Ryutarou Ohbuchi, Masaki Tezuka, Takahiko Furuya, Takashi Oyobe, Squeezing Bag-of-Features for Scalable and Semantic 3D
Model Retrieval, Proc. 8th International Workshop on Content-Based Multimedia Indexing (CBMI) 2010, 23-25 June 2010,
Grenoble, France.

Squeezing Bag-of-Features for Scalable and Semantic 3D Model Retrieval
Ryutarou Ohbuchi1, Masaki Tezuka2, Takahiko Furuya3, Takashi Oyobe4
Department of Computer Science and Engineering, University of Yamanashi
4-3-11 Takeda, Kofu-shi, Yamanashi-ken, 400-8511, Japan1
ohbuchiAT yamanashi.ac.jp, 2g08mk022AT yamanashi.ac.jp, 3snc49925AT gmail.com,
4
g09mk005AT yamanashi.ac.jp
Abstract
We have previously proposed a multiple-view,
densely-sampled, bag-of-visual features algorithm forshape-based 3D model retrieval [2]. The method
achieved good retrieval performance for moderately
sized benchmark datasets (~1,000 3D models),
including both rigid and articulated 3D shapes. It isalso much faster than the other methods having similar
retrieval performance. However, the method does not
exploit semantic knowledge. We want the retrieval
results to reflect multiple (e.g., ~100) semantic classes.
Also, if applied to a larger database (e.g., ~1M
models), search through the database can be expensive
due to its large feature vector size (e.g., 30k
dimensions). This paper proposes a method to“squeeze” its length feature vector by projecting it
onto a manifold that incorporates multiple semantic
classes. Experimental evaluation has shown that
retrieval performances equal or better than original
feature can be achieved while reducing feature vector
size, e.g., from 30k down to less than 100.

1. Introduction
Effective and efficient content-based retrieval of 3Dmodels, especially by their shape, is about to become
an important tool in such diverse areas as mechanicaldesign, medical diagnosis, as well as movie, game, and3D TV content production [6][16].
We have previously proposed a shape-based 3Dmodel retrieval algorithm that performed quite well forboth articulated and rigid 3D models [2][12]. An
advantage of the algorithm is its ability to accept manyand often mutually incompatible 3D shape
representations, such as polygon soup and point set,since the algorithm is appearance based. It extracts tensof thousands of local visual features from a set of range
images of a 3D model rendered from dozens ofviewpoints. Combination of multiple viewpoint
rendering and a rotation invariant local image featureenables the retrieval algorithm to achieve 3D rotation
invariance. Another advantage is its invariance toarticulation and global deformation of 3D shapes.
Invariance to articulation has been dealt with by only asmall number of algorithms, and for a limited subset ofshape representation, such as manifold mesh.
Articulation invariance can be important, for example,
to retrieve a human figure in different pose. The
algorithm integrates tens of thousands of local visualfeatures into a feature vector per 3D model by using
bag-of-features (BoF) approach. The BoF integrationof local features gives the algorithm its articulation
invariance. The integration also makes comparison
among a pair of 3D models much less expensive.
Without the integration, comparison among sets, eachcontaining thousands of features, need to be carried out.
Experimental evaluation of the algorithm has shownthat the method achieves high retrieval performances
for several different benchmark databases. For the
Princeton Shape Benchmark (PSB) [14] containing
rigid yet diverse 3D models, retrieval performancemeasured in R-precision is 56%. For the articulated
shapes in the McGill Shape Benchmark (MSB) [20], Rprecision of 76% is achieved.
Despite its high retrieval performance, the algorithm
left issues to be solved, namely, (1) incorporation ofmulti-class semantics, and (2) scalability in searching
through a database. Incorporation of semantic
knowledge from multi-class semantic labels obviously
benefits retrieval. In a classical object recognition
setting, classifiers such as Support Vector Machine(SVM) are used to recognize a semantic class. The
framework has been extended to recognize multiple
classes. However, classification is not necessarily
desirable for similarity based 3D shape retrieval. We
sometimes want objects that are not in the “correct”
class but have similar enough shape and/or semantics.
Thus, we do not want a cut-off at the classification
boundary. A distance metric space we aim for retrieval

Ryutarou Ohbuchi, Masaki Tezuka, Takahiko Furuya, Takashi Oyobe, Squeezing Bag-of-Features for Scalable and Semantic 3D
Model Retrieval, Proc. 8th International Workshop on Content-Based Multimedia Indexing (CBMI) 2010, 23-25 June 2010,
Grenoble, France.

is a smooth, continuous one that reflects dozens oreven hundreds of semantic classes.
The scalability issue arises since the dimension of
the feature vector is high; in case of the PSB, forexample, optimal feature vector size is ~30k
dimensions [2]. Computing 10M distances among 10M
pairs of such vectors by using L1-norm or KullbackLeibler divergence would take significant amount oftime. In addition to computational cost, (on-memory)storage cost for a high dimensional feature vector isalso an issue, especially if we want to recruit CPU
cache memory or Graphics Processing Unit (GPU) for
an efficient computation. There are studies (e.g., [7])that address ccompression of BoF feature vectors, forexample, via binary quantization or inverted files.
While these approaches aim only for compression, we
also aim to incorporate semantic knowledge for an
improved retrieval results.
This paper addresses the issues of featurecompression and semantic similarity-based retrieval(not recognition) by means of supervised feature
dimension reduction. Empirical evaluation showed thatthe dimension of the feature may often be reduced
from 30k down to about 50 by semi-supervised
dimension reduction, while achieving significantly
better retrieval performance.

2. Algorithm
We first outline the 3D model retrieval algorithms,
the Bag-of-Features Salient SIFT (BF-SSIFT) [12] andthe Bag-of-Features Dense SIFT (BF-DSIFT) [2]. A
feature vector per 3D produced by either of thesealgorithms then goes through dimension reduction,
whose methods are described in Section 2.2.

2.1. Multi-view bag-of SIFT features
Both BF-SSIFT and BF-DSIFT are based on bag-of
visual features. After normalizing the model for its
position and scale, a set of depth images of the model
is generated by using multiple virtual cameras looking
inward at the model. From each depth image, dozens oflocal visual features are extracted.
In the BF-SSIFT algorithm [12], we used asaliency-based local image feature Scale Invariant
Feature Transform (SIFT) by David Lowe [9] with its
interest point detector enabled. Typically, a 3D modelis rendered into 42 depth images, each one of whichthen produces 30 to 50 interest points. Thus, a 3Dmodel is described by a set of 1.5k SIFT features.
Directly comparing a pair of such feature sets would be
too expensive, especially to search through a 3D model
database containing a large number of models. To
reduce the cost of model-to-model similarity
comparison, the set of thousands of visual features is

integrated into a feature vector per model by using BoF
approach. The BoF approach vector quantizes, orencodes, the SIFT feature into a representative vector,or “visual word”, using a previously learned codebook.
The visual words are accumulated into a histogram,which becomes the feature vector.
The BF-DSIFT algorithm employs dense andrandom sampling of each range image without using
interest point detector [2]. The “random” sampling
actually employs a prior so that the samples are on ornear the 3D models to be compared in the images.
With the dense sampling, number of SIFT features per
range image increased from a few dozens to a few
hundreds. That is, number of SIFT features per 3Dmodel increased about tenfold, from thousands to tensof thousands. These features are again integrated into afeature vector by using BoF approach.
To bring down the query processing time, we
employed two accelerations. For SIFT feature
extraction, we employed a fast GPU-based
implementation of SIFT called SiftGPU by Wu [19].
We modified the SiftGPU for dense sampling for the
BF-DSIFT. We adopted Extremely Randomized
Clustering Tree, or ERC-Tree, by Guerts, et al [3], forboth feature set clustering during codebook learningand for vector quantization (VQ) of SIFT featuresduring retrieval. The ERC-Tree is much faster than the
combination of k-means clustering and naive linear

Multi-view
range image
rendering View 1 View 2
SIFT
featureextraction
ERC-treeencoder

Histogramgeneration
Dimension
reduction

Bags-ofvisual
words
FeaturevectorView V…
k clusters

Vocabulary
size k( x1 ,...xk )k = 10,000 ~ 100,000m = 10 ~ 100( x1 ,...xm )Distancecomputation

Distance
Figure 1. Local visual features from multiple viewpoints areintegrated into a vector by using BoF approach. Dimension
reduction produces a compact feature vector.

Ryutarou Ohbuchi, Masaki Tezuka, Takahiko Furuya, Takashi Oyobe, Squeezing Bag-of-Features for Scalable and Semantic 3D
Model Retrieval, Proc. 8th International Workshop on Content-Based Multimedia Indexing (CBMI) 2010, 23-25 June 2010,
Grenoble, France.

search for the nearest representative vector.

2.2. Dimension Reduction Algorithms
For dimension reduction, we compared three
dimension reduction algorithms (Figure 2) below.
They are adopted from our earlier work [9].
(1) Unsupervised Dimension Reduction (UDR):
Extract a k-dimensional feature from each modelin the unlabeled set of 3D models MUL of size p
for learning manifold for the UDR. Given the setof p unlabeled features, an UDR algorithm learns
the l-dimensional subspace SUDR spanned by theset. The resulting SUDR maps an input kdimensional feature to the interim, l-dimensionalfeature in which l < k . For the LLE [13], we must
approximate the SUDR so that it is defined
everywhere in the input space. We used RBFnetwork algorithm for the approximation, as
proposed by He, et al [5].
(2) Supervised Dimension Reduction (SDR):
Extract k-dimensional features from the set oflabeled 3D models M SL for learning manifold for
the SDR. Note that the size q of the M SL istypically much smaller than the size p of the MUL .
A SDR algorithm then learns categories from the qlabeled features in a batch and encodes theknowledge into the m-dimensional subspace SSDR
to be used for later SDRs. The manifold maps kdimensional input feature onto salient, mdimensional feature used for retrieval. We used
Supervised Locality Preserving Projections(SLPP) [4] for the SDR.
(3) Semi-Supervised Dimension Reduction (SSDR):
Semi-supervised dimension reduction performs the
UDR and the SDR in tandem. For each kdimensional input feature of all the models in the
database M D , employ the UDR and SDR in
succession to produce m-dimensional salientfeature that incorporates semantic concepts
learned from the labeled models in the training set
M SL .
For retrieval, store the salient feature together with thecorresponding 3D model for later retrieval. As thedimension m of a salient feature is much smaller thanthe dimension k of the corresponding input feature,
cost of distance computation and feature storage are
significantly reduced.
For the UDR, we used the LLE code available in theStatistical Learning Toolbox for the MatLab. For the
LLE, we used the 0/1 weights (as opposed to the heat
kernel) on the edges during the mesh construction step.
The algorithm employs RBF-network to continuously
approximate the discrete map of the LLE. We used theimplementation of RBF-network included in the
Neural Network Toolkit for the MatLab. Parameters of
the RBF-network, such as neighbourhood size, are

(a)

Input
featurek-dim.
featureSalient
featurem-dim.
featureUDRk >mp unlabeled p >> qfeatures

(b)

(c)

Input
featurek-dim.
featureInput
featurek-dim.
featureSDR

UDRp >> qk>m
q labeledfeaturesInterimfeaturel-dim.
featureSDR

Salient
featurem-dim.
featureSalient
featurem-dim.
featurek>ll>mp unlabeled p >> q q labeled
featuresfeatures
Figure 2. Three dimension reduction approaches used in thispaper; Unsupervised Dimension Reduction (UDR) (a),Supervised Dimension Reduction (SDR) (b), and SemiSupervised Dimension Reduction (SSDR) (c).

found experimentally. We used the code provided by
Xaofei He at his web site [4] for the SLPP.

3. Experiments and Results
We evaluate, for UDR, SDR, and SSDR, therelationship between feature dimension reduction andretrieval performance. We also evaluate, forcomparison, effectiveness of a simple quantizationlevel reduction of BoF histogram for featurecompression.
Evaluation experiments were performed using threebenchmarks, the McGill Shape Benchmark (MSB) [20]for highly articulated but less detailed shapes, the
SHREC 2006 (SHREC) [17] for a set of diverse anddetailed shapes, and the SHREC 2007/2008 CAD track(CAD) [10][18] for mechanical parts. Examples of 3Dmodels found in these databases are shown in Figure 3.
The MSB consists of 255 models categorized into 10classes. The MSB include such highly articulated
shapes as “humans”, “octopuses”, “snakes”, “pliers”,
and “spiders”. The SHREC 2006 uses the 1814
Princeton Shape Benchmark (PSB) [14] models as thetarget, and has 30 out-of-sample queries. The SHREC
2007 CAD track employs the Engineering ShapeBenchmark (ESB)[7], which includes 867 models
divided into 45 classes. The SHREC 2007/2008 CAD
track uses 45 out-of-sample queries for evaluation. The
SHREC benchmark models (that are, those in the PSB)
are more diverse in shape and are generally more

Ryutarou Ohbuchi, Masaki Tezuka, Takahiko Furuya, Takashi Oyobe, Squeezing Bag-of-Features for Scalable and Semantic 3D
Model Retrieval, Proc. 8th International Workshop on Content-Based Multimedia Indexing (CBMI) 2010, 23-25 June 2010,
Grenoble, France.

(a)
(b)

(c)
Figure 3. Examples of 3D models from the Princeton ShapeBenchmark (a) [12], the McGill Shape Benchmark (b) [20],and the Engineering Shape Benchmark (c) [7][10].

3.1. Feature compression via quantization level
reduction
In the first experiment, we evaluated simple feature
vector compression via reduction in quantization levelsof each bin of the BoF histogram. The method simply
clips a value in a histogram bin to the maximum agiven number of bits could represent. That is, if 4 bit isallotted to the bin, any counts larger than 15 will beclipped to 24=15.
Figure 4 shows the effect of number of bits per bin
on retrieval performance (in R-Precision). We used
BF-DSIFT feature having 30,125 dimensions for thisexperiment. To maintain retrieval performance of fullquantization levels (8bit/bin), the PSB requires
3 bit/bin, while the MSB requires 2 bit/bin. Higher
diversity and/or higher model complexity of the PSB
than the MSB could explain this discrepancy.
As the original feature used a 32bit integer for a bin,a feature having 30,125 dimensions required 964 kbits
to represent. For the PSB, this simple quantizationlevel reduction produced a feature of size 90 kbits, orabout 10 to 1 compression, without losing retrieval
performance.

80
R-Precision [%]detailed than those in the CAD and the MSB
benchmarks.
The same database is used for VQ codebook
training and VQ during retrieval experiments. That is,
the VQ codebook generated by using the ESB, forexample, is used to query the ESB in the SHREC 2007
CAD track benchmark. We used the training set size
N t = 50, 000 of SIFT features extracted from multiview images of models in a database. Size of eachrange image is 256 × 256 for both codebook training
and for query experiments.
We use R-precision as the performance index,
which is a ratio, in percentile, of the models retrieved
from the desired class C k (i.e., the same class as thequery) in the top R retrievals, in which R is the size ofthe class Ck .

70
60
50

MSB
PSB

40
0

1

2
3
4
5
6
7
8
Bin quantization [bit]Figure 4. Number of histogram bin quantization bits andretrieval performance for BF-DSIFT.

3.2. Feature
reduction

compression

viadimension

Second set of experiments evaluated theeffectiveness of the proposed feature compression
using manifold-based dimension reduction algorithms.
Bar graphs in Figure 5 shows, for both BF-SSIFT and
BF-DSIFT, retrieval performances due to three
dimension reduction methods for three retrieval
benchmarks. Figure 5(a), Figure 5(b), and Figure 5(c)show, respectively, the result obtained by using the
SHREC 2006 (“generic” and diverse models), theMSB (articulated models), and the SHREC 2007 CAD
track (mechanical parts models). Table 1 shows thesame performance figures for three databases, but withdimension of features used. Overall, the dimension
reduction is able to compress feature significantly,
while at the same time improving retrieval
performance. Several observations can be made ofthese results.
The first observation is that, for most of the cases,
dimension reduction resulted in quite significant
performance gain.
If supervision is not possible, the UDR can be used
to compress feature vector dimension while improving
or at least maintaining the retrieval performance. For
the MSB, the UDR produced 5 to 10% gain in RPrecision, while decreasing the dimension nearly by
about 1/10. For the CAD benchmark and for the
SHREC benchmark, small performance loss over theoriginal feature is observed for the BF-SSIFT. For the
BF-DSIFT, however, the UDR either improved or
maintained the retrieval performance of the original
feature vector. The UDR often suffers from insufficienttraining set. It is very likely that the 867 models of the
CAD benchmark is not sufficient for the LLE to learn
the structure of feature manifold. The SHREC
benchmark has twice as many model, 1,814, as the
CAD benchmark. But the SHREC database is morediverse. Thus learning manifold for the SHREC
benchmark could have been more difficult than the
CAD benchmark. The MSB with it 255 models couldRyutarou Ohbuchi, Masaki Tezuka, Takahiko Furuya, Takashi Oyobe, Squeezing Bag-of-Features for Scalable and Semantic 3D
Model Retrieval, Proc. 8th International Workshop on Content-Based Multimedia Indexing (CBMI) 2010, 23-25 June 2010,
Grenoble, France.

also be too small for the LLE, but lack of diversity inthe database might have saved the LLE. The MSB
appears to lack diversity in visual vocabulary; for the
BF-SSIFT, the number of vocabulary, i.e., feature
dimension for the MSB is the smallest among the three(See Table 1.)
If supervision is allowed, the SDR using SLPP [4]produced very good retrieval performance for the MSB
and CAD benchmarks. In case of the MSB, SDR using
SLPP produced near perfect retrieval score of RPrecision over 99%. In case of the CAD, R-Precision is
82.2% for the BF-DSIFT processed with the SDR. This
figure compares favorably with the best score of the
SHREC 2008 CAD track with R-Precision=78.2%.
(There was no CAD track for the SHREC 2009.) For
the SHREC benchmark, results are a bit complex; theSDR worked the best for the BF-SSIFT, while the
44.6
50.6
56.9
65.6
38.5
36.3
48.5
45.0

BF-DSIFTBF-SSIFT
0
None

50
UDR

SDR

100
SSDR

(a) SHREC benchmark.
74.5
84.0

BF-DSIFT

99.9
89.9

70.3
76.6

BF-SSIFT

83.7
0
None

UDR

50
SDR

99.1

100
SSDR

(b) MSB benchmark.

BF-DSIFT

42.1
41.5

BF-SSIFT

47.2
40.0
41.6
39.4
0

None

UDR

50
SDR

82.2

71.7
100
SSDR

(c) CAD benchmark.
Figure 5. Dimension reduction methods and retrieval
performance for three features applied to three benchmarks.
Horizontal axis indicates retrieval performance in R-Precision.

SSDR worked the best for the BF-DSIFT. Simple SDR
using SLPP worked for the MSB and the CAD
benchmarks as they are “easier” than the SHREC
benchmark; the former two have smaller number ofground truth classes and larger number of models perclass than the PSB. For the SHREC database having
more diverse set of 3D models, and has smaller class(e.g., only 4 models/class), the SSDR appears to work
better. Note that the SSDR worked for the BF-DSIFT,
but not for BF-SSIFT. A possible explanation for thisis the interference of interest point detector in BFSSIFT with the manifold estimation of the LLE.
Figure 6 shows, for the case of SDR using SLPP,
retrieval performance of BF-DSIFT for three databases
as a function of compressed feature dimension. A plot
with “baseline” shows the performance of the original
feature vector. For both MSB and CAD, dimension
reduced feature wins over the original everywhere. For
the MSB benchmark, the SDR produced very highscore regardless of feature dimension. The plot for the
CAD benchmark has a clear peak. The plot for the
SHREC benchmark has many dips and peaks, apossible indication of its difficult nature.
Table 1. Dimensions of compressed features and retrieval
performance.
Database

Dimension
reduction
SSDR
SDR
SHREC
2006
UDR
None
SSDR
SDR
MSB
UDR
None
SSDR
SHREC
SDR
2007
UDR
CAD
None

BF-SSIFT
Dim
R-P
30
45.0
140
48.5
50
36.3
1500
38.7
5
83.7
10
99.1
10
76.6
900
70.3
15
39.4
70
71.7
25
41.6
1200
40.0

BF-DSIFT
Dim
R-P
60
65.6
110
56.9
50
50.0
32236
44.6
8
89.9
10
99.8
10
84.0
75581
74.5
40
47.2
40
82.2
100
41.5
32362
42.1

The second observation is that, as Table 1 shows,very significant reduction in feature size has beenachieved. Such reduction should reduce the featurestorage feature comparison costs. For example, for the
SHREC benchmark, 32,236 dimensions of the BFDSIFT is reduced to only 50 using the UDR withperformance gain of 5%, from 44.6% to 50.0%. Whensupervision is allowed, the SSDR produced a 60
dimensional feature having a significantly better RPrecision of 65.6%. Note that the dimension reduction
produces floating point numbers, so that a 60D feature
would consume 60 × 32 = 1,920 bit. However, this is
still significantly smaller than 32, 236 × 3 = 96,708 bit

Ryutarou Ohbuchi, Masaki Tezuka, Takahiko Furuya, Takashi Oyobe, Squeezing Bag-of-Features for Scalable and Semantic 3D
Model Retrieval, Proc. 8th International Workshop on Content-Based Multimedia Indexing (CBMI) 2010, 23-25 June 2010,
Grenoble, France.

R-Precision [%]of the original, uncompressed feature encoded using
reduced quantization levels of 3 bit/bin.
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
0
SHREC
CAD
MSB

50

100

150

200

SHREC(baseline)
CAD(baseline)
MSB(baseline)

Figure 6. Dimensions after supervised dimension reduction(SDR) using the SLPP [4] and retrieval performance. (BFDSIFT)

4. Conclusion and Future WorkIn this paper, we proposed, in a similarity-based 3D
shape retrieval setting, a method to reduce size offeature vector produced by bag-of-features approach
while incorporating semantics provided by multiple
class labels. We wanted to reduce the feature size forcomputational efficiency in searching though a large
database. We also wanted the reduced feature vector tohave better retrieval performance by exploiting
semantics.
We employed supervised and semisupervised dimension reduction algorithms for the task.
Empirical evaluation showed that the proposed
approach often boosted retrieval performance while
compressing the feature very significantly. Reduced
size of compressed features would allow efficient us of
CPU cache or Graphics Processing Units (GPU)memory. The reduced feature also showed significantly
improved retrieval performance.
A weakness in the proposed algorithm is thescalability (or lack of thereof) of learning algorithms
for dimension reduction. The dimension of original
feature and/or the number of training samples
determine space and time complexity of thesealgorithms. We are currently experimenting withmethods to make these learning algorithms morescalable.

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