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DRAFT
Large Scale Image Retrieval Using Vector of
Locally Aggregated Descriptors
Giuseppe Amato, Paolo Bolettieri, Fabrizio Falchi, Claudio Gennaro
{giuseppe.amato, paolo.bolettieri, fabrizio.falchi claudio.gennaro}@isti.cnr.it
ISTI - CNR, Pisa, Italy
Abstract. Vector of locally aggregated descriptors (VLAD) is a promis-
ing approach for addressing the problem of image search on a very large
scale. This representation is proposed to overcome the quantization er-
ror problem faced in Bag-of-Words (BoW) representation. However, text
search engines have not be used yet for indexing VLAD given that it is
not a sparse vector of occurrence counts. For this reason BoW approach
is still the most widely adopted method for finding images that represent
the same object or location given an image as a query and a large set of
images as dataset.
In this paper, we propose to enable inverted files of standard text search
engines to exploit VLAD representation to deal with large-scale image
search scenarios. We show that the use of inverted files with VLAD
significantly outperforms BoW in terms of efficiency and effectiveness on
the same hardware and software infrastructure.
Keywords: bag of features, bag of words, local features, compact codes, image
retrieval.
1 Introduction
In the last few years, local features [16] extracted from selected regions [22]
have emerged as a promising method of representing image content in such a way
that tasks of object recognition, and other similar (e.g. landmark recognition,
copy detection, etc.) can be effectively executed. A drawback of the use of local
features is that a single image is represented by a large set (typically thousands)
of (local) descriptors that should be individually matched and processed in order
to compare the visual content of two images. In principle, a query image should
be compared with each dataset object independently. In fact, each local feature of
the query should be compared with all the local features of any dataset image in
order to find a possible match. Moreover, candidate matches should be validated
evaluating a geometric transformation (typically an Homography) able to map a
region of the query to a region of the dataset image. Even though data structures
as kd-tree [9] are used to efficiently search candidate matching pairs in any two
images, still the approach is not scalable.
2
A very popular method to achieve scalability is the Bag-of-Words (BoW)
[21] (or bag-of-features) approach that consists in replacing original local de-
scriptors with the id of the most similar descriptor in a predefined vocabulary.
Following the BoW approach, an image is described as a histogram of occur-
rence of visual words over the global vocabulary. Thus, the BoW approach used
in computer vision is very similar to the traditional BoW approach in natural
language processing and information retrieval [5]. However, as mentioned in [24],
“a fundamental difference between an image query (e.g. 1500 visual terms) and
a text query (e.g. 3 terms) is largely ignored in existing index design”. From the
very beginning [21] a words reduction technique was used (e.g. removing 10% of
the more frequent images). In [2], removing query words with small tf*idf [20]
revealed very good performance in improving efficiency of the BoW approach
with a reduced lost in effectiveness. In this work, we make use of the parametric
tf*idf approach for facilitating trade-offs between efficiency and effectiveness in
the BoW approach.
Efficiency and memory constraints have been recently addressed by aggre-
gating local descriptors into a fixed-size vector representation that describe the
whole image. In particular, Fisher Vector (FV) [18] and VLAD [12] have shown
better performance than BoW [15]. In this work we will focus on VLAD which
has been proved to be a simplified non-probabilistic version of FV. Despite its
simplicity, VLAD performance is comparable to that of FV [15].
Euclidean Locality-Sensitive Hashing [7] is, as far as we know, the only in-
dexing technique tested with VLAD. While may other similarity search indexing
techniques [23] could be applied to VLAD, in this work we decide to investi-
gate the use of inverted files for allowing comparison of the VLAD and BoW
approach on the same index. Permutation-Based Indexing [6, 4, 8] allows using
inverted files to perform similarity search with an arbitrary similarity function.
Moreover, in [10,1] a Surrogate Text Representation (STR) derivated from the
MI-File has been proposed. The conversion of the image description in a textual
form allows us to employ the search engine off-the-shelf indexing and searching
abilities with a little implementation effort.
In this paper, we applied the STR technique to the VLAD method compar-
ing both effectiveness and efficiency with the state-of-the-art BoW approach on
the very same hardware and software infrastructure using the publicly available
and widely adopted 1M photos dataset. Given that the STR combination gives
approximate results with respect to a complete sequential scan, we also com-
pare the effectiveness of VLAD-STR with the one of standard VLAD. Moreover,
we considered balancing efficiency and effectiveness with both BoW and VLAD-
STR approaches. For the VLAD-STR, a similar trade-off is obtained varying the
number of results used for re-ordering. Thus, we do not only compare VLAD-
STR and BoW on specific settings but we show efficiency vs effectiveness graphs
for both. For the VLAD-STR, a trade-off is obtained varying the number of
results used for re-ordering.
Results confirm the higher performance obtained by VLAD with respect to
BoW already showed in [12,15] even when VLAD is combined with STR a off-
3
the-shelf text search engine (i.e., Lucene) is used. Thus, our main contribution is
proving that the proposed VLAD-STR approach, can be used, in place of BoW,
in combination with traditional text search engines achieving good scalability
and preserving the improvement in effectiveness already showed in [15]
The paper is organized as follows. Section 2 presents relevant previous works.
In Section 3 we present the STR approach that is used for indexing VLAD with
a text search engine. Results are presented in Section 4. Finally, in Section 5 we
present our conclusions and describe future work.
2 Related Work
2.1 Local Features
Local features [16] describe the visual content of local interest regions computed
for local interest regions [22]. Good local features should be distinctive and at
the same time robust to changes in viewing conditions as well as to errors of
the detector. Developed mainly in Computer Vision, their typical applications
include finding locations and particular objects, detecting image near duplicates
and deformed copies. A drawback of the use of local features is that a single
image is represented by a large set (typically thousands) of descriptors that
should be individually matched and processed in order to compare the visual
content of two images.
2.2 Bag of Words (BoW)
State-of-the art techniques for performing large scale content based image re-
trieval using local features typically involve the BoW approach. BoW was ini-
tially proposed in [21] and has been studied in many other papers. The goal of
the BoW approach is to substitute each local descriptor of an images with visual
words obtained from a predefined vocabulary in order to apply traditional text
retrieval techniques to CBIR.
The first step is selecting some visual words creating a vocabulary. The visual
vocabulary is typically built clustering, using k-means, local descriptors of the
dataset ad selecting the centroids. The second step assigns each local descriptor
to the identifier of the first nearest word in the vocabulary. For speeding-up this
second phase approximate kd-tree is often used at a small effectiveness price. At
the end of the process, each image is described as a set of visual words. The
retrieval phase is then performed using text retrieval techniques considering a
query image as disjunctive text-query. Typically, the cosine similarity measure in
conjunction with a term weighting scheme is adopted for evaluating the similarity
between any two images.
Even though inverted files offer a significant improvement in efficiency, in
many cases efficiency is not yet satisfactory. In fact, a query image is associated
with thousands of visual words. Therefore, the search algorithm on inverted files
4
has to access thousands of different posting lists. From the very beginning [21]
words reduction techniques were used (e.g. removing 10% of the more frequent
images). However, as far as we know, no experiments have been reported on the
impact of the reduction on both efficiency and efficacy.
In [2], various techniques to reduce the number of words describing an image
obtained with the BoW approach were evaluated. tf*idf [20] revealed very good
performance in improving efficiency with a reduced lost in effectiveness. In this
work, we make use of the parametric tf*idf approach to allow trade-offs between
efficiency and effectiveness.
2.3 Fisher Vector
Fisher kernels [11] describe how the set of descriptors deviates from an average
distribution, modeled by a parametric generative model. Fisher kernels have been
applied in the context of image classification [17] and large scale image search
[18]. In [15] it has been proved that Fisher vectors (FVs) extend the BoW. While
the BoW approach counts the number of descriptors assigned to each region in
the space, FV also encodes the proximate location of the descriptors in each
region and has a normalization that can be interpreted as an IDF term. The FV
image representation proposed by [17] assumes that the samples are distributed
according to a Gaussian Mixture Model (GMM) estimated on a training set.
Results reported in [15] reveal that FV indexed using LSH outperforms BoW.
2.4 VLAD
The VLAD representation was proposed in [12]. As for the BoW, a codebook
{µ1, . . . , µK}is first learned using a cluster algorithm (e.g. k-means). Each lo-
cal descriptor xtin each image is then associated to its nearest visual word
NN (xt) in the codebook. For each codeword the differences between the vectors
xtassigned to µiare accumulated:
vi=X
xt:NN (xt)=i
xt−µi
VLAD is the concatenation of the accumulated vectors, i.e. V= [vT
1. . . vT
K].
Please note that all vi(i= 1, ...K) have the same size which is equal to the size
of the used local feature (e.g. 128 for SIFT). Given a codebook {µ1, . . . , µK},
Kis fixed (typically 16 ≤K≤128. Thus the dimensionality of the whole
vector Vdescribing any image is fixed too. In other words, VLAD evaluates a
global descriptor statistically describing a set of local features with respect to a
predefined codebook.
In order to improve the effectiveness of the VLAD approach, two normaliza-
tion are performed: first, a power normalization with power 0.5; second, a L2
normalization. After this process two global descriptor V1and V2related to any
two images can be compared using the inner product.
5
The observation that VLAD descriptor has high dimensionality but is rela-
tively sparse and very structured suggests a principal component analysis (PCA)
that is usually performed to reduce the size of the K-dimensional VLAD vectors.
In this work, we decide not to use dimensionality reduction techniques because
we will show that our space transformation approach is independent from the
original dimensionality of the description. In fact, the STR approach that we
propose, transforms the VLAD description in a set of words from a vocabulary
that is independent from the original VLAD dimensionality. In our proposal,
PCA could be used to increase efficiency of the STR trasformation.
In [15], it has been shown that VLAD is a simplified non-probabilistic ver-
sion of FV: VLAD is to FV what k-means is to GMM clustering. The k-means
clustering can be viewed as a non-probabilistic limit case of GMM clustering.
In [15] Euclidean Locality-Sensitive Hashing and its variant have been pro-
posed to efficiently search VLAD descriptors.
3 Perspective Transformation and Surrogate Text
Representation
In this paper, we propose to index the VLAD descriptors using a surrogate
text representation. This allows using any text retrieval engine to perform image
similarity search. As discussed later, for the experiments, we implemented these
ideas on top of the Lucene text retrieval engine.
The approach to encode global features (as VLAD) used in this paper lever-
ages on the perspective based space transformation developed in [4, 10]. The
idea at the basis of this technique is that when two descriptors are very similar,
with respect to a given similarity function, they ’see’ the ’world around’ them
in the same way. In the following, we will see that the ’world around’ can be
encoded as a surrogate text representation (STR), which can be managed with
an inverted index by means of a standard text-based search. The conversion of
the visual descriptor in a textual form allows us to employ the search engine
off-the-shelf indexing and searching abilities with a little implementation effort.
3.1 STR Generation
Let Dbe the domain of the global descriptors o, and d:D × D → Ra dis-
tance function able to assess the dissimilarity between any two o1, o2∈ D.
Let R∈ Dm, be a vector of mdistinct reference descriptors (or pivots)ri,
i.e., R= (r1, . . . , rm). We denote the vector of positions of the reference ob-
jects in Rranked by increasing distance with respect to an object o∈ D as
P(o) = (p1(o), . . . , pm(o)). As an example, if p3(o) = 2 then r3is the 2nd near-
est object to oamong those in R.
The objective is to define a function that transforms a global descriptor
into a sequence of terms (ie, a textual document) that can be fed into a text
search engine as for instance Lucene. Of course, the ultimate goal is to obtain
that the distance between the documents and the query is an approximation
6
of the original distance function of the global descriptors. To achieve this, we
associate each element ri∈Rwith a unique alphanumeric keyword τi, and define
a function tk(o) that returns a space-separated concatenation of zero or more
repetitions of τikeywords, as follows:
tk(o) =
m
[
i=1
(k+1)−pk
i(o)
[
j=1
τi
where pk
i(o) = pi(o) if pi(o)< k and pk
i(o) = kotherwise. By abuse of notation,
we denote the space-separated concatenation of keywords with the union opera-
tor ∪. The inner ∪simply repeat (k+ 1) −pk
i(o) times the alphanumeric keyword
τiused for indicating the reference object ri∈R. The outer ∪concatenates the
repeated occurrences, if any, of keywords τifor i= 1...m. The function tk(o) is
used to generate the STR to be used for both indexing and querying purposes.
kis used to consider only the knearest reference object in Rto o, and typically
assumes two distinct values for the query qand for the objects in the dataset (kx
for indexing and kqfor querying). For instance, consider the case exemplified in
Figure 1, and let us assume τ1=A, τ2=B, etc. The function tkwill generate the
following outputs
tkx(o1) = “E E E B B A”
tkx(o2) = “D D D C C E”
tkq(q) = “E E A”
As can be seen intuitively, strings corresponding to o1and qare more sim-
ilar to those corresponding to o2eq, this approximate the original distance d.
Without going to the mathematical details, we leverage on the fact that a text
based search engine will generate a vector representation of STRs generated with
tkx(o) and tkq(q) containing the number of occurrences of words in texts. This
is the case of the simple term-frequency weighting scheme. This means that, if
for instance keyword τicorresponding to the reference object ri∈Rappears n
times, the i-th element of the vector will contain the number n, and whenever
τidoes not appear it will contain 0. With simple mathematical manipulations,
it is easy to see how applying the cosine similarity on the query vector and a
vector in the database corresponding to tkx(o) and tkq(q) respectively, we get
a degree of similarity that reflects the similarity order of reference descriptors
(pivots) around descriptors in the original space.
For more information on how the technique works from the mathematical
point of view, we remind the reader to [10, 1]. The impact of kxon the effective-
ness of the search has been studied in [3].
3.2 Reordering Search Results
The idea described so far uses a textual representation of the descriptors and a
matching measure based on a similarity offered by standard text search engines
to order the descriptors in the dataset in decreasing similarity with respect to
the query. The result set is more precise if we order it using the original distance
function d.
7
Fig. 1. Example of perspective based space transformation and Surrogate Text Rep-
resentation. a) Black points are reference objects; white points are data objects; the
gray point is a query. b) Encoding of the data objects in the STR.
Suppose we are searching for the kmost similar (nearest neighbors) descrip-
tors to the query. We can improve the quality of the approximation by re-ranking,
using the original distance function d, the first c(c≥k) descriptors from the
approximate result set at the cost of more cdistance computations. We will show
that this technique significantly improves the accuracy, though only requiring a
very low search cost. In fact, when cis much smaller than the size of the dataset,
this extra cost can be considered negligible with respect to the cost of accessing
the inverted file. For instance, when kis 10 and c=1,000, with a dataset size of
1,000,000 it means that we have to reorder a number of descriptors equivalent
to just 0.1% of the entire dataset. Usually, this is not true for other access meth-
ods, for instance tree-based access methods, where the efficiency of the search
algorithms strongly depends on the amount of descriptors retrieved.
4 Experiments
4.1 Setup
INRIA Holidays [14, 15] is a collection of 1,491 holiday images. The authors se-
lected 500 queries and, for each of them, a list of positive results. To evaluate the
approaches on a large scale, we merged the Holidays dataset with the Flickr1M1
collection as in [13, 12, 15]. The ground–truth is the one built on the INRIA Hol-
idays dataset alone, but it is largely accepted that no relevant images can be
found between the Flickr1M images. SIFT descriptors and various vocabulary
were made publicly available by Jegou et al. for both the Holidays and the Flickr
1M datasets2. For the BoW approach we used the 20K vocabulary.
1http://press.liacs.nl/mirflickr/
2http://lear.inrialpes.fr/~jegou/data.php
8
avg#Words mAP avg mSec
7 0.03 525
16 0.07 555
37 0.11 932
90 0.14 1463
233 0.15 2343
BoW
Table 1. Effectiveness (mAP) and effi-
ciency (mSec) with respect to the average
number of distinct words per query ob-
tained with the BoW approach varying the
query size.
#reordered mAP avg mSec
0 0.13 139
100 0.24 205
1000 0.29 800
2000 0.30 1461
4000 0.31 2784
VLAD
Table 2. Effectiveness (mAP) and effi-
ciency (mSec) obtained with the VLAD
approach in combination with STR, with
respect to the number of results used for
reordering.
For representing the images using the VLAD approach, we selected 64 ref-
erence descriptors using k-means over a subset of the Flickr1M dataset. As ex-
plained Section 3, a drawback of the perspective based space transformation used
for indexing the VLAD with a text search engine is that it is an approximate
technique. However, to alleviate this problem, we reorder the best results using
the actual distance between the VLAD descriptors. For the STR we used 4,000
references (i.e., m= 4,000) randomly selected from the Flickr1M dataset.
During the experimentation also 256 references for VLAD and up to 10,000
references for the STR were selected but the results were only slightly better
than the ones presented while efficiency significantly reduced.
All experiments were conducted on a Intel Core i7 CPU, 2.67 GHz with 12.0
GB of RAM a 2TB 7200 RPM HD for the Lucene index and a 250 GB SSD
for the VLAD reordering. We used Lucene v3.6 running on Java 6 64 bit over
Windows 7 Professional.
The quality of the retrieved images is typically evaluated by means of preci-
sion and recall measures. As in many other papers [19, 13, 18, 15], we combined
this information by means of the mean Average Precision (mAP), which repre-
sents the area below the precision and recall curve.
4.2 Results
In Table 1, we report the mAP obtained with the BoW approach varying the
size of the query in terms of average number of distinct words. The query words
have been filtered using the tf*idf approach as mentioned in Section 2.2. The
average number of words per image, as extracted by the INRIA group, is 1,471
and they were all inserted in the index without any filtering. The filtering was
used only for the queries and results are reported for average number of distinct
words up to 250. In fact, bigger queries result in heavy load of the system. It is
worth to mention that we were able to obtain 0.23 mAP performing a sequential
scan of the dataset with the unfiltered queries.
9
The results show that while the BoW approach is in principle very effective
(i.e. performing a sequential scan), the high number of query visual words needed
for achieve good results significantly reduces his usability. As mentioned in [24],
“a fundamental difference between an image query (e.g. 1,500 visual terms) and
a text query (e.g. 3 terms) is largely ignored in existing index design. This
difference makes the inverted list inappropriate to index images”.
In Table 2, we report the results obtained using the VLAD approach in
combination with the use of the STR illustrated in Section 3. As explained in 4.1,
given that for indexing the images we used a STR, it is useful to reorder the better
results obtained from the text search engine using the actual VLAD distance.
Thus, we report mAP and avg mSec per query for the non–reordering case and
for various values of results used for reordering. The reordering phase dominates
the average query time but it significantly improves effectiveness especially if
only 100 or 1,000 objects are considered for reordering. As mentioned before, we
make use of SSD for speed-up reordering phase but even higher efficiency could
be obtained using PCA as proposed in [15]. Please note that even though the
reordering phase cost for VLAD can be reduced, the reported results already
show that VLAD outperform BoW.
It is worth to mention that we also performed a sequential scan of the en-
tire dataset obtaining a mAP of 0.34 for VLAD. In fact, as depicted in 3, the
results obtained with the VLAD-STR approach are an approximation of the re-
sults obtained with a complete pair wise comparison between the query and the
dataset object. The same is true when LSH indexing is used as in [15]. Results
show that the approximation introduced byt STR does not impact significantly
the effectiveness of the system when at least 1,000 objects are considered for
reordering.
In Figures 2 and 3 we report the precision and recall curves for BoW and
VLAD. The results essentially confirm the ones reported in Table 1 and 2. In
fact, no significant differences can be found in the distribution of the precision
with respect to the recall.
In Figure 4 we plot mAP with respect to the average query execution time for
both BoW and VLAD as reported in Table 1 and Table 2. The graph underlines
both the efficiency and effectiveness advantages of the VLAD with respect to
the BoW approach.
5 Conclusions and Future Work
In this work, we proposed the usage of STR in combination with VLAD
descriptions in order to index VLAD with off-the-shelf text search engines. Using
the very same hardware and text search engine (i.e., Lucene), we were able to
compare with the state-of-the-art BoW. Results obtained for BoW confirm that
the high number of visual terms in the query significantly reduces efficiency of
inverted lists. Even though results showed that this can be mitigated reducing the
number of visual terms in the query with a tf*idf weighting scheme, the VLAD-
STR significantly outperforms BoW in terms of both efficiency and effectiveness.
10
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Precision
Recall
BoW
233
90
37
16
7
Fig. 2. Precision and recall curves ob-
tained with the BoW approach in combi-
nation with STR for various query size.
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Precision
Recall
VLAD
4000
2000
1000
100
0
Fig. 3. Precision and recall curves ob-
tained with the VLAD-STR for various
number of results used for reordering.
The efficiency vs effectiveness graph reveals that VLAD-STR is able to obtain
the same values of mAP obtained with BoW for an order of magnitude less
in response time. Moreover, for the same response time, VLAD-STR is able to
obtain twice the mAP of BoW.
Future work includes VLAD-STR improving the reordering phase. With re-
gards to efficiency, PCA could be used on VLAD as suggested in [15]. Moreover,
in recognition scenarios (e.g., landmark recognition) the reordering phase typ-
ically involves geometric consistency checks performed using RANSAC. This
could be also done with the VLAD description.
As mentioned in the paper, VLAD is essentially a non probabilistic version
of the Fisher Kernels that typically results in almost the same performance. It
would be interesting to test the STR approach also with Fisher Kernels compar-
ing with both VLAD-STR and BoW.
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