QBT method. The method by Goldfeder et al [3] is a
QBT approach, in which text tags are propagated from tagged 3D models to tag-less
3D models. To propagate tags, it uses local structure of the shape feature space via
nearest neighbor search. For experiments, they used a set of 192,343 mesh-based 3Dmodels having text tags in a snapshot of Google 3D Warehouse (G3W). The G3W isan evolving set of a large number of 3D models contributed by users, and it contains
errors and inconsistencies in its tags. Unfortunately, the G3W snapshot they haveused is not available for use at this time. Goldfeder et al evaluated tagging
performance of their method by using a retrieval task, by comparing retrieval
performance of their auto-tagging based QBT algorithm with that of a QBE algorithm
that uses 3D models as its queries. The paper [3] reported that the QBT performed
equal or better than the QBE algorithm they have compared against.
In this paper, we propose a novel off-line semi-supervised algorithm for
autotagging 3D model collections that exploits both local and global distribution oftagged and tag-less shape features by means of the Manifold Ranking (MR) algorithm
by Zhou, et al. [17, 18]. From a set of shape features extracted from a set of tagged
3D models that shares a same text tag, the MR algorithm diffuses a relevance rank
value indicating the likelihood of tag-less models to have the tag. This MR process isperformed once for each of keyword to determine a set of tags a tag-less model should
receive. To discard an unreliable tag attached to the tag-less model, compactness ofthe distribution of the tagged models sharing the tag is taken into consideration. An
evaluation of the proposed algorithm by using a 3D model retrieval scenario showedthat a QBT retrieval method by using the text tags added by the method significantly
outperforms a QBE retrieval method that used 3D shape feature comparison

2

Autotagging 3D Models via Multiple Manifold Ranking

Our algorithm, whose outline is shown in Figure 1, consists of the following threesteps. Details of the steps will be described in the following subsections.
(1) Shape feature extraction: Extract a shape feature from the input 3D model.

Shape-Based Autotagging of 3D Models
for Retrieval 3(2) Tag propagation: For each tag, propagate, in the shape feature space, thelikelihood of a 3D model having the tag from the tagged “training example” 3Dmodels to the tag-less models. The tag likelihood propagation is performed byusing the Manifold Ranking (MR) algorithm by Zhou, et al [17, 18]. Repeat theMR-based tag likelihood propagation for all the tags.
(3) Tag selection: A tag-less model now has multiple likelihood values for multiple
tags. Select, based on the mutual distance of the tagged and tag-less models, themost likely tags to be attached to the model.
Extract feature

Estimate TRR

Select tags
Chair:0.5

Untagged model
0.3
0.5

0.5

Feature space
Tagged models
Fig. 1. The method estimates a Tag Relevance Rank (TRR), a likelihood of a model having atext tag, by Manifold Ranking [17, 18]. Estimation of TRR is performed for every tag. Then
most relevant of the tags are selected for a 3D model by using tag-specific threshold values.

2.1

Feature extraction

So far as a shape descriptor, or a feature, of a 3D model is a vector, it can be used in
the proposed autotagging algorithm. A feature for comparing 3D shapes is required tohave a set of invariances. Typically, certain invariance to shape representation,
invariance to geometrical transformation up to similarity transformation, andinvariance to geometrical and topological noise are expected. One might need tocompare a CAD model defined as a 3D solid by using curved surface patches with apolygon soup model or a point set model. Invariance against three rotational degrees
of freedom is not trivial to achieve [14]. Topological and geometrical noises, such asholes, variation in vertex connectivity in a mesh, displacements of vertices, need to be
tolerated. Depending on an application, additional invariance, such as invarianceagainst joint articulation, may be required.
For the experiment described in this paper, we used our extension of Wahl’s Surflet
Pair Relation Histograms (SPRH) [15], a shape feature that has nice invarianceproperties, readily available, and has reasonable retrieval performance. The Windows
32bit executable of our extension of the SPRH is available at our web site [8]. The
SPRH was originally developed for oriented point set models acquired by Laser range
scanners. We added a step to convert a surface based model to an oriented point-set
model by using quasi-Monte Carlo sampling of surfaces [10]. As a result, theextended SPRH is able to accept popular surface-based shape representations such as
polygon soup and closed polygonal mesh. The SPRH feature is a joint histogram of

Ryutarou Ohbuchi and Shun Kawamura, Shape-Based Autotagging of 3D Models for Retrieval,
accepted, 4th International Conference on Semantic and Digital Media Technologies (SAMT2009), Graz, Austria, Dec. 2-4, 2009.

4

Ryutarou Ohbuchi, Shun Kawamura

quadruples (δ, α, β, γ), in which δ is the distance and α, β, and γ are the angles
between a pair of oriented points. By default, each of the four quantities has 5 bins,
625 vector. The SPRH is invariant to similarity
making a SPRH feature a 5transformation without requiring pose normalization. It is also insensitive to various
noises, such as variation in mesh tessellation or connectivity, holes, or small vertex
displacements.

2.2

Tag propagation and selection

Our method uses the Manifold Ranking (MR) [17, 18] algorithm to estimate therelevance of a text tag to tag-less 3D models. The MR algorithm is a graph-basedlearning algorithm that can be used either in unsupervised, supervised, or semisupervised modes. Our method uses the MR in semi-supervised mode. Intuitively, theMR resembles to solving a diffusion equation on an irregular connectivity mesh in ahigh-dimensional feature space. The mesh is created by connecting, by theirproximity, the feature points in the feature space. For example, given the 625Dfeature of the SPRH, the mesh is embedded in a 625D space with its feature points
having 625D coordinate. In our autotagging framework, the mesh for the MR iscreated from union of feature vectors of the tagged as well as tag-less 3D models.
Typically, a text tag is associated with multiple tagged (or “source”) 3D models sothat a MR process would have multiple sources for diffusion. Given N text tags, or
keywords, the proposed algorithms runs N such MR processes to diffuse Tag
Relevance Rank (TRR) value for the N tags onto all the tag-less 3D models. At theequilibrium of solving the diffusion equation iteratively, the higher the diffused TRR
value, the higher the likelihood of the tag-less model having the tag.
Let us assume propagation of a tag from a set of tagged 3D models to the other 3Dmodels without the tag. Let χ = { x1 ,", xs , xs +1 ,", xt , xt +1 ,", xn } be a set of nfeatures in a m-dimensional feature space \ m , in which first s + t points from x1 to
xt are the feature points for the tagged models. Among the tagged points, points fromx1 to xt are the source set, and the point from xs +1 to xt are the probe set. This
splitting of the tagged points is done to estimate a TRR threshold value th, which
decides if a tag should be attached to a tag-less point or not. The source set and theprobe set is of equal size, and are drawn randomly from the set of s + t points sharing
the same tag. To put it briefly, by performing TRR diffusion within a set of models
sharing a tag, the tightness of the distribution of the tag is estimated to compute the th.
Details on tag selection will be explained below. The rest of the points from xt +1 to
xn are the tag-less ones for which the TRR values need be computed. Letd : χ × χ → \ denote a distance metric on χ , e.g., L1-norm or Cosine distance, thatassigns a pair of points xi and xi a distance d ( xi , x j ) . Let f : χ → \ be a ranking
function that assigns each xi a ranking score fi , thereby forming a rank vectorTT
f = ⎡⎣ f1 , " , f n ⎤⎦ . Let the n-dimensional binary-valued vector y = ⎡⎣ y1 , " , y n ⎤⎦ be alabel vector, in which yi = 1 for the tagged (“source”) point and yi = 0 for the rest,i.e., points to which tags are assigned.
We first create the affinity matrix W where Wij indicates the similarity between
samples xi and x jShape-Based Autotagging of 3D Models
for Retrieval 5⎧⎛ d ( xi , x j ) ⎞⎪ exp ⎜⎜ −⎟⎟ if i ≠ j
Wij = ⎨σ⎝⎠⎪otherwise⎩ 0(1)

The distance metric d ( xi , xi ) used in forming W affects ranking performance. We
will compare several distance measures for their performance in Section 3.1. The
positive parameter σ defines the radius of influence. Note that Wii = 0 since there
is no ark connecting a point with itself. The matrix W is positive symmetric. A
normalized graph Laplacian S is then defined as;
−

1

−

1

S = D 2 WD 2(2)

where D is a diagonal matrix in which Dij equals to sum of i-th row of W, that is,T
Dij = ∑ j Wij Then the ranking vector f = ⎡⎣ f1 ," , f n ⎤⎦ can be estimated by iterating
the following until convergence;f (t +1) = α Sf (t ) + (1 − α ) y(3)

As the equilibrium is reached, each tag-less point would have a TRR value
associated with them, indicating the likelihood of the point having the tag. We call the
ranking vector at the equilibrium f * .
The algorithm performs the tag propagation process describe above n times, once
for each of the n tags. After all the tags have been diffused, a point in the feature
space would have n positive TRR values corresponding to the n tags. A TRR value
indicates how relevant the tag is to the point i. The system must now decide what
subset of the n tags should be attached to the point. To decide, our method employs asimple proving to estimate the cut-off threshold th of the TRR for each tag. As
described above, the method randomly splits the set of s + t tagged points sharing thesame tag into two (roughly) equal-sized subsets, the source set and the probe set.
After the MR, the TRR values of the points in the probe set, that is, the points fromxs +1 to xt in the set of features χ , are used to estimate a threshold th by using thefollowing equation;
min

(4)

th at a tag-less point,
The threshold th is computed for each tag. If the TRR
the tag i is attached to the point. The tag is also given the TRR value as its
confidence value at the point. In general, a point may be associated with multiple tags
if more than one tag has TRR values greater than or equal to their respective thresholdvalues. As a reviewer pointed out, the use of minimum to compute the threshold th isdebatable, as it is not robust against outliers. However, given small size of some of
the classes in the benchmark dataset, e.g., just 4 models per class and 2 models in its
prove set, we could not come up with a better method that is statistically robust.

Ryutarou Ohbuchi and Shun Kawamura, Shape-Based Autotagging of 3D Models for Retrieval,
accepted, 4th International Conference on Semantic and Digital Media Technologies (SAMT2009), Graz, Austria, Dec. 2-4, 2009.

6

Ryutarou Ohbuchi, Shun Kawamura

In the example of Figure 2, tagged points belonging to the tag “car” has the tightest
distribution, with the similarity threshold th=0.8. The TRR of the “car” tag at the tagless point in question is 0.5, which is below the threshold th=0.8. Thus, the “car” tagis not attached to the point. Similarly, the “animal” tag is not attached to the point.
The “chair” tag, on the other hand, has the TRR=0.5, while the threshold for the“chair” tag is th=0.4. Thus, the point is associated with the tag “chair”.

3. Experiments and Results
As the research on autotagging, or automatic annotation of 3D models just started,
there is no established benchmark for an objective evaluation. Ideally, one should use
a large enough corpus, something similar to the snapshot of G3W containing 190k
models used by Goldfeder et al, for tagging. Unfortunately, the G3W snapshot usedby Goldfeder et al is not available for us. In addition to the database, one also needs amethod to evaluate the tagging performance numerically and objectively.
We resorted to using a well accepted benchmark for QBE 3D model retrieval, thePrinceton Shape Benchmark (PSB) [13] for our evaluation. The 1,814 model PSB
contains two equal-sized subsets, the train set and test set, each consisting of 907
models. We regard class labels of the PSB train set as text tags, and transfer the tags
from the train set to the test set. We then regarded the retrieval performance derived
under the QBT framework as the performance index of the autotagging method.
The PSB has a 4-level class hierarchy, from the most detailed “Base” level classes
to the most abstract “Coarse 3” level classes containing only two classes; “natural”
and “manmade”. Of these four levels, we use the Base level classes only in thefollowing experiments. The Base level class itself has four internal levels ofhierarchy. If leaf nodes of the Base level are counted, there are about 90 classes in theBase level of both train and test set. Note that some of the classes in the Base class ofthe train set do not have their counterparts in the Base level of the test set, and vice versa. If
both leaf and non-leaf nodes of the Base level classes are counted there are about 130
classes. (To be exact, there are 129 classes in the train set and 131 classes in the test
Tag Propagation
animalTag-less
model

Tag Selection
animal: th=0.6
TRR=0.3
TRR=0.5

Tag(s):
animalcar
chair

TRR=0.5car

chair

car: th=0.8

chair: th=0.4

Fig. 2. A tag is attached to a feature if its Tag Relevance Rank (TRR) propagated from featureswith the tag exceeds the threshold th specific to the tag. The threshold is the estimatedminimum TRR of the prove set of features having the tag.

Shape-Based Autotagging of 3D Models
for Retrieval 7set.) Note also that the size of a class at the leaf-node of the Base class can be quite
small, ranging from just four per class to a couple of dozen per class.
As the feature vector, we used the SPRH by Wahl [15] modified to accept polygon
soup and polygonal mesh models found in the PSB. Note that the performance of the
SPRH is only modest by current state of the art. Here we do not aim for the highest
retrieval performance, but we want to evaluate our autotagging algorithm by using a
QBT framework.

3. 1. Distance measures for similarity matrix
This set of experiments compares, using the retrieval performance, the autotagging
performance of various distance measures used in forming the affinity matrix W inequation (1).
For this experiment, we used 63 class labels that are common among the train andtest sets of the PSB. These 63 classes are selected from the Base level, and include
both leaf and non-leaf nodes in the Base level. These 63 classes correspond to 811
models in the train set and 823 models in the test set. We used the 3D models in the
train set as the tagged models, and propagated their class labels to the models in thetest set.
We compared five distances measures, that are, Lk -norm having k=0.5, 1.0, and2.0, the cosine (cos) measure, and the Kullback-Leibler divergence (KLD). In thefollowing equations, x = ( xi ) and y = ( yi ) are the feature vectors and n is thedimension of the vectors. The Lk -norm is defined by the following equation;⎡d k ( x, y ) = ⎢⎣∑ ( x − y )⎤⎥⎦
n

i

i

i

k

1

k

(5)

The original paper on MR used the Euclidian distance, or L2 -norm with k=2.0, toform the affinity matrix [17, 18]. The Manhattan distance with k=1.0 is often said toperform better in higher dimension. Aggarwal, et al in [1] argued that k<1.0, e.g.,
k=0.5, works even better in higher dimension than k=1.0. As the cosine measure is ameasure of similarity having the range [ 0,1] , we converted it to a distance using thefollowing equation;
x⋅y
x ⋅ y

d cos ( x, y ) = 1 −(6)

The KLD is sometimes referred to as information divergence, or relative entropy,
and is not a distance metric, for it is not symmetric. We use a version of KLD that issymmetric as below;nd KLD (x, y ) =∑ ( y − x ) ln x
i

i =1

i

yi
i

(7)

Ryutarou Ohbuchi and Shun Kawamura, Shape-Based Autotagging of 3D Models for Retrieval,
accepted, 4th International Conference on Semantic and Digital Media Technologies (SAMT2009), Graz, Austria, Dec. 2-4, 2009.

8

Ryutarou Ohbuchi, Shun Kawamura

Figure 3 shows the retrieval performance in R-precision of various distancemeasures d ( xi , x j ) used in forming the affinity matrix W of equation (1). Both theL0.5 -norm and the KLD performed equally well, finishing at the top. The L2 -norm
employed in the original paper on manifold ranking [17, 18] finished the last in thiscase. The result will likely be different for other features and databases having
different distribution of feature points. However, it is definitely worth experimenting
with several different distance measures. We will use the L0.5 -norm for theexperiments that follow.
33%

35%

37%

39%

41%

L05

41.3%

L1
L2
COS

43%

39.4%
37.1%
38.5%

KLD

41.0%

Fig. 3. Distance measures used in forming the affinity matrix W (Equation (1)) and retrieval
performance measured in R-precision.

3.2. Query By Text v.s. Query By (3D model) Example
In this set of experiments, in an effort to quantify autotagging performance,
retrieval performances of the QBT and QBE frameworks are compared. The QBE
retrieval and the autotagging step for the QBT used the same shape feature, the SPRH
modified by us to accept polygon-based models. As tags, we used 21 class labels of
21 leaf nodes in the Base level that are common among the PSB train and test set.
This is different from the 63 class labels using in the previous experiment, which
included both leaf and non-leaf nodes in the Base level of the PSB. This experimentused the leaf node only since performance evaluation in QBE framework could only
use the leaf-nodes as its query. That is, it is not possible for the QBE framework toquery by using a “super shape” corresponding to a super class.
Figure 4 shows the recall-precision plots for the QBT and QBE frameworks. The
QBT outperformed the QBE almost everywhere except at the lowest recall. The QBE
won at the lowest recall since the top ranked retrieval in the QBE is always correct, as
it is the query itself. For the QBT retrieval, however, the top-ranked result may be
wrong if the tagging step made mistakes.
Figure 5 compares the retrieval performance of the QBT and the QBE for when
only leaf classes in the Base level are considered (case “leaf”) and both leaf classes
and non-leaf classes in the Base level are considered (case “all”). The R-precision
values are averaged over the classes and models used in each experiment. R-precision
for both QBT and QBE dropped for when non-leaf classes are included in the queries.
Still, the QBT performed better than the QBE in both cases.

Shape-Based Autotagging of 3D Models
for Retrieval 9

We observe that that the QBT retrieval performance of average R-precision=55%
is on a par with some of the state-of-the-art QBE methods evaluated by using thesame database but with different set of classes. (For reference, the Light Field
Descriptor (LFD) by Chen et al. [2] has average R-precision=45% if evaluated byusing all the 93 leaf node classes of the Base level PSB test set.) Such an apparently
good performance of the QBT may be explained as follows. The proposed algorithm
adds a tag by propagating TRR from multiple feature points sharing the tag.
This resembles to the case in which the MR is used in a relevance-feedback based
3D model retrieval system [11]. The system described in [11] produced a highretrieval performance after multiple 3D models are marked as relevant after a few
relevance feedback iterations.
1.0
QBT

0.9

QBE

0.8

Precision

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0

0.2

0.4

0.6

0.8

1.0

RecallFig. 4. Recall-precision plot for the QBE and QBT retrieval experiments. Overall, the QBT
using the automatically added tags significantly outperformed the QBE using the shape feature.
20%

25%

30%

35%

40%

40.6%

leaf
all

45%

36.8%

41.3%

50%

55%

60%

55.2%
QBE
QBT

Fig. 5. The QBT based on the autotagging performed significantly better than the QBE for
both the “leaf” case, which included only leaf classes in the Base level PSB, and the “all” case,which included both leaf and non-leaf classes in the Base level PSB.

Ryutarou Ohbuchi and Shun Kawamura, Shape-Based Autotagging of 3D Models for Retrieval,
accepted, 4th International Conference on Semantic and Digital Media Technologies (SAMT2009), Graz, Austria, Dec. 2-4, 2009.

10

Ryutarou Ohbuchi, Shun Kawamura

3.3. Tagging Examples
Figure 6, Figure 7, and Figure 8 show examples of tags attached to models by using
the proposed algorithm. Figure 6, Figure 7, and Figure 8 show, respectively, thesuccessful, unsuccessful, and mixed cases. The tags in red are correct tags, while
those in blue are incorrect tags. The size of the letters indicate the estimated quality ofthe tag; the larger the letter, the more confident the system is about the tag.
Successful examples in Figure 6 are associated with both correct and incorrecttags. However, the incorrect tags should matter little in practice as they have low
confidence values. Unsuccessful examples, e.g., a balloon (m1345) mistakenly tagged
as “body part” and “head”, seem to suggest the need for a better shape feature as well
as more training examples. For example, a multiresolution feature acquisition method
similar to the one used in [10] might help.

4. Conclusion and Future WorkIn this paper, we proposed and evaluated a shape-based algorithm for automatic
annotation, or autotagging, of 3D models with text keywords by learning the tags
from a corpus of tagged 3D models. The algorithm first extracts shape features from
3D models both with tags (training corpus) and without tags (autotagging target.) The
algorithm then computes, for each tag, the relevance of each 3D model to the tag. To
compute the relevance, the algorithm takes into account distribution of shape featuresin the ambient feature space with both local and global consistency by using theManifold Ranking (MR) algorithm of Zhou, et al [17, 18]. The algorithm chooses
those tags that are reasonably high in confidence based on the mutual distance oftagged models sharing tag.
We evaluated the autotagging algorithm by using a 3D model retrieval scenario,
assuming a good tagging result should produce a good retrieval performance by using
the Query By Text (QBT) framework. Our experiment showed that the QBT retrievalthat employed the automatically added tag significantly outperformed the Query By
Example (QBE) retrieval that employed query 3D models and their shape features.
In the future, we definitely would like to employ more “realistic” corpus, e.g.,larger size, presence of noise and error, etc., to evaluate the proposed algorithm. To
this end, availability of a snapshot of the G3W will greatly benefit the researchcommunity. Assuming the availability of a large corpus, we need to improve thescalability of the MR algorithm so that it could handle a large number of features. We
also would like to enhance the method, for example, by using a feature refined byusing other learning based algorithms, or by using a combination of multiple shapefeatures.

Shape-Based Autotagging of 3D Models
for Retrieval 11

Acknowledgements
This research has been funded in part by the Ministry of Education, Culture, Sports,
Sciences, and Technology of Japan (No. 18300068).

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Ryutarou Ohbuchi and Shun Kawamura, Shape-Based Autotagging of 3D Models for Retrieval,
accepted, 4th International Conference on Semantic and Digital Media Technologies (SAMT2009), Graz, Austria, Dec. 2-4, 2009.

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Ryutarou Ohbuchi, Shun Kawamura

Fig. 6. Examples of tags (successful cases.)Fig. 7. Examples of tags (unsuccessful cases.)Fig. 8. Examples of tags (mixed cases.)