SLIM-TREE AND BITMATRIX INDEX STRUCTURES IN IMAGE RETRIEVAL SYSTEM USING MPEG-7 DESCRIPTORS

Esra Açar1, Serdar Arslan1, Adnan Yazıcı1 and Murat Koyuncu2

1Dept. of Computer Engineering, Middle East Technical University, Ankara, Turkey 2Dept. of Computer Engineering, Atilim University, Ankara, Turkey

esraacar@gmail.com, aserdar@metu.edu.tr, yazici@ceng.metu.edu.tr, mkoyuncu@atilim.edu.tr

ABSTRACT

Content-based retrieval of multimedia data has still been an active research area. The efficient retrieval in natural images has been proven a difficult task for content-based image retrieval systems. In this paper, we present a system that adapts two different index structures, namely Slim-Tree and BitMatrix, for efficient retrieval of images based on multidimensional low-level features such as color, texture and shape. These index structures also use metric space. We use MPEG-7 Descriptors extracted from images to represent these features and store them in a native XML database. The low-level features; Color Layout (CL), Dominant Color (DC), Edge Histogram (EH) and Region Shape (RS) are used in Slim-Tree and BitMatrix and aggregated by Ordered Weighted Averaging (OWA) method to find final similarity between any two objects. The experiments included in the paper are in the subject of index construction and update, query response time and retrieval effectiveness using ANMRR performance metric and precision/recall scores. The experimental results strengthen the case that uses BitMatrix along with Ordered Weighted Averaging method in content-based image retrieval systems.

Keywords: Content-Based Image Retrieval, MPEG-7, Slim-Tree, BitMatrix, OWA, XML Database.

1. INTRODUCTION

Multimedia data are of high importance in many areas and the growth for these data brings the need for more effective methods in retrieval. In general, content-based image retrieval (CBIR) systems [1-4] index images on the basis of low-level features.

In this work, we focus on several aspects of a CBIR system. First issue is the extraction and description of low-level features which is a very expensive process [5]. In order to describe the low-level features, we use MPEG-7 descriptors [6]. The MPEG-7 descriptors used in this study are Color Layout (CL), Dominant Color (DC), Edge Histogram (EH) and Region Shape (RS). These descriptors are extracted in XML format by using MPEG-7 eXperimentation Model (XM) [7] [8] and stored in a native

XML database system called Berkeley DB XML [9] for further processing and retrieval.

In general, the critical part of the CBIR system is the retrieval performance of the system. There are some multidimensional access methods proposed to increase the effectiveness of search and retrieval in terms of time and efficiency [1-5]. In this study, two multidimensional index structures, Slim-Tree [10] and BitMatrix [11, 12] are adapted to the system to improve search and retrieval time.

Slim-Tree is a dynamically organized similarity based index structure in metric spaces for multidimensional data and indexes distance between any two objects. BitMatrix is another index structure proposed for similarity searching of multimedia data by using a data approximation approach. Similarity measurement for both structures is carried out by using a metric distance function called Euclidean Distance. Index construction, update and retrieval performances are evaluated in tests for both structures.

In general, when more than one feature is being processed in similarity searching with weighted distance functions, same weights are used for same features of all images in database. However, when comparing two images one feature may be more distinctive than others; therefore that feature must be associated with higher weight. Thus, we adapt Ordered Weighted Averaging (OWA) [13] method to solve this problem. The retrieval efficiency of the system is evaluated by using Average Normalized Modified Retrieval Rank (ANMRR) [14] metric. Finally, precision and recall values are evaluated and compared for both structures.

The rest of this paper is organized as follows: In Section 2 we present our proposed CBIR system. The performance tests of the system introduced in this paper are given in Section 3. Finally, Section 4 concludes the paper.

2. THE IMAGE RETRIEVAL SYSTEM

In this section, we describe our approach to image retrieval using MPEG-7 Descriptors with two index structures. The OWA method along with the similarity measurement is also presented.

978-1-4244-2044-5/08/$25.00 c©2008 IEEE. 402 CBMI 2008

2.1. Mpeg-7 MPEG-7 [6] is introduced as a standard for representing the audio-visual content. MPEG-7 focuses on the description of multimedia content and does not standardize the way to obtain these descriptions or how to use them, but only standardizes the descriptions and the way of structuring them [6]. In [15], MPEG-7 visual descriptors are analyzed from the statistical point of view. The main results show that the best descriptors for combination are Color Layout (CL), Dominant Color (DC), Edge Histogram (EH), and Texture Browsing (TB). The others are highly dependent on these. In this work, we use two color descriptor; Dominant Color (DC) and Color Layout (CL), one texture descriptor; Edge Histogram (EH) and one shape descriptor; Region Shape(RS). These descriptors are extracted by using MPEG-7 eXperimentation Model (XM) [7][8]Software. XM software is the simulation platform for the MPEG-7 Descriptors and divided in two application types: the server (extraction) applications and the client (search, filtering and/or transcoding) applications. We only use server applications for low-level feature extraction.

2.2. Index Structures For indexing multimedia data, we use Slim-Tree, known as a dynamic and balanced access structure, and BitMatrix which is a highly parametrizable structure. Before discussing the used index structures, we define similarity measurement and OWA method. 2.2.1. Similarity Measurement In metric space structures, what is actually measured is the distance between feature values [16, 17], so the distance function returns a dissimilarity value between any two objects where high distance corresponds to low similarity and low distance corresponds to high similarity.

Similarity measurement is carried out by using a distance function. Commonly used distance function is Minkowski-form distance (Lp) [2]:

)( ( ) ( )

∑

=−=

d

iiyix

piwyx,D

p

1

1

(1)

where x and y are feature vectors and d is feature

dimension. If p = 1, L1 is Manhattan distance p = 2, L2 is Euclidean distance p = ∞, L∞ is maximum distance In this work, we use the following distance function

for the CL feature:

( )

( )

( )∑

∑

∑

=

=

=

−+

−+

−=

2

0

2

2

0

2

5

0

2

]['][

]['][

]['][

i

i

iCL

iCrCoeffiCrCoeff

iCbCoeffiCbCoeff

iYCoeffiYCoeffD

(2)

and for the EH feature:

∑=

−=n

iEH iBincountsiBincountsD

1

2])['][(

(3)

where n is 80. The distance function for RS is as follows:

∑=

−=n

iRS iMagOfArtiMagOfArtD

1

2])['][( (4)

where n is 35. The distance function for Dominant Color (DC) is a

fuzzy distance function which is introduced in [18] and differs from the distance computation of other features. The fuzzy distance computation of DC is as follows: firstly, if color value differences are less than a predefined threshold value, then color distance is evaluated in the specified color space, which is RGB for our system, by using the following function:

∑=

−=n

iDC iColorValiColorValD

1

2])['][( (5)

where n is 3. In the second phase, minimum percentage of the related

dominant colors of two images is normalized and multiplied by the color similarity to find final DC similarity of the two images.

2.2.2. Ordered Weighted Averaging (OWA) Method An OWA operator of dimension n is a mapping:

F : R• • R, (6)which has an associated weighting vector W

[ ]T21 ... W nwww= (7)

such that

∑=

n

iiw

1 = 1 (8)

where wi Є[0, 1] and where

( ) ∑=

⋅=n

iiin bwaaF

11,..., (9)

403

where bi is the ith largest element of the collection of the aggregated objects a1,…,an. The function value F(a1,…,a

n)

determines the aggregated value of the arguments, a1,…,an. To compute the overall distance between two images,

we compute CL, DC, EH and RS distances and apply normalization to each of them separately so that the range is from ‘0’ (similar) to ‘1’ (dissimilar). After normalization of each feature’s distances, we compute the overall distance value from these four distances by using the OWA operator. From the definition of OWA method [13], the overall distance is also in [0, 1].

Suppose that (d1, d2, .., dn) are the n distance values and the order of these numbers are d1 ≤ d2 ≤…≤ dn. The OWA operator associated to the n nonnegative weights (w1, …, wn) where wi Є [0,1] and wn ≤ … ≤ w2 ≤ w1. It should be noted that the weight wn is linked to the greatest distance value, dn, and w1 is linked to the lowest distance value, d1 , to emphasize similarity between two objects.

For example, for two images O1 and O2, we want to compute distance between them, let’s say d(O1, O2). Assume that, for each feature, CL, DC, EH and RS, the normalized Euclidean distance values are;

d

DC(O

1, O

2) = 0.325, d

CL(O

1, O

2) = 0.570,

dEH

(O1, O

2) = 0.450, d

RS(O

1, O

2) = 0.250

and the OWA weights are; w1 = 0.4, w2 = 0.3, w3 = 0.2, w4 = 0.1,

where w1 + w2 + w3 + w4 = 0.4+0.3+0.2+0.1 = 1, then the overall distance is:

d(O1, O2) = F(d

CL(O

1, O

2), d

DC(O

1, O

2), d

EH(O

1, O

2),

dRS

(O1, O

2) )

= w1 * dRS

(O1, O

2) + w2 * d

DC(O

1, O

2)

+ w3 * dEH

(O1, O

2)+ w4 * d

CL(O

1, O

2)

=0.4*0.250+0.3*0.325+0.2*0.450+0.1*0.570 = 0.3445. In this work, we use Euclidean distance function for

all features and we implement two versions of both Slim-Tree and BitMatrix, one is with weighted sum of distance functions by using equal weights and the other is one adapted with OWA method. Since there are four low-level features that represent the image content, the system evaluates the distance values for each feature, by using Euclidean distance and combines these values into single value by using OWA method or giving same weight to each value and summing them up. The weight values for OWA method for these four features are {0.4, 0.3, 0.2, 0.1}. 2.3. Slim-Tree

The Slim-Tree is a balanced and dynamic paged structure that can be efficiently used to index multimedia data in metric space [10]. Slim-Tree has two kinds of nodes; data

nodes as leaves, and internal nodes as index nodes which are shown in Figure. 1. The multimedia data are presented by means of complex features and similarity between any two objects is defined by a time consuming distance function. Like M-Tree, Slim-Tree indexes these distances not the features. However, Slim-Tree differs from M-Tree in the following aspects; Slim-Tree has faster split algorithm which is based on Minimal Spanning Trees, higher storage utilization and smaller overlapped region in the tree [10].

The increase in overlaps is directly related to query performance. Since, more paths and nodes are to be visited to find related objects; this yields an increase in the number of distance computations. Thus, the main aim of the Slim-Tree is to organize the objects in a hierarchical structure using a distance function to cover the objects in a sub-tree having minimum bounding region to minimize overlap. The details of the Slim-Tree index structure and the algorithms for construction are reported in [10].

2.3.1. Building the Slim-Tree We implemented a single-tree for indexing all the features of images together. There are two trees; one with OWA adapted and another with equal weights. Bulk loading algorithm is used to construct the Slim-Tree with Minimal Spanning Tree split strategy. When a distance computation is necessary, the system computes distance values of each feature and combines these values into a single distance value by using OWA method or giving equal weights for each feature. After this step, the tree is constructed according to this final distance value.

2.3.2. Querying the Slim-Tree Firstly, feature descriptors of query object are extracted. Then, the query processor starts to compare the query object with the objects in the tree by computing distance values. Query results are set according to query type. If query is a range query then the objects which have less distance value than range radius are returned. Otherwise, query is a k-NN query and the most k similar objects to the query object are ranked and returned. 2.4. Bit Matrix In this study, BitMatrix [11, 12] index structure is implemented for image databases. During its implementation, Weka API [19] is used to cluster the low-level visual features of images; and Colt API [20] is used to hold the constructed BitMatrix index structure and to make operations on the BitMatrix such as taking the intersection of two bitmatrix signatures during similarity queries. As in Slim-Tree implementation, we implemented two versions of BitMatrix, with equal weights and with OWA adapted.

404

Figure 1: Slim-Tree Overview

2.4.1. Building the BitMatrix The first step to build a BitMatrix is to cluster the objects to be indexed along each dimension d into kd ranges. Images are separately clustered into predefined number of clusters according to their CL, DC, EH and RS values,. K-means clustering algorithm of the Weka API is used as the clustering algorithm. After the clustering process, Bitmatrix signatures are constructed. Bitmatrix signatures contain 1 for the cluster to which the feature value of the image belongs and 0 for the other clusters.

Finally, the resulting BitMatrix index structure which contains all the bitmatrix signatures for images in the data set is built using the constructed bitmatrix signatures. The size of a BitMatrix index grows linearly with the number of indexed objects and with the dimensionality.

The clustering results of Color Layout (CL) and Edge Histogram (EH) feature values of ten images from the Corel dataset are given in Figure 2 and the clustering results of Dominant Color (DC) and Region Shape (RS) feature values of ten images from the same dataset are given in Figure 3. The resulting sample BitMatrix index structure is shown in Figure 4.

Insertion of an object into BitMatrix can be summarized as follows:

Compute bitmatrix signature of the object to be indexed.

Add the resulting bitmatrix signature of the object to the end of BitMatrix as a new line.

Figure 2: Sample Clustering of CL and EH

Figure 3: Sample Clustering of DC and RS

Deletion/Update of an object from/in BitMatrix can be summarized as follows:

Locate the bitmatrix signature of the object to be removed/updated.

Remove/Update the bitmatrix signature from/in the BitMatrix index.

2.4.2. Querying BitMatrix BitMatrix supports two main types of queries: k-NN (k-Nearest Neighbor) query and range query. Since exact match query is a range query whose range radius is zero, it is not mentioned explicitly. Querying BitMatrix can be summarized as follows:

405

CL EH DC RS

0 1 2 3 4 5 6 7 0 1 2 3 0 1 2 3 4 5

66 7 0 1 2 3

Img1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0

00 0 0 1 0 0

Img2 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0

00 0 0 0 0 1

Img3 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0

00 0 0 1 0 0

Img4 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1

00 0 0 1 0 0

Img5 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0

00 0 1 0 0 0

Img6 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0

00 0 0 0 0 1

Img7 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0

00 0 0 0 1 0

Img8 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0

00 0 0 1 0 0

Img9 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1

00 0 0 0 0 1

Img10 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0

00 0 0 0 1 0

Figure 4: Sample BitMatrix for 10 Images

k-NN Search on BitMatrix [12]: Step 1: Given a query object q = [q1,..., qN], where N is

the number of feature dimensions, obtain the query object’s bitmatrix signature.

Step 2: Iterate through the objects, performing bitwise AND between their bitmatrix signatures and the query object’s bitmatrix signature. If the cardinality of the resulting bitmatrix signature is above a predefined cardinality threshold (ct), the object is retained for the next phase.

Step 3: Access the full feature values of the remaining objects, compute their exact distance to the query object and rank them. Range Search on BitMatrix:

Step 1: Given a query object q = [q1,..., qN], where N is the number of feature dimensions, obtain the query object’s bitmatrix signature.

Step 2: Iterate through the objects, performing bitwise AND between their bitmatrix signatures and the query object’s bitmatrix signature. If the cardinality of the resulting bitmatrix signature is above a predefined cardinality threshold (ct), the object is retained for the next phase.

Step 3: Access the full feature values of the remaining objects, compute their exact distance to the query object. If the distance is smaller than or equal to the radius of the range search, put the related object to the result set.

3. PERFORMANCE EXPERIMENTS

In this section, we provide the experimental results of both structures. We run experiments comparing Slim-Tree with

BitMatrix. Both structures were implemented in Java language and we used Berkeley DB XML to store descriptors. Slim-Tree was implemented by using XXL API [21] and BitMatrix was implemented by using two APIs; Weka API [19] and Colt API [20]. Weka API was used for clustering low-level features while Colt API was used to hold the constructed BitMatrix index structure and to make operations on the BitMatrix. We used various numbers of images from Corel Database[22] for the tests.

To compare these two structures, we tested the system for index construction and update. Also, the retrieval efficiency of the index structures is analyzed in terms of retrieval effectiveness and response time.

Table 1 reports number of distance computations and time values for creating the Slim-Tree and BitMatrix for 700 images. Since we need clustering of low-level features in BitMatrix, creating this structure needs more time than Slim-Tree. For Slim-Tree, the number of distance computations, and therefore construction time, is decreased when we use higher storage utilization values, because node overlap and the number of path to access any object are decreased.

Since, there is no distance computation in insertion and deletion these operations are performed much more efficiently in BitMatrix contrary to index construction, as we can see from Table 2 and Table 3. For insertion, only the clustering results of image’s feature values are used and for deletion, only the related bitmatrix signature is removed from the BitMatrix index structure.

To evaluate the query performance, we have used nearest neighbor and range queries. The number of distance computations and query cost time are computed and evaluated. The retrieval efficiency of the system is also

406

evaluated by using ANMRR performance metric [14]. Basically, if the ANMRR value is equal to 0 (zero) then that means the system has a perfect retrieval process, but if this value is equal to 1 (one) then the system has an inefficient retrieval process. Precision and recall values are also computed and compared for these structures.

Table 1. Construction time and # of distance

computations for 700 images (EQW = Equal Weighted).

Index Structure Storage Utilization

# of Dist. Comp.

Const. Time (ms)

BitMatrix with OWA

N/A 0 1391

BitMatrix with EQW

N/A 0 1375

SlimTree with OWA

0.3 35482 1078.0

SlimTree with EQW

0.3 35825 1093.5

SlimTree with OWA

0.5 33048 1047.5

SlimTree with EQW

0.5 33945 1070.5

SlimTree with OWA

0.7 32240 1000.0

SlimTree with EQW

0.7 33635 1062.0

We have performed 1000 queries over BitMatrix, Slim-Tree and Sequential Scan. Table 4 and Table 5 report the results of comparing retrieval time and number of distance computations of each structure for k-Nearest Neighbor (k-NN) queries and range queries, respectively. The number of distance computations is an important factor for these index structures. When there is a distance computation to compare any two objects, those objects may not be in memory and must be read from disk or database. As we know, this disk or database access is a high-cost process and affects the system performance. Also since the distance function is complex, the computation time of this distance function is another performance issue.

We also compare the ANMRR results of our system. We use OWA operators for aggregation of distance values of four low-level features. It should be noted that the features have different effects to the retrieval results. Among four features, the most relevant feature (or the most distinctive one) to the query image is treated as the main feature when comparing query object with database objects. The results of ANMRR tests included in Table 6 show that BitMatrix with OWA adapted has the best ANMRR values. Besides this, the index structures with OWA adapted are more efficient than the index structures used equal-weighted aggregation in terms of query relevancy. Precision and recall scores shown in Table 7 also confirm this result.

Table 2. Insertion time and # of distance computations for 500 images.

# of Dist. Comp. Insertion Time (ms) Index Structure

Storage Utilization min max total Min Max total

BitMatrix with OWA

N/A N/A N/A N/A 0.116775 1.24513 65.052119

BitMatrix with EQW

N/A N/A N/A N/A 0.116774 1.336482 66.207312

SlimTree with OWA

0.3 26 386 29503 0.6336 9.765767 744.908084

SlimTree with EQW

0.3 28 379 30999 0.591137 9.660725 776.155629

SlimTree with OWA

0.5 34 381 29492 0.764343 9.215697 734.420163

SlimTree with EQW

0.5 32 370 30110 0.701486 11.65176 768.061016

SlimTree with OWA

0.7 27 365 29413 0.675225 9.612115 750.13891

SlimTree with EQW

0.7 32 363 30359 0.696737 8.823747 763.444232

407

Table 3. Deletion time and # of distance computations for 500 images.

# of Dist. Comp. Deletion Time (ms) Index Structure

Storage Utilization min max total Min Max total

BitMatrix with OWA

N/A N/A N/A N/A 0.002234 0.020115 1.511098

BitMatrix with EQW

N/A N/A N/A N/A 0.002234 0.020394 1.514446

SlimTree with OWA

0.3 21 439 80798 0.547835 11.160636 2092.689426

SlimTree with EQW

0.3 24 479 85936 0.611809 12.888509 2210.811165

SlimTree with OWA

0.5 20 461 79931 0.502858 12.506617 2073.247853

SlimTree with EQW

0.5 20 517 87052 0.474362 14.135316 2302.004573

SlimTree with OWA

0.7 17 689 153647 0.463467 18.40178 4125.052499

SlimTree with EQW

0.7 20 823 164268 0.440559 23.303241 4281.226238

Table 4. Query response time and # of distance computations for 10-NN queries over 1000 images.

# of Dist. Comp. Resp. Time (ms) Index Structure

Storage Utilization min max Min Max

BitMatrix with OWA N/A 71 366 2.764 15.74

BitMatrix with EQW N/A 71 366 2.833 15.588

SlimTree with OWA 0.7 499 997 14.853 39.709

SlimTree with EQW 0.7 578 1000 15.363 40.009

Seq. Scan with OWA N/A 1000 1000 26.4 43.692

Seq. Scan with EQW N/A 1000 1000 26.459 43.064

Table 5. Query response time and # of distance computations for range queries over 1000 images (r = 0.2).

# of Dist. Comp. Response Time (ms) Index Structure

Storage Utilization min max min max

BitMatrix with OWA N/A 71 366 2.725 15.554

BitMatrix with EQW N/A 71 366 2.924 15.501

SlimTree with OWA 0.7 494 1066 15.241 50.606

SlimTree with EQW 0.7 485 1055 14.452 50.689

Seq. Scan with OWA N/A 1000 1000 25.382 44.413

Seq. Scan with EQW N/A 1000 1000 25.176 44.23

Table 6. ANMRR results for 100 queries over 1000 images.

408

8

OWA Equal Weights

BitMatrix 0.24524 0.25409

SlimTree 0.26793 0.27053

Sequential Scan 0.28020 0.28131

Table 7. Precision and recall values for 100 queries over

1000 images.

Precision Recall

OWA EQW OWA EQW

BitMatrix 0.3280 0.3182 0.8062 0.7840

SlimTree 0.3191 0.3178 0.7916 0.7760

Seq. Scan 0.3183 0.3175 0.7889 0.7748

4. CONCLUSION

In this paper, we present a system that adapts two different index structures, namely Slim-Tree and BitMatrix, for efficient retrieval of images based on low-level descriptors, such as texture, color and shape. These structures use distance function to evaluate similarity between objects. For the distance evaluation between objects, we use the weighted sum of Euclidean distance and each weight is evaluated by using the OWA method. For low-level features, we use four descriptors of MPEG-7 which are CL, DC, EH and RS. These features are extracted by using MPEG-7 XM Software and stored in an XML database, Berkeley DB XML. The system has been tested on images of the Corel database.

From the test results, we observed that BitMatrix is much faster than Slim-Tree in insertion and deletion process. Since, BitMatrix performs no distance computation in these processes. However, Slim-Tree’s construction time is less than that of BitMatrix’s because of clustering step in BitMatrix. BitMatrix outperforms Slim-Tree and Sequential Scan in query response time tests. From the test results, we also observed that BitMatrix performs less number of distance computations during k-NN and range queries. Thus, query response time values are much better.

The retrieval efficiency of the system is also evaluated by using ANMRR performance metric and by precision/recall scores. From the test results, we observed that BitMatrix with OWA adapted has the best results. These results also show that index structures with OWA adapted outperform the same structures that have equal weighted aggregation. By using OWA, among four low-level features, the most relevant feature (or the most distinctive one) to the query image is treated as the main feature for comparing query object with database objects. This property yields better performance when compared to equal weighted similarity measurement method.

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