Location Coding for Mobile Image Retrieval
Sam S. Tsai ∗ , David Chen ∗ , Gabriel Takacs ∗ , Vijay Chandrasekhar ∗ ,
Jatinder P. Singh † and Bernd Girod ∗
∗
Information Systems Laboratory, Stanford University, Stanford, CA 94305, U.S.A.
†
Deutsche Telekom Inc. R&D Lab, Los Altos, CA 94022, U.S.A.
∗
{sstsai, dmchen, gtakacs, vijayc, bgirod}@stanford.edu,
†
jatinder.singh@telekom.de
ABSTRACT
For mobile image retrieval, efficient data transmission can
be achieved by sending only the query features. Each query
feature is composed of a descriptor and a location in the image.
The former is used to find candidate matching images
using a “bag-of-words” approach while the latter is used in
a geometric consistency check to map features in the query
image to corresponding features in the database image.
We investigate how to compress the location information
and how lossy compression affects the geometric consistency
check. The location information is converted into a location
histogram and a context-based arithmetic coding with
location refinement method is then proposed to code the
histogram. The effects of lossily compressing the location
information are evaluated empirically in terms of the errors
in corresponding features and the error of the estimated geometric
transformation model. From our experiments, rates
at ∼5.1 bits per feature can achieve errors comparable to
lossless coding. The proposed scheme achieves a 12.5× rate
reduction compared to the floating point representation, and
2.8× rate reduction compared to a fixed point representation.
Categories and Subject Descriptors: H.3 [Information
Storage and Retrieval]: Miscellaneous
General Terms: Algorithm
Keywords: scale-invariant feature, scalable vocabulary tree,
mobile augmented reality, content-based image retrieval
1. INTRODUCTION
Handheld mobile devices, such as camera-phones or PDAs,
are expected to become ubiquitous platforms for visual search
and mobile augmented reality applications [1, 2]. For mobile
image matching, a visual database is typically stored
at a server in the network. Hence, for a visual comparison,
information must be either uploaded from the mobile to the
server, or downloaded from the server to the mobile. With
relatively slow wireless links, the response time of the system
critically depends on how much information is transferred in
both directions.
1.1 Background on Image Retrieval
Image retrieval based on local features has become an attractive
approach [3] since they are robust to lighting, rotation,
scale, and mild viewpoint changes. A local feature consists
of two pieces of information: the location of the feature and
the descriptor of the local region around a feature. Features
are formed at interest points in the image that have specific
structures such as corners or blobs [4, 5, 6, 7]. These
structures are typically invariant to changes in luminance,
scale, rotation, and translation. Descriptors are then calculated
from the image intensity values in a local region
centered at the interest point. A wide range of descriptors
were tested in [8] and gradient distribution-based descriptors
were shown to perform best. These type of descriptors,
such as the Scale Invariant Feature Transform (SIFT) [5],
the Gradient Location and Orientation Histogram (GLOH)
[8], the Speeded Up Robust Features (SURF) [7], and Compressed
Histogram of Gradients (CHOG) [9], are histograms
of the image intensity gradients of the local region.
Fast large-scale image retrieval is enabled by using a Scalable
Vocabulary Tree (SVT) [11] for matching. Features are extracted
from the database of images to form a set of features.
A hierarchical k-means clustering algorithm is applied to the
set of features, forming the SVT. This method is also known
as Tree Structured Vector Quantization (TSVQ). When performing
a match in the SVT, descriptors of the query image
are quantized through the SVT and a histogram of the
node visits on the tree nodes is generated. Candidate images
are then sorted according to the similarity of the candidate
database image histogram to the query image histogram.
The descriptors are treated as a visual “bag-of-words” in the
SVT matching.
Geometric consistency check is applied to validate or re-rank
the list of candidate images [1, 12]. This is done by pairwise
matching the features extracted from a query image to the
features extracted from a database image. Typically, the
ratio test [5] is used to predict a set of corresponding features
between the two images. Then, RANSAC [10] is applied
on the predicted set of features to estimated a geometric
transformation model and a set of matching correspondences.
For image matching applications, a good number of
matching correspondences represents a confident match. For
augmented reality applications, a good geometric transformation
model provides spatially accurate overlaying display.
A typical mobile image retrieval system is illustrated in Fig.
1.Client
Image
Feature
Extraction
Display
Feature
Compression
Query Data
Network
Identification Data
Scalable Vocabulary
Tree (SVT)
Geometric Consistency
Check (GCC)
Server
Figure 1: A mobile CD cover recognition system where the server is located at a remote location. Query
data is sent over the network and the identification data is sent back to the mobile-phone (from [2]).
1.2 Rate-Efficient Image Retrieval
As mobile phones are equipped with camera devices, they
have naturally become an input device for image retrieval
systems. However, due to the limited memory and processing
power on the mobile phone, large-scale retrieval databases
must be stored at a remote location (Fig. 1). In this case, the
mobile phone has to send the data over a wireless network
to the server. Wireless connections have limited bandwidth,
prompting the need to send as little data as possible. In the
scenario in which the phone is capable of carrying out feature
extraction on the device, only the feature data required
for the retrieval system needs to be sent.
Recent work has explored the compression of descriptors.
Random projections of SIFT descriptors were proposed to
reduce the bit rate [13]. Chandrasekhar et al. studied transform
coding of SIFT and SURF descriptors [14]. CHOG,
a low bit rate descriptor, was proposed in [9]. CHOG, at
the rate of 8 bytes per descriptor, can achieve matching
capabilities comparable to the uncompressed features. In
[15], the local image patch around the interest point is compressed
and sent over the network at low bit rate, which also
shifts the workload of descriptor computation to the server
side. Unlike the other approaches, the retrieval system in
[16] sends a tree histogram in place of individual descriptors,
which enables significant additional rate reduction.
1.3 Contributions
A novel method to compress the location information is proposed.
The location information is typically of floating point
precision, and its size comparable to the size of the descriptors
in [9]. The location information is converted into a location
histogram and the location histogram is compressed.
Empirical evaluation on the effect of lossily compressing
the location information is made by examining the errors
of the matching correspondences and geometric transformation
model estimated by the geometric consistency check. A
suitable rate is then chosen for mobile image matching and
augmented reality applications.
In Sec. 2, we apply different methods to compress the location
histogram, and describe the proposed context-based
arithmetic coding with location refinement scheme. Experimental
results of the proposed scheme applied in the mobile
image retrieval framework and the effects of lossy compression
of the location information are presented in Sec. 3.
2. LOCATION CODING
Features are structurally distinguishable points in the image.
Ideal distinguishable points are corners or blobs in an
image. Because of their distinctive structure, the features
are invariant to lighting, scale, and mild viewpoint changes,
i.e., they can be reliably detected in different camera views.
Figure 2: Features in the CD Database (left column)
and the Zurich Building Database (right column) are
randomly scattered but still cluster near structures.
In SIFT [5], Lowe proposed to detect features by finding extrema
points in a pyramid of Difference of Gaussian (DoG)
images. A 3D quadratic function is fitted to the local samples
in the images to find the sub-pixel location of the interest
point. The Hessian of the interest point is then examined
to rule out edge responses. Typical DoG interest points
within query images are shown in Fig. 2. We use SIFT for
our evaluation in this section, and show experimental results
of other Hessian-based interest point detectors in Sec. 3.2.
In the following section, we describe how to compress the
location information in a rate-efficient manner.
2.1 Location Histogram
We aim to reduce the number of bits needed for the location
information of each feature. A natural approach to lossily
coding the feature locations is to quantize the locations and
entropy code the quantized data. In our approach, instead
of coding the location information of each feature, we convert
the location information of the features into a location
histogram, and code the location histogram.
There are two benefits in converting the location information
into a location histogram and coding the histogram. First, inTable 1: Entropy of the Histogram Map
32×32 16×16 8×8 4×4 2×2
Bits/Image 222 807 2014 3730 5552
Bits/Feature 0.247 0.900 2.246 4.160 6.192
1
2
1
1
1
1
3
1 1 1
Figure 3: The histogram of the features contains the
histogram map and the histogram count.
[16], it was shown that by discarding the order information
of the coded items the bit rate can be reduced. Second,
the interest points are structural points in the image, and
hence, spatial structure relationship can be exploited when
they are coded.
2.2 Compression of Location Histogram
The location histogram is represented as the histogram map
and histogram count, Fig. 3. The histogram map is formed
by the map of empty and non-empty histogram blocks, while
the histogram count is the number of features in the nonempty
block. Different sizes of histogram block yield different
quantization levels on the location information. The
histogram map and histogram count is coded separately.
Spatial relationship of the interest points is exploited when
coding the histogram map.
Histogram Map Coding. The histogram map resembles
a binary image with ‘1’ indicating a non-empty block and
‘0’ otherwise. To find a suitable method for coding this type
of data, we experiment with the following methods to code
the histogram map to find which method performs the best:
• Runlength. The empty blocks in the histogram map
is converted into runlengths in raster scan order. The
runlengths are then coded using an entropy coder.
• Quad-tree. The histogram map is converted into a
quad-tree [17]; the map is divided into four squares,
and each square containing non-empty blocks is divided
into four squares recursively to form a tree. A binary
representation of the tree is generated by traversing
the tree breadth first using symbols that indicate
whether the square has children or not. The binary
representation is entropy-coded with different entropy
codes for different levels of the tree.
• Context-based. The histogram map is entropy-coded
block by block in the raster scan order with similar
context information used in coding binary images [18].
The neighboring blocks of the current coded block is
used as context, Fig. 5. Here, we use 14 nearest available
pixels to form the context.
We examine the coding performance of the different coding
methods described above by compressing DoG interest
points extracted from the Zurich Building Database (ZuBuD)
and CD Database (CDD) images, which we will describe in
Sec. 3.
Table 2: Entropy of the Histogram Count
32×32 16×16 8×8 4×4 2×2
Bits/Feature 0.699 0.967 0.948 0.766 0.708
In Fig. 4, we plot the entropy for different histogram block
sizes of the three coding methods. We find that Contextbased
coding method performs the best among the three.
However, the gains of the Context-based coding method decreases
as the block size becomes smaller. Runlength coding
for larger histogram block size does not provide any
gain. Based on these results, Context-based coding method
is most suitable for coding histogram maps. We show the
entropy of the proposed method in bits per feature and bits
per image in Table 1, with an average of 900 features per
image.
Bits Per Block
1.2
1
0.8
0.6
0.4
0.2 Runlength Method
Quadtree Method
Context-based Method
0
32 16 8 4 2
Histogram Block Size
Figure 4: Rate of three coding methods on the histogram
map.
Histogram Count Coding. The histogram count is coded
separately from the histogram map. We show the entropy of
the histogram count in bits per feature for the ZuBuD and
CDD datasets in Table 2. For histogram block sizes smaller
than 8×8, the rate of the histogram count is much smaller
than the rate of the histogram map.
2.3 Context-based Arithmetic Coding with
Location Refinement
Context-based coding provides the best compression performance
as shown in the previous section. In this section,
we further examine how the context size affects the coding
performance, and will describe the two stage context-based
arithmetic coding with location refinement scheme that we
propose.
Different Context Size. We examine how larger context
sizes can affect the coding performance. In Fig. 5, a map
labeling the neighboring pixels in the order of the distance
to the coded pixel is shown. We increase the context size by
adding more neighboring pixels in the context, with nearest
first. Context-k denotes a context consisting of k nearest
neighboring pixels. We code the histogram map using no
context and also code the histogram map using differentsizes of context. The entropy of using different contexts
shown in Fig. 6. The coding performance improves as the
context size increases, but the improvement saturates when
the number of pixels in the context grows beyond 16. This
is due to context dilution, i.e., the context size has grown
too large for effective training. In our experiments, we use
Context-14 as the context model.
15
13
11
7
5
9
3
1
14
6
2
X
Figure 5: When coding pixel ‘X’ the neighboring
pixels are included in the context. Context-8 denotes
a context map consisting of neighboring pixels
1, 2, 3, 4, 5, 6, 7, 8.
Bits Per Block
1
0.8
0.6
0.4
Context-0
0.2 Context-8
Context-14
Context-16
0
32 16 8 4 2
Histogram Block Size
Figure 6: Rate of different sizes of context on the
histogram map.
Context-based Arithmetic Coding with Location Refinement
(CBAC-LR). Structures in the image vary little
in local regions. The distance between interest points usually
is greater than 4 pixels. Thus, the benefits of using
context-based coding on histogram maps with histogram
block size smaller than 4×4 is smaller. In Fig. 4, better
coding performance of the context-based coding method is
observed for only histogram block sizes of 4×4 and larger.
Thus, we propose another approach for coding smaller histogram
block sizes.
The proposed two-stage coding method of the location histogram
is as follow. To code the location information in a
histogram with histogram block size greater than 2×2, the
context-based binary arithmetic coder is applied to code the
histogram map, and a multi-symbol arithmetic coder is used
to code the histogram count. To code the location information
in a histogram with histogram block size smaller than
4×4, we code the location histogram with histogram block
size 4×4, and use refinement bits to specify the vertical and
horizontal location of each feature in the histogram block.
For example, an additional 2, 4 refinement bits are used for
2×2 blocks and 1×1 blocks respectively for each feature.
10
4
12
8
16
3. EXPERIMENTAL RESULTS
We apply the proposed scheme to compress query features
in a mobile image retrieval framework and empirically evaluate
the results. We assume a matching candidate image
to a query image is found from a large database using SVT
histogram matching. Geometric consistency check (GCC) is
applied to validate the match between the candidate image
and the query image.
In our experiments, two datasets are used. The first is the
widely used Zurich Building Database 1 , which consists of
different views of 201 different building facades in Zurich.
The second is our CD Database 2 . 50 CD covers are randomly
chosen from a CD image database of 10,597 entries,
and photographed in different angles and backgrounds. For
our experiments, we resize the query images to 640×480 resolution.
The geometric consistency check is described in detail in
Sec. 3.1. In Sec. 3.2, we show the results on how the rate
trades off with the loss of matching correspondences after
the geometric consistency check. In Sec. 3.3, we empirically
examine how lossy compression of the location information
causes errors in the GCC.
3.1 Geometric Consistency Check
GCC is used to validate the match between the query image
and the candidate image. The check consists of two steps:
1) the ratio test [5], and 2) RANSAC [10].
We describe the process using the following notations. For a
query image IQ, a set of features FQ = {lq,i, dq,i}i∈1,2,...N Q
is extracted. l denotes the location, d denotes the descriptor,
and NQ denotes the total number of features. We match the
query image to a candidate database image IC, where a set
of features FC = {lc,i, dc,i} is extracted with a total of NC
number of features.
The ratio test establishes a set of correspondence ĈRT =
{ ˆmq,j, ˆmc,j}
j∈1,2,... ˆ NRT
given FQ and FC. ˆmq,j, ˆmc,j are
indices to the features in FQ, FC respectively and indicate
matching features. NRT ˆ is the total number of estimated
correspondences. In our experiments, we use 0.8 as the ratio
threshold in the ratio test.
RANSAC is applied to the set of correspondences, ĈRT ,
to find a geometric transformation, ˆ MGCC. We can transform
the database feature locations in ĈRT using ˆ MGCC.
The transformed location is noted as T ˆ MGCC
(lc, ˆm c,j
), where
TM (l) is the new image location of the location l using M
as the geometric transformation model. The location error
of each pair in ĈRT is given as ‖T ˆ MGCC
(lc, ˆm c,j
) − lq, ˆm q,j
‖2.
We say the pair agrees with the model ˆ MGCC if its location
error is smaller than Θl. The set of correspondences that
agrees with the model is denoted as ĈGCC.
3.2 Compression of Location Information
Compression of the location information of query features
is carried out using our scheme. As the rate allocated for
location information is decreased, the distortion in the location
information increases. Location error of each pair in
ĈRT increases, and thus reducing the number of correspondences
in ĈGCC. We define feature loss percentage as the
1
http://www.vision.ee.ethz.ch/showroom/zubud/
2
http://msw3.stanford.edu/∼dchen/CDD/index.htmlpercentage of losses in the number of correspondences when
compared to a scheme without compression. This measure
is typically used when no ground truth data is available.
We show the feature loss percentage of two coding schemes:
CBAC-LR and fixed-length coding. The former is the proposed
scheme described in Sec. 2.3 and the latter is a coding
scheme where the horizontal and vertical coordinates of each
feature is coded in a fixed number of bits separately.
In addition, we also present two other results: entropy and
histogram. Entropy is the entropy of the CBAC-LR. Histogram
is the theoretical rate achieved by representing the
location information in a location histogram. The location
histogram is an orderless representation in which the information
of order is discarded. Therefore, there is a potential
bit rate reduction of log2(N!) [16], where N is the total number
of features in the image. The average number of features
per query image in the data set is 750. Using the Stirling’s
approximation to calculate log2(N!), we find that a theoretical
rate reduction of ∼8.1 bits per feature over fixed-length
coding can be achieved.
In Fig. 7, we show the results feature loss percentage. Although
the training set of the Context-based coding method
is different from the test set, the rate is close to entropy, suggesting
that the context model is applicable across different
images. The proposed method provides a ∼9 bit rate reduction
per feature when compared with fixed-length coding
method and provides a ∼1 bit rate reduction per feature
over the theoretical rate shown as histogram.
Feature Loss Percentage
80%
60%
40%
20%
CBAC-LR
Fixed-length Coding
Entropy
Histogram
0
0 5 10 15 20
Location Bits Per Feature
Figure 7: Feature loss percentage vs. rate of the
proposed scheme
Compression of Hessian-based Detectors. We experiment
with two other types of detectors, the Hessian-Laplace
detector [6] and the SURF Fast Hessian detector [7], and
show the results in Fig. 8. The parameters of the detectors
were tuned to give an average of 750 feature counts per image.
For fair comparison, we examine the results using the
location quantization error with the purpose to rule out the
influences of descriptors.
3.3 Effect of Lossy Compression of Location
In this section, we examine how lossily compressing the location
information will affect the GCC. To simplify the presentation,
we describe the levels of lossy compression using
different histogram block sizes.
Location Quantization Error
14
12
10
8
6
4
2
SIFT DoG
Hessian Laplace
Fast Hessian
0
0 4 8 12
Location Bits Per Feature
Figure 8: Location quantization error vs.
different interest point detectors
rate for
We first create a set of ground truth data for the GCC using
the CD dataset. We first manually find a homography MGT
between the database image and the query image. Then,
ground truth correspondences are established if they satisfy
the following criteria: 1) the projected database image feature
patch and the query image feature patch have overlap
error [8] smaller then 40%, 2) the location error between
projected database feature location and the query feature
location is within 2 pixels, and 3) the orientation difference
of the projected database feature and the query feature is
smaller than 45 ◦ . The set of ground truth correspondences
is denoted as CGT .
To quantify the comparison, we use two error measurements:
1) correspondence error, and 2) geometric transformation
model error. The first is the error of matching correspondences
between the pair of images. The geometric transformation
model error depicts the displacement in augmented
displays to the query image.
3.3.1 Correspondence Error
The correspondence error is the error of ĈGCC when compared
with the ground truth correspondences, CGT . For
each pair of correspondence in CRT , it is labeled as true
if it is in CGT and false if otherwise. We plot the location
error distribution of true and false matches in Fig. 9,
while using MGT to project the true location. When larger
histogram block sizes are used, the error distance of true
matches increase. False matches are uniformly distributed
over the image and the distribution changes not much due
to compression. The peak in small location errors for false
matches corresponds to interest points at the wrong scale or
orientation.
The set ĈGCC is determined by the geometric transformation
model and the given error threshold Θl. We assume that
the estimated model is found to be MGT . Then, by varying
the threshold Θl, we plot the receiver operating characteristic
curve, Fig. 10. The equal error rate curve representing
equal false positive and false negative probabilities is shown
in Fig. 11. To operate at the equal error rate curve, larger
Θl is used for larger histogram block sizes. An inherent error
of 10% is observed for GCC. For histogram block size 4×4
and 4×4, the additional error is 3% and 8% compared with
the lossless case.Probability
0.5
0.4
0.3
0.2
0.1
True - Lossless
True - 4x4 block
True - 8x8 block
True - 16x16 block
0
0 5 10 15 20
Location Error
True Positive Percentage
100%
90%
80%
70%
Lossless
1x1 block
60%
2x2 block
4x4 block
8x8 block
50%
0% 10% 20% 30% 40% 50%
False Positive Percentage
0.08
0.06
(a)
False - Lossless
False - 4x4 block
False - 8x8 block
False - 16x16 block
Figure 10: Receiver operating characteristic curve
for different histogram block sizes.
0.35
Probability
0.04
0.02
Equal Error Rate
0.3
0.25
0.2
0
0 10 20 30 40 50
Location Error
(b)
Figure 9: Distribution of location error for (a) true
matches, and (b) false matches for different histogram
block sizes.
3.3.2 Geometric Transformation Model Error
The geometric transformation model error is the deviation of
the estimated model, found by GCC, to the true geometric
transformation. Here, we use a homography. To evaluate
the estimated homography ˆ MGCC, we compare it with the
ground truth homography MGT using the following measure:
Error( ˆ MGCC) = 1
NC∑ ‖T ˆ (li) − TM MGCC GT
(li)‖2. (1)
NC
i=1
Examples of projecting items using the estimated homography
model are shown in Fig. 12. Different quantization
level is applied to the location information, resulting in the
different estimated models.
For a matching query feature set and database feature set,
we run the GCC for 100 times and average the errors. The
estimated model error for four different image pairs is shown
in Fig. 13. Each pair corresponds to a different number of
corresponding matches. The error is correlated with the
number of corresponding matches. As more observations on
the unknown model is made, the error becomes smaller. The
error of the model is approximately the same for histogram
block sizes smaller than 4×4.
0.15
0.1
0.5 1 2 4 8 16 32
Histogram Block Size
Figure 11: Equal error rate operating curve for different
histogram block sizes.
4. CONCLUSIONS
We have proposed a novel method of compressing location
information for mobile image retrieval systems based on
feature-based matching. Location information is converted
into a location histogram and the location histogram is compressed.
Of the three different schemes examined, contextbased
coding of the location histogram performed the best.
It is further improved by introducing a two-stage coding
method using refinement bits. We empirically evaluated the
effects of lossily compressing location information on geometric
consistency check. Errors is quantified using the correspondence
error and geometric transformation model error.
From our experimental results, it is shown that by coding
the location information in 4×4 histogram blocks, the error
of the model is smaller than 1 pixel and correspondence
match is within 90% error of the lossless compression case.
When coding the location information using the 4×4 histogram
block size, the rate is ∼5.1 bits per feature. Thus,
we have achieve 12.5× rate reduction compared with the
floating point representation, and 2.8× rate reduction compared
with a fixed point coding.Figure 12: Top-left: database image with features
and an overlay box. Top-right: query image with
projected features and overlay box using a homography
model estimated from compressed feature locations
using histogram block size 4×4. Bottom-left:
histogram block size 8×8. Bottom-right: histogram
block size 16×16.
Estimated Model Error
20
15
10
5
No. Matches = 40
No. Matches = 78
No. Matches = 130
No. Matches = 255
0
0.5 1 2 4 8 16 32
Histogram Block Size
Figure 13: Estimated model error of four different
images with different number of matching features.
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