ACCURATE FEATURE MATCHING AND SCORING
FOR RE-RANKING IMAGE RETRIEVAL RESULTS
Yusuke Uchida, Shigeyuki Sakazawa
KDDI R&D Laboratories, Inc., Japan
ABSTRACTIn this paper, a new reranking approach is proposed to refine
the results obtained with a bag-of-visual words (BoVW) image retrieval method. First, a simple but effective criterion to
reject unreliable feature matches is proposed, where the information of nearest neighbors from a large dataset is used
to accurately estimate feature density. Second, by adopting a
product quantization-based nearest neighbor method in boththe voting and reranking steps, it becomes possible to reuse
the information obtained in the BoVW method in the reranking step. Finally, a density ratio-based scoring method is naturally integrated to calculate a new score from inliers.
Index Terms— Specific object recognition, bag-of-visual
words, product quantization, geometric verification, feature
matching
1. INTRODUCTION
With the advancement of both stable interest region detectors [1, 2] and robust and distinctive descriptors [1, 3], local feature-based image or object retrieval has attracted agreat deal of attention. It has become particularly applicableto large-scale databases with a bag-of-visual words (BoVW)
framework [4]. In the BoVW framework, local feature points
or regions are detected from an image, and feature vectors
are extracted from them. These feature vectors are quantized
into visual words (VWs) using a visual codebook, resulting
in a histogram representation of VWs. Image similarity ismeasured by L1 or L2 distance between the normalized histograms. As VW histograms are generally very sparse, aninverted index data structure and a voting function enables anefficient similarity search. A term frequency-inverse document frequency (TF-IDF) weighting scheme is naturally integrated with the voting function [4].
Although the BoVW framework realizes efficient retrieval, there is some room for improvement in terms of accuracy. One significant drawback of VW-based matching isthat two features are matched if and only if they are assigned
to the same VW [5]. There are two major expansions of thevoting function to alleviate this problem: post-filtering [5, 6]
and multiple assignment [7, 5]. In post-filtering, after VWbased matching, unreliable matches are filtered out according

to (estimated) distances between query and reference features.
In multiple assignment, query features vote not only for reference features in the nearest VW but also for reference featuresin the k-nearest VWs. The use of weak geometric informationin conjunction with the BoVW framework also improves theperformance [5, 8], where the IDF scores are voted for orientation and scale space associated with feature matches [5],or position space of target objects [8]. Finally, query expansion [9] and geometric verification [10] are performed to refine scores obtained with the voting function.
Geometric verification is a very important step to refine the scores obtained with the voting function by filteringout outliers of feature matches and reranking the first result.
However, reranking based on geometric verification sometimes degrades accuracy in real applications because target
objects are generally assumed to be planar and rigid. Thisis the case when recognizing non-planar product packages ordeformable objects such as magazines or books. Although
there are a few approaches to detect or track deformable objects [11], it is time consuming in one-to-many matchingwhich is required in reranking.
In this paper, in order to improve the results obtainedwith the voting function without geometric information, a
new reranking approach based on effective feature matchingand scoring is proposed. In Section 2, conventional feature
matching methods and their problems are explained. In Section 3, a simple and effective criterion to reject unreliablefeature matches based on the probabilistic density function(PDF) of local features is proposed, where the informationof nearest neighbors from a large dataset is used to accurately estimate the PDF. In Section 4, the proposed criterion is
integrated with a state-of-the-art product quantization-based
framework [6, 12], where the information of nearest neighbors obtained in the BoVW framework is reused in the reranking step for efficiency. An effective density ratio-based scoring method [13] is adopted in the framework to obtain finalscores.
2. RERANKING BASED ON GEOMETRICVERIFICATIONThe results obtained in voting can be improved with reranking
based on geometric verification [10], where the spatial consis-

tency among a query image and reference images is used as aconstraint to filter out outliers. Because geometric verification
is more time consuming than BoVW scoring, it is performed
only on a shortlist of top scoring images. Reranking based ongeometric verification mainly consists of the following steps:(1) for each feature q in a query image Q, perform nearest
neighbor matching against features in a target image and obtain a tentative match, (2) estimate an affine or homographymatrix using the tentative matches, and (3) replace the score
between the query image and the target image by the numberof inliers or the sum of IDF scores of inliers which satisfy
the affine or homography matrix constraint. Because tentative matches include many outliers, it is necessary to filter out
unreliable matches to obtain stable results.
There are two directions to improve the accuracy of tentative matches. One is to use sophisticated (dis)similarity
measures: Chi-squared distance [14], Hellinger kernel [9], or
earth mover’s distance (EMD) [15] is used as (dis)similarity
measures. The other is to filter out unreliable matches basedon a matching criterion. The most frequently used criterion
is ratio criterion [1, 3, 14, 16] to filter out unreliable matches:
if the ratio of the best distance d1 and the second best distance d2 is greater than a threshold α (typically 0.8), the tentative match is rejected. This ratio criterion works better thanthe distance criterion [3] because SIFT features are not distributed uniformly in the feature space [12] and a constantthreshold cannot cope with this aspect. The ratio criterion isadaptive to some extent according to feature distribution, and
it is also generic and not restricted to the Euclidean distance(e.g., it is applied to the Hamming distance [16], the Chisquared distance [14], and EMD [15]). However, the ratio
criterion does not work well in some situations. First, it does
not work if multiple similar features are detected from near regions; this is often the case for the Hessian-Affine detector [2]or the multi-scale FAST detector [17], for instance. Second,
its performance degrades if approximate distances are usedbecause feature distribution is estimated using only a single
target image, and is thus sensitive to noise. This often happens when features are encoded into compact codes [6, 16, 5]
for memory and time efficiency. In the next section, to addressthese issues, we propose a new criterion based on the densityof local features, which is estimated using a large dataset independent of the target image.
3. PROPOSED CRITERION
Using the proposed criterion, the tentative match between q
and its nearest neighbor r̂ is rejected if the likelihood ratiop(q|r̂)/p(q) is smaller than the threshold th, where r̂ denotes
the nearest neighbor feature in the target image R, p(q|r̂) denotes the probability that q is generated from r̂, and p(q) denotes the probability that q is generated independently of R.
Denoting by p(q|R) the probability that q is generated fromone of the features in the target image R, it is clear that an

inequality p(q|r̂) ≤ p(q|R) holds. Due to the long-tail characteristic of feature distributions, almost all of the features
are rather isolated in the feature space [18]. In other words,p(q|r) ≈ 0 for r ̸= r̂. Hence, p(q|R) is a good approximationof p(q|r̂). The likelihood ratio p(q|r̂)/p(q) is now approximated by p(q|R)/p(q).
Here, we assume a distance list (d1 , · · · , dT ) with size T
is available, where dt is the distance between q and the t-thnearest neighbor feature in a large, independent database as
shown in Figure 1 (a). Using the distance list, p(q|R) andp(q) are estimated via k-nearest neighbor density estimation:p(q|R) =1t̂, p(q) =,|R| · Vdˆ|RDB | · Vdˆ(1)where |R| is the number of features in R, |RDB | is the numberof features in the database, Vdˆ is the volume of a hypersphereˆ dˆ is the distance between q and r̂, and t̂ is thewith radius d,smallest t that satisfies dˆ < dt . As shown in Figure 1 (b), forp(q|R) and p(q), k = 1 and k = t̂ are respectively used in
k-nearest neighbor density estimation; in the case of p(q|R),
one feature r̂ out of R exists in the hypersphere, while, in thecase of p(q), t̂ features including r̂ out of RDB exist in thehypersphere. Now the criterion to reject the tentative match
associated with q is:p(q|r̂)|RDB |< th.
≈p(q)t̂ · |R|(2)

As Eq. (2) can be written as t̂ > |RDB |/(|R| · th), we can use
T ′ = |RDB |/(|R| · th) (T ′ ≤ T ) as a new threshold for t̂.
To summarize, the proposed method consists of the following simple procedures: (1) calculate the distance dˆ fromq to its nearest neighbor r̂ in a target image R, (2) calculate
the distances d1 , · · · , dT from q to its T nearest neighbors ina large dataset, and (3) reject the tentative match associatedwith q if dˆ > d′T .
In this paper, we refer to the criterion as a rank criterion
because t̂ corresponds to the rank of r̂ in a distance list. In thecase of Figure 1 (a), where T ′ = T = 4, the tentative match
associated with q1 is considered to be an inlier, while thatwith q2 is rejected. It is desirable to obtain distance lists froma large database, because, if an infinite number of samples
is available, the density estimated using the k nearest neighbor method converges to the true density. However, obtaining
distance lists from a large database imposes a heavy computational burden. In the next section, we propose the framework
where a overhead becomes negligible because we reuse distance lists of query features which have been already obtainedin the process of index search.
4. PROPOSED FRAMEWORKIn this section, we describe the proposed framework, which
naturally integrates the state-of-the-art product quantizationbased image retrieval method [6, 12, 13] with the proposed

DatabaseDistance list of q1

0.3
q1

Query image

Reference image

Local feature detection

Local feature detection

Local feature description

Local feature description

Quantization

Quantization

0.12 0.2 0.25 0.4

r1

0.3

Inverted index

Distance list of q2

0.5

q2

r2

0.1 0.14 0.21 0.3

Target image

0.5

d4

d̂

d1

ID Short code

Voting result

q

d3

Vdˆ

Reference image 2

Final result
Features in target image
Features in database(b) An example of k-nearest neighbor density estimation.

Reference image 1

Nongeometric reranking

...

d2

w

...

r̂

Distance lists
Voting...

(a) The relationship among a query image, a target image, and a database.

...

...

Query image

1
2

Index search

Short code

Database

Fig. 2: Framework of the proposed image retrieval system.

Fig. 1: Overview of the proposed method.

reranking method. In the reranking step, we also adopt the
product quantization-based distance calculation method withdifferent settings. This enables efficient matching and makes
distance lists obtained in the index search compatible with
distances calculated in the reranking step. New scores arecalculated and voting results are refined according to feature matches which satisfy the proposed criterion describedin Section 3. Figure 2 provides an overview of the proposed
framework and the data structure used in the framework.

l
bl = arg min ∗ ||r̄jh− plb ||2 .

4.1. Feature detection and description

1≤b≤k

From query and reference images, a set of feature vectors is
extracted. We adopt Hessian-Affine [19] and SIFT [1] as thefeature detector and descriptor, respectively. We denote thei-th feature vector of the query image by qi ∈ Q and the h-thfeature vector of the j-th reference image by rjh ∈ Rj .
4.2. Feature indexing with product quantization
We adopt a product quantization-based method [6] to improve
the BoVW framework, namely IVFADC. In the indexing (offline) step in IVFADC, a reference vector rjh with d dimension is quantized with a coarse quantizer in the same way
as the BoVW framework. We refer to the codebook used incoarse quantization as the CQ codebook. This is the same aswhat is referred to as visual words or a visual codebook in thecontext of BoVW-based image retrieval or recognition.
In the indexing step, a reference vector rjh is first quantized into câ using the CQ codebook C with k ′ centroids
c1 , · · · , ck′ ∈ Rd , whereâ = arg min ′ ||rjh − ca ||2 .
1≤a≤kSubsequently, the residual vector r̄jh from the corresponding
centroid câ is calculated as r̄jh = rjh − câ . Then, the residual1uvector r̄jh is decomposed into u subvectors r̄jh
, · · · , r̄jh∈d∗∗
R , where d = d/u. Subsequently, these subvectors arequantized separately using u codebooks P1 , · · · , Pu . Thisis referred to as product quantization. In this paper, a codebook used in product quantization is referred to as a PQ codebook. We assume that each PQ codebook Pl has k ∗ centroids∗
pl1 , · · · plk∗ ∈ Rd . Using the l-th PQ codebook, the l-th subl
vector r̄jh
is quantized into plbl , where

(3)

(4)

Finally, the short code (b1 , · · · , bu ) is stored in the â-th list of
the inverted index with the identifier j of the reference image.
The size of the short code is represented by u log2 k ∗ bits.
In addition, local features are stored independently of
the inverted index for reranking. This is needed because inreranking each local feature of a query image should be compared with the features of each of the images in a shortlist. In
IVFADC, residual vectors are encoded by product quantization, while original SIFT vectors are encoded here, which isreferred to as ADC in [6]. Note that we can choose an arbitrary number u′ of vector decomposition independent of u.
4.3. Index search
In the search step in IVFADC, the T nearest features NT (qi )of qi are obtained from the inverted index. A query vector
qi is first quantized using the CQ codebook, and the residual vector q̄i from the corresponding centroid is calculated in
the same manner as the indexing. Subsequently, the distance
between the residual vector q̄i and short codes (b1 , · · · , bu )in the corresponding list in the inverted index are calculated.

These distances correspond to the approximate distances between the query vector qi and the reference vectors rjh :vu uu∑d(qi , rjh ) = d(q̄i , r̄jh ) ≈ t||q̄il − plbl ||2 .

5.1. Evaluation of matching accuracy
(5)

l=1

This distance calculation is performed efficiently using a precomputed lookup table [6]. Finally, the T nearest features
NT (qi ) of qi are obtained by sorting according to the distances. The distances obtained in this process are reused in
the reranking step described in Section 4.5.

4.4. Voting scores
Once the T nearest neighbors NT (qi ) of qi are obtained with
the index search, the scores are voted for the reference images
associated with NT (qi ). We adopt density ratio-based scoring [13], which has been shown to be superior to IDF scoring.
The voting score sij from query feature qi to reference image
Rj is calculated using the k nearest neighbors of qi as
sij = log(

λ |NT (qi )j |/|Rj |+ 1),
1 − λ |NT (qi )|/|RDB |(6)

where |NT (qi )| = T , and |NT (qi )j | is the number of featuresin NT (qi ) associated with Rj , and λ denotes an adjustableparameter that controls the strength of the prior distributionof p(qi |Rj ). For each qi∑, the voting score sij is assigned toeach Rj . The resulting i sij corresponds to the similarity
measure between Q and Rj , and a voting result is obtained.

4.5. Nongeometric reranking with density ratio scoring
For each of the top M images in a voting result (shortlist),
new scores are calculated to refine the first result. First, approximate distances are calculated in the manner described in
Section 4.3, and the distance dˆi from qi to its nearest featurer̂i in a target image in the shortlist is obtained.
The distance lists from the index search are used to reject unreliable matches: given a distance list di1 , · · · , diT for
query feature qi , the tentative match associated with qi is rejected if dˆi > diT ′ . In this paper, as the proposed criterion isvery reliable, geometric verification is skipped and reranking
is performed using the non-rejected tentative matches. Insteadof simply counting the number of inliers, sum of modified
version of scores in Eq. (6) is used as the new score:si = log(

λ
1/|R|
+ 1),
1 − λ t̂/|RDB |5. EXPERIMENTAL EVALUATION(7)

The proposed rank criterion described in Section 3 is compared with the conventional ratio criterion in terms of thematching accuracy of local features. The Graffiti dataset [2] isused for the evaluation. The dataset consists of 8 scenes andeach of the scenes contains 6 images with a gradual geometric or photometric transformation such as viewpoint changes,
image blur, JPEG compression, or illumination. We use thefirst and second images from each of the scenes for the evaluation. In order to obtain distance lists, 10,000 images areused out of the MIRFLICKR-1M dataset1 . Approximate distance lists are obtained with the approximate nearest neighborsearch method described in Section 4.3. The ground truth homographies between the first image and the others in eachscene are also provided, tentative matches with projection error greater than 5.0 pixels are considered as outliers.
Figure 3 shows 1−precision vs. recall curves for the proposed rank criterion and the conventional ratio criterion. Bothexact distances and approximate distances are used in matching: the prefixes A8 and A16 indicate that approximate distances are calculated using 8-byte (u′ = 8) and 16-bytes(u′ = 16) short codes, respectively. For the proposed method,
the threshold T ′ ranges from 1 to 10, and for the conventional
method, the threshold α ranges from 0.8 to 1.0. It is shownthat the proposed criterion outperforms the conventional criterion even if approximate distances are used for the proposed
criterion and exact distances are used for the conventional criterion. It can also be said that, with the proposed criterion, thedegradation of the performance caused by approximate distances is also alleviated owing to the use of an independent,
large dataset. The memory requirement is the same for boththe proposed method and the conventional method; A8, A16,
and Exact requires 8, 16, and 128 bytes per descriptor, respectively. Computational costs are explored in the following
section.
5.2. Evaluation of reranking methods
In this section, the proposed framework is evaluated in termsof image retrieval accuracy using the University of Kentucky
recognition benchmark dataset2 provided by the authors of[20]. The dataset includes 2,550 different objects or scenes.
Each of these objects is represented by four images takenfrom four different angles, giving a total of 10,200 images.
These images are used as both reference and query images.
Mean average precision (MAP), the area under the precisionrecall curve, is used as an indicator of performance [20, 5].
Standard parameter settings [5, 6, 12] are used in our experiments. The size k ′ of the visual codebook is set to 20K. In
indexing, reference features are divided into 8 16-dimensional
1 http://press.liacs.nl/mirflickr/

where the same density estimation is performed as Eq. (1).

2 http://www.vis.uky.edu/

˜stewe/ukbench/

1

1

1

T’ = 10

Prop A8
Prop A16
Prop Exact
Conv A8
Conv A16
Conv Exact

α = 1.0

0.5

Prop A8
Prop A16
Prop Exact
Conv A8
Conv A16
Conv Exact

recallT’ = 1

recallrecallProp A8
Prop A16
Prop Exact
Conv A8
Conv A16
Conv Exact
0.5

α = 1.0

T’ = 10

0.5T’ = 1

α = 1.0

T’ = 10

α = 0.8

T’ = 1

α = 0.8

α = 0.800

0.51−precision

0
0

1

0.5
1−precision(a) bark

1T’ = 10

Prop A8
Prop A16
Prop Exact
Conv A8
Conv A16
Conv Exact

α = 1.0

α = 1.0

Prop A8
Prop A16
Prop Exact
Conv A8
Conv A16
Conv Exact

T’ = 10
T’ = 1
α = 1.0

recallT’ = 1

recallT’ = 101(c) boat

1
Prop A8
Prop A16
Prop Exact
Conv A8
Conv A16
Conv Exact

0.5

0.5
1−precision(b) bikes

1

recall

0
0

1

0.5

0.5

T’ = 1
α = 0.8
α = 0.8
α = 0.800

0.51−precision(d) graffiti

1

0
0

0.5
1−precision

0
0

1

0.5
1−precision(e) light

1(f) ubc

Fig. 3: 1−precision vs. recall curves for the ratio criterion and the proposed criterion. Both exact distance and approximate distance are usedin matching. From 3,000 to 5,000 features are extracted with default parameters.

Figure 4 shows accuracy as a function of λ before andafter reranking. The MAP score of the baseline system (before reranking) is 0.882. The scores of the top 20 images
in a shortlist are refined with the proposed method for Prop
using exact and approximate distances. We can see that theaccuracy in image retrieval is also improved by the proposed
method without geometric information. It is also shown thatthe accuracy of A16 is comparable with Exact, which is consistent with the results in Section 5.1.
Table 1 shows the processing time required for the proposed method. The processing time required for A8 and A16
can be decomposed into two parts; processing time for table
construction (for each query) and distance calculation with table lookups (for each of the images in the shortlist). Top20,
Top50, and Top100 represent the processing times required
to rerank the top 20, 50, and 100 images in the shortlist, respectively. All distance calculations are optimized with SIMD
operations. In the experiment more than 3,000 features areused. As computational cost is proportional to the square of
the number of features, if the number of features is reduced toaround 1,000, the computational cost is reduced by an orderof magnitude. Table 2 also summarizes the MAP scores of

0.9

Mean average precision

subvectors (u = 8), and encoded by a product quantizer with
256 centroids (k ∗ = 256), resulting in 8 × 8 bit code. For
the proposed method, we set T = 24 and T ′ = 10. These
parameters were not particulary sensitive to the performance(greater is better) in preliminary experiments.

0.89

Prop A8
Prop A16
Prop Exact
Without reranking

0.88
0

0.01

0.02

0.03

0.04

0.05

λ

Fig. 4: Accuracy of the proposed framework with different distancecalculation scenarios as a function of λ.

the proposed method with the same parameter settings. We
observe: (1) there is no significant differences in accuracy between A16 and Exact while Exact requires a large computational cost (almost three times larger than A16), (2) using top
50 and 100 images does not improve accuracy greatly, whilecausing a linear increase in computational cost.
We also conducted reranking based on geometric verification, where a score in a shortlist is replaced by a new score
if the number of inliers is greater than a threshold. The MAP
was degraded from 0.882 to 0.871 due to failures in homography estimation for nonplanar or textureless objects and false

Table 1: Processing time required in the proposed system [sec].
Table Distance Top20 Top50 Top100
A8
0.027
0.058
1.193
2.942
5.857
A16
0.040
0.102
2.074
5.125
10.210Exact
0.291
5.810 14.525 29.050

Table 2: Comparison of different parameter settings for the proposed
method.
Top20 Top50 Top100
A8
0.890
0.891
0.890
0.897
0.902
0.904
A16
Exact
0.899
0.904
0.907

positives. Figure 5 shows examples of nonplanar or textureless objects in the database for which homography estimation failed. The proposed method can improve accuracy evenagainst these queries.
6. CONCLUSIONSIn this paper, we proposed a new feature matching criterion
and nongeometric reranking method for large-scale image retrieval. The reuse of the information obtained in the BoVW
framework enables accurate feature matching and sophisticated scoring in the reranking. In the experiments, we confirmed that the proposed method can improve the results even
if geometric information is not used. As a future research
topic, we are interested in the utilization of the proposed
rank criterion as a priority measure for tentative matches in
PROSAC [21].
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Fig. 5: Examples of nonplanar or textureless objects in the database.
The top, middle, and bottom row correspond to the 94, 384, and2274-th objects, respectively.

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