Coding and Indexing Shape Feature using Golomb-Rice Coding for CBIR Applications

International Journal of Engineering Research and Development
e-ISSN: 2278-067X, p-ISSN: 2278-800X, www.ijerd.com
Volume 13, Issue 1 (January 2017), PP.47-55
47
Coding and Indexing Shape Feature using Golomb-Rice Coding
for CBIR Applications
P. Sumathy1
1
Department of Computer Science, Bharathidasan University, Trichy, Tamilnadu, India.
ABSTRACT:- The Content-Based Image Retrieval application uses large amount of low-level features of images for
retrieving relevant images. Numerous low-level features are used for retrieval and among them the shape based feature is
important and can be represented in the form of histogram. It is well known that the low-level feature requires more storage
space and thus entire content has to be coded, indexed etc. to reduce the storage requirement, feature processing time and
accessing time. In this work, indexing and encoding mechanism is proposed to effectively access the feature and represent
the feature in lesser space. The bin values are used as reference for reducing the dimension of the histogram. The non-zero
values are coded using Golomb-Rice coding and represented as compact histogram. The size of the compact histogram is
variable in size and thus a similarity measure is proposed to handle the issue. Various well-known benchmark datasets are
used for experiments to evaluate the performance. It is found that the truncated and encoded histogram performs well and
achieves high precision of retrieval.
Keywords:- Encoding, Golomb-Rice code, Shape Histogram, Similarity measure, Image Retrieval.
I. INTRODUCTION
Recently, multimedia information retrieval is fetching attention from both academia and industry. For
multimedia image retrieval applications, the low-level features are extracted for capturing the semantics. These
extracted low-level features are higher in dimension and requires large storage space and the transmission and
processing time is huge. It is understood that the feature has to be indexed, encoded and compressed to reduce
disk space and to improve the processing speed for image retrieval. The feature can be reduced by using suitable
coding scheme with less decoding time. Even if there is information loss during coding, the precision of
retrieval should not be affected. During encoding, number of bits that are needed to be transferred and stored
should be reduced considerably. Though the encoding/decoding overhead increases the communication latency
and decreases the bandwidth, the encoding technique reduces the size of the low-level feature to a smaller size.
Multimedia applications use adaptive predictors, entropy coders, de-correlating transforms with quantizes [1, 2]
as coders and typical entropy coders used are Run-Length, Huffman, Golomb-Rice coders [3]. Due to huge
variations in the statistics of blocks of integers to be encoded, designing the efficient entropy coders for such
applications is found to be difficult. Among various entropy coders, Golomb-Rice (GR) coders [4] have been
used widely in modern compression systems because of its flexibility in changing the encoding tables by
modifying a single integer parameter [5, 15, 16, 17, 18]. The output code words are easily computed for the
corresponding input symbols so that explicit tables are not required. This approach makes GR coders quite
attractive and computations are much faster compared to memory access.
In this work, the size of the low-level feature vector is reduced by retaining only the necessary
information for indexing purpose. The GR coding is used to encode the bin values adaptively for achieving
lower average bit length. During retrieval, the similarity is calculated in encoded form and observed that
precision of retrieval is encouraging. It is observed that performance of normal and encoded feature has
achieved similar precision of retrieval. The quotient code of the encoded histogram alone is sufficient to retrieve
relevant images. The rest of the paper is organized as follows. In Section II, we review the related work. Section
III explains the proposed approach in detail. Section IV presents the experimental results and we conclude in the
last section of the paper.
II. LITERATURE REVIEW
It is observed that most of the research work that involves encoding and compression techniques uses
floating-point number that focuses on audio, image, scientific measurement and simulation domains. Encoding
and compression technique have been proposed for the double-precision output of a numerical solver for
ordinary differential equations [6]. Integer delta and extrapolation algorithms are used to encode and compress
the data. However, this method is particularly beneficial for data, which gradually changes and may not be
suitable for real-time applications. An efficient encoding and compression scheme for image data has been
designed with an emphasis on 2D and 3D data [7]. The data is predicted using the Lorenzo predictor and
encoded the residual with a range coder based on Schindler’s quasi-static probability model [8]. A technique
that combines differentiation and zero suppression is presented to encode and compress floating-point data
arising from experiments conducted at the Laser Interferometer Gravitation Wave Observatory [9]. It is

Coding And Indexing Shape Feature Using Golomb-Rice Coding For CBIR Applications
48
observed that the compression ratio of this approach is same as GZIP and is significantly faster. However, its
success is realized only with the nature of LIGO data and thus value changes gradually. An algorithm has been
proposed to encode the audio data [10]. It transforms the floating-point values into integers and generates an
additional binary stream for the lossless reconstruction of the original floating-point values [19]. An extension to
the JPEG2000 [12, 15] standard has been proposed that allow data to be encoded efficiently with bit-plane
coding algorithms where the floating-point values are represented as big integers [11]. An arithmetic encoder is
used for single-precision floating-point fields that represent residual vectors between the actual and the
predicted vertex positions in triangular meshes [13]. In an extended precision algorithm, the Haar wavelet
transform and Huffman coding is used to achieve lossless compression in 3D curvilinear grids [14]. This
approach performs differential coding and clustering to generate separate data residuals for the mantissa and
exponent. The Huffman coder and GZIP have been used to encode the mantissa and exponent residuals.
An approach has been proposed to encode and compress the histogram by run length coding of
nonempty leaf nodes [20]. The statistical analysis inaccurately models the underlying random process
generating the histogram. A feature descriptor codec is presented in [21], where each descriptor is transformed
by a decorrelating transform, quantized and entropy-coded using Huffman coding or arithmetic coding. A lossy
buffer compression/decompression technique has been used to find the error [23]. While the error grows
relatively more, the method uses a lossless compression approach. However, this algorithm has operated only on
Low Dynamic Range (LDR) data. A new color buffer compression algorithm is presented in [24] for coding
floating-point buffers. It is considered that the approximate mode is error bounded and the amount of error
introduced is accumulated and is controlled via few parameters. Hierarchical quad tree decomposition is
performed and subsequently, hierarchical prediction as well as Golomb- Rice encoding are applied. However,
this method is applicable for low-dynamic range color buffer. A method for encoding and compressing 16-bit
floating-point color is presented and depth buffers in a unified manner, with several limitations [25]. This
scheme does not allow negative values and assumes that the alpha channel is 1.0f. Compressing the alpha
channel [26] has addressed complexity using two separate compressors for color data.
Based on the above discussion, it is observed that none of the above method is found to be suitable for
CBIR applications and also the encoding approach is found to be more complex. As a result, we propose a
simple indexing and adaptive coding scheme for encoding the bin values of low-level features. The encoding
scheme has reduced the storage requirement space considerably. The shape histogram is truncated and retained
only necessary feature values for indexing. The floating point bin values are converted to integer for GR coding.
We have retrieved the images using only quotient part of GR encoding and found that the precision of retrieval
is encouraging compared to the retrieval using original histogram. In addition, fast retrieval is achieved with
lower bit length and low disk space
The proposed approach has three stages such as indexing, encoding and distance calculation. The
schematic diagram of the proposed work is shown in Fig. 1. In the primary stage, an indexing scheme is
proposed for reducing the dimension of the shape feature and has used indexing parameter. The indexed
histograms are encoded using Golomb-Rice coding approach in the second stage. A new distance measure is
proposed in the third stage, where the common bin indices between the query and database features are used to
calculate the distance.
III. PROPOSED APPROACH
A. Indexing through Reducing Shape Histogram Dimension
In this paper, we have used shape features of objects in an image for capturing the fuzzy boundary
information to estimate the degree of closeness of objects with well-known primitive shapes. The radius
properties of the object are used for obtaining information about the shape irregularity. In this paper, Mr and mR
are the maximum and minimum length that bisects the diagonal in each of the primitive shapes. For the sake of
convenience and better understanding, in the rest of the paper, Mr and mR are considered as the maximum
radius (Mr) and minimum radius (mR) of the object. Also, these values are second maximum (omitting the
diagonal) and minimum distance between the centre to edge of the object respectively. The minimum and
maximum radius is measured from the centre of the object. The centre of the object is the centroid and from
which the distance to the boundary is measured with certain angular displacement. Among the measured sample,
minimum and maximum value is considered as minimum and maximum radius. It is well known that while
Mr=mR, the object is a perfect circle. However, for an object with irregular boundaries, the fuzzy membership
function is defined in Table I for primitive shapes circle, ellipse, square, rectangle, rhombus, cone and cylinder.

49
Fig.1. Schematic Diagram of the Proposed Work
Table I Fuzzy Membership Function for Primitive Shapes
Primitive Shapes Fuzzy Membership Function
Circle     2
1
e 
 cx
C x
Ellipse    1
e 
 elx
EL x
Square     2
1
e

 sqx
SQ x
Rectangle     2
1
e 
 recx
REC x
Rhombus     2
1
e 
 rhx
RH x
Cone     2
1
e 
 cnx
CN x
Cylinder     2
1
e

 cyx
CY x
The extracted shape feature is represented as histogram and it is a normalized histogram in the form of
single-precision floating-point format of the IEEE 754 standard as shown in Fig. 2.
Fig. 2: 32-bit IEEE Floating-Point Representation
The trivial bins of the shape histogram are removed to reduce their dimension and the bins having four
digits after the decimal points are also truncated. Apart from this, bins having 0 values and the bins having four
0's after the decimal point are removed. As a result, the shape histogram dimension is reduced to a great extent
having only non-zero bins. As each shape histogram represents the shape information of the individual object,
the presence of unequal non-zero bins results in the structural variation of the histogram as shown in Fig. 3.

50
Fig. 3: Schematic Structural variation of the Reduced Histogram
Since, the shape histogram bins are normalized, the floating point values are converted as integer
without losing information. This is done since, GR coding uses integer values. Here, suitable multiplication
factor (Multi-Fact) is found by counting number of zero's after the decimal point to convert floating point values
to integer values. Here, we preferably selected Multi-Fact as 1000 since, more shape histograms bin values are
having two 0's after the decimal point. Table.2 represents the Multi-Fact used in this approach and the entire bin
values of the shape histograms are converted into integer values. Thus, the obtained integer histogram values
can now use for indexing.
Table II Units for Magnetic Properties
No. of zeros after decimal point Multi-Fact
0.0 100
0.00 1000
0.000 10000
The original shape histogram and reduced shape histogram representation is shown in the form of
sparse matrix. Fig. 4(a) represents the original normalised shape histogram. Fig 4(b) represents the reduced
shape histogram which gives the impact of data compressed and thereby encouraging increased computation
speed. The Eq. (1) represents the indexing scheme (Cm) with 8 index levels (m) having different dimensions at
each level.
  )1(*)()1(*)(1 mIFRmIFC mm 
In the above Eq, IF represents Index Factor=8, Rm is shape histogram dimension range and m is the
index level [1-8]. A sample indexing structure with the shape histogram dimension range is depicted in Table. 2.
In this work, the value of m and IF is fixed based on exhaustive retrieval experiments only. For instance, the
shape histogram having 15 bins fit in index 2, since it falls in the dimension range of [9-16].
(a)
(b)
Fig 4: Sparse Matrix Representation (a) Original Shape Histogram (b) Reduced Shape Histogram

51
Table III Sample Indexing Structure
Index Histogram
Dimension
Range
between
M-
Parameter
1 8 [1-8] 108
2 16 [9-16] 82
3 24 [17-24] 74
4 32 [25-32] 63
5 40 [33-40] 44
6 48 [41-48] 32
7 56 [49-56] 25
8 64 [57-64] 12
The entire image database is grouped into several small blocks. For a given query image, the features
are extracted, pre-processed, dimension is reduced and compared with the images in the matched block in lesser
time.
B. Encoding the Indexed shape Histograms
Each block index has their header value in the form of M-parameter for which the encoding and
decoding offset is calculated. The value of M for each block is calculated adaptively based on the indexed block
size. The shape histogram blocks indexing works well even with uncontrolled data set of WWW. The indexing
technique can be used to find out the ground truth of images easily for each block. Thus, considering the ground
truth of each block index, the M-parameter is calculated using Eq. (2).
(2)
1














n
i
i
W
n
h
M
In above equation W is constant parameter ih is fixed to 0.69, n is the total number of reduced shape
histogram bins of respective block index, ih is the reduced shape histogram bin value of respective block, M is
the tunable parameter for quotient and remainder encoding. The shape histogram bin values are in the form of
integer N and are encoded using tunable parameter M. The bin values are divided into quotient (Q) and
remainder (R) part using Eq. (3) and Eq. (4).
)3(][int)( MNQQuotient 
)4(]mod[)(Re MNRmainder 
While coding, if power of M is 2, then rice code is applied to the remainder and   M2log bits are
needed for encoding. Alternatively, if M is not a power of 2, Eq. (5) is applied for encoding the remainder.
   )5(log2 Mb 
Further, two important conditions are noted and they are:
1. If [(r<2)]^b - M, code r in plain binary using b-1 bits
2. If [(r>2)]^b - M, code the number [(r+2)]^b-M
in plain binary, using b bits. Based on the quotient and remainder values, code words are generated as per code
format given in Eq.(6)
)6(Re  CodemainderCodeQuotientCodeFormat
The sample encoded shape histogram is shown in Table. 3. The average bit length of the encoded shape
histogram is calculated and it is found that the average bit length of dimension reduced shape histogram is
always low.
The C Code, R Code and Q Code of sample block index is obtained and used for the retrieval. The
retrieval performance is tested for all the code formats. It is noticed that the retrieval performance of Q Code C
Code is similar. The performance of R Code is poor due to the fact of minimum information content. As a result,
Q Code information alone is sufficient to achieve good result, which shown that Q Code information is equal to
C Code information. This is represented in terms of entropy in Eq. (7)

52
 
 
  )7()(
0
)(
CodeQECodeCE
CodeQE
CodeRCodeQECodeCE



since <R Code> is negligible in (7)
The entropy for C Code and Q Code for various images are calculated and it is noticed that the
information content of C Code is slightly greater [w=0.1-0.4] compared to the Q Code and is represented in Eq.
(7). This is due to the fact that C Code includes both Q Code and R Code. Thus, the difference between the
entropy of C Code and Q Code is very low and Q Code alone is sufficient for representing the histogram,
thereby reducing the bit length.
)8()(*)( CodeQEwCodeCE 
C. Common Bins Similarity Measure (CBSM)
The conventional distance measures face the curse of dimensionality issue due to nearest-neighbor
search. Here, CBSM is proposed, which has good response time without affecting the precision. The entire
database image is split various blocks and indexed as DB= (B1, B2,…, Bm). The block contains unstructured
shape histograms with non-zero bins and represented as Bm = (h1, h2, h3,…, hk). The shape histogram bin is
represented as hk(Nj), such that Nj represents the bin value for the bin index j where j=(1, 2, 3, ...). Given a
query hq(Ni), the matching Block Index (B1,B2,…,Bm) is identified using its shape histogram dimension range
(R1,R2,…,Rm). The CBSM computes the distance between query histogram (hq) and histogram (hk) in matched
block database. Since, there exist a structural variation in the shape histograms; the similarity approach
considers common bins of the shape histogram to compute the distance between them. The non-zero bin counts
of query (Count_q) and block database histogram (Count_k) are considered. The common bins (Common (q))
between hq and hk are identified and degree of common bins (Common(Degree)) is computed using Eq. (9).
)9(
)_(
C
)(
(Degree) 






qCount
Common
ommon
q
The common bin values of both the shape histograms (hq and hk) are compared. As the bits are binary,
XOR logic is used for comparison which gives the difference in the common bin values (CB [diff]) for complete
histogram. This is represented in Eq. (10). Here, Ni(hq)represents the value of ith
bin index of query histogram
(hq) and Nj(hk) is the value of jth
bin index of clustered database histogram (hk), which are common (i==j) where,
i=(1,2, 3,....,n) and j=(1,2,3,...,n).
 

n
ji
kjqidiffdiff hNhNCBCB
1
)()( )10()()(
In Table. 4, sample hq and hk is presented for better understanding of the working principle of CBSM.
The non-zero bins of both the histograms are counted and analysed. It is observed that only five bins are
common between them and considered for calculating the similarity. The Common (Degree) of query shape
histogram is computed using Eq. (9). The encoded values (Q Code) of common bins of both histograms are
compared and represented as CB (diff) using Eq. (10). Similarly, Common (Degree) and CB [diff] between query hq
and all the other histograms (h1, h2, h3,…,hk) in the Block Bm are calculated. The CB (diff) (dist) is calculated by
counting number of 1’s in CB (diff) of the histograms as shown in Eq. (11).
  )11()'1()()( sNumberofCBdistCB diffdiff 
The Common (Degree) and CB(diff) (dist) are normalized and their combined values give distance between hq and
(h1, h2, h3,…, hk) of the Block Bm. This is represented in Eq. (12).
   )12()()( Degreediff CommondistCBCBSM 

53
Table IV Comparison of Encoded Values Between Query and Clustered Database Histogram
Common(q) count_q Common(Degree) hq
<Q Code>
hk
<Q Code>
XOR CB(diff)=∑
XOR
3
4
5
54
55
23 5/(23) 1110
1110
11110
111110
1110
110
111110
11111110
110
10
1000
110000
11100000
111000
1100
11111100
IV. EXPERIMENTAL RESULT
The effectiveness of the proposed encoded histogram is evaluated in an image retrieval system. For our
experiment, we have used label me benchmark dataset (http://www.cucl.mit.edu/database.html) with 9356
images in which 9144 are object images categorized into 101 classes and 212 are texture images categorized
into 19 classes. We have selected query images from various classes for computing recall and precision and the
top 50 retrieval images are considered. The CBSM is used as the distance metric to measure the distance
between query and database are images the Recall Vs. Precision is depicted in Fig.5 (a). It is observed that for
lower values of recall, the precision is getting higher, which is reaching around 94%. The difference in precision
for various recalls for both encoded and original shape histogram is almost zero. Further to consolidate the
performance of the proposed approach, the F-measure is calculated using Eq. (13) which represents harmonic
mean of recall and precision.
)20(
2








RP
PR
F
(13)
It can be noticed from the Fig. 5(b) that the difference in F-Measure between encoded and original
histogram for various nearest neighbours is almost zero. This performance enhancement is due to the fact that
the encoding procedure just assigns the code for minimizing the size of the histogram and the information is not
lost. It is noticed from the result that the proposed approach performs well and retrieve the same result set as
original histogram and also consume less space with good computation time.
0
0.2
0.4
0.6
0.8
1
0.1 0.2 0.3 0.5
F1-Score
Nearest neighbor
OriginalHist
Encoded Hist
(b)
Fig. 5. Performance between Original and Encoded Shape Histograms
(a) Precision Vs. Recall (b) F-Measure

54
To consolidate the performance of the proposed approach, we compared with other similar approaches
such as RLE and arithmetic encoding. In RLE approach, a rate-efficient codec is designed for tree-based
retrieval and run length encoding is used in [22]. But the approach had a limitation that runs length encoding is
not able to work well at continuous-tone images. In arithmetic coding, the images are divided into histograms
blocks. The maximum and minimum pixel value for the entire image is found, with range (R). Further, block
size (R× R) is set using contrast of the image and arithmetic coding is performed. The performance measures for
all the approaches are estimated in terms of Precision, Recall and F-measure and shown in Fig. 6 and it
represents Precision vs. Recall for different query images. The ground truth and Precision vs. Recall is taken
individually for various blocks and then average Precision vs. Recall is calculated. Proposed approach gives
70% and RLE approach gives 68% for recall at 0.1.
Fig. 6. Precision Vs. Recall of Proposed and Comparative Approach
Thus, the proposed approach encourages good precision of retrieval apart from reduced bit length,
retrieval time and computation speed along with better search process.
V. CONCLUSION
The paper has considered the issues related to coding scheme for feature, storage and indexing for
achieving higher retrieval time. An encoding scheme is proposed along with suitable distance measure to handle
variance in structure of the histogram of query and database. The feature is coded using GR coding and the
dimension of the histogram is used for indexing and clustering the features. The appropriate cluster is identified
based on the dimension of the query histogram. Only quotient part of the histogram for image retrieval is used
and retrieves the images without decoding. The performance of the proposed approach is evaluated using
precision, recall and F-Measure and found that the difference in precision of retrieval between original and
encoded histogram is almost negligible.
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Coding and Indexing Shape Feature using Golomb-Rice Coding for CBIR Applications