Fast indexing and searching strategies for feature

Journal of Electronic Imaging 14(1), 013019 (Jan – Mar 2005)

Fast indexing and searching strategies for feature-based image database systems Li-Wei Kang Jin-Jang Leou National Chung Cheng University Department of Computer Science and Information Engineering Chiayi, Taiwan 621 E-mail: [email protected]

Abstract. Because visual data require a large amount of memory and computing power for storage and processing, it is greatly desired to efficiently index and retrieve the visual information from image database systems. We propose efficient indexing and searching strategies for feature-based image database systems, in which uncompressed and compressed domain image features are employed. Each query or stored image is represented by a set of features extracted from the image. The weighted square sum error distance is employed to evaluate the ranks of retrieved images. Many fast clustering and searching techniques exist for the square sum error distance used in vector quantization (VQ), in which different features have identical weighting coefficients. In practice, different features may have different dynamic ranges and different importances, i.e., different features may have different weighting coefficients. We derive a set of inequalities based on the weighted square sum error distance and employ it to speed up the indexing (clustering) and searching procedures for feature-based image database systems. Good simulation results show the feasibility of the proposed approaches. © 2005 SPIE and IS&T. [DOI: 10.1117/1.1866148]

1 Introduction Multimedia database systems become more and more popular with the advent of high-powered PCs, low-cost computer storage devices, broadband networks, and visual/ audio compression standards. Because visual data require a large amount of memory and computing power for storage and processing, it is greatly desired to efficiently index and retrieve 共search兲 the visual information from multimedia database systems. Some existing systems include the famous QBIC system from IBM, the Safe system from Columbia University, the VIR Image Engine from Virage, and the Photobook from Massachusetts Institute of Technology.1–3 Traditionally, database systems are usually accessed by text-based queries,4,5 such as keywords, captions, and filenames, which are not suitable for a modern image database system. Image retrieval based on image content is greatly desirable in a number of applications.6 As shown in Fig. 1, feature vectors representing images are usually extracted, organized, and stored properly in a multimedia database system when it is created. In the query process, a feature Paper 020030 received Apr. 10, 2000; revised manuscript received Feb. 22, 2001; accepted for publication May 14, 2004; published online Feb. 24, 2005. 1017-9909/2005/$22.00 © 2005 SPIE and IS&T.

Journal of Electronic Imaging

vector 共or a set of features兲 representing a query image is extracted from the query image, and then the similarity 共or distance兲 measures between the query image and stored images in the image database system are evaluated. Finally, the most similar image共s兲 will be presented to the user. For a feature-based image database system, each image can be represented by a k-dimensional feature vector, i.e., an image is converted into a k-attribute numeric data in a k-dimensional Euclidean space. To make the image database scalable to a very large size, efficient multidimensional indexing and searching techniques must be explored. Traditional multidimensional data structures, such as R-tree, kDB-tree, and grid files, are not suitable for image feature indexing due to inability to scale to high dimensionality.7 A kind of famous multidimensional indexing structure is the tree-based indexing technique that can be classified into data partitioning 共DP兲-based and space partitioning 共SP兲-based index structures. A DP-based index structure consists of bounding regions arranged in a spatial containment hierarchy, such as R-tree, X-tree,8 and SR-tree.9 An SP-based index structure consists of space recursively partitioned into mutually disjoint subspaces. The hierarchy of partitions forms the tree structures, such as kd-tree,10 kDB-tree,11 and hB-tree.12 Berchtold et al.13 proposed an indexing method, called the pyramid-technique, for high-dimensional data spaces. It is claimed that the pyramid technique outperforms the X-tree and the Hilbert R-tree. Kim et al.14 proposed an enhanced version of the R*-tree. Chakrabarti and Mehrotra7 proposed a multidimensional data structure called the hybrid tree for indexing high-dimensional feature spaces. It is claimed that the hybrid tree outperforms both purely DPbased and SP-based indexing structure. Wu15 presented a context-based indexing technique, called ContIndex, which is formally defined by adapting a classification tree concept. A special neural network model was developed to create node categories by fusing multimodal feature measures. Gong et al.16 presented an indexing scheme using color histogram, in which a B⫹ -tree is used to store the numerical keys of color histograms in the database system. Vazirgiannis et al.17 proposed two indexing schemes using the R-tree indexing structure for large multimedia applications.

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fast algorithms is to use some inequalities to reject many unlike vectors, without detailed calculating of the distance functions between vectors. Several fast algorithms for VQ are introduced briefly as follows. 2.1 Mean Difference Method Fig. 1 Generalized content-based image database (retrieval) system.

For other existing image indexing and searching strategies, Jain and Vailaya6 developed an efficient image retrieval method using a clustering technique and a branch and bound-based matching scheme, whereas Jain and Vailaya18 proposed a trademark image retrieval method using object shape information and a two-stage hierarchy. In this study, each query or stored image is represented by a set of uncompressed and compressed features extracted from the image and a new distance measure is used to evaluate the ranks of the retrieved images. In the imageindexing phase, the feature vectors and the auxiliary information for all stored images are first calculated and stored in the database system. Then all the images 共or feature vectors兲 in the database system are classified into a prespecified number K of clusters by fast clustering techniques, based on the new distance measure. In the image searching phase, the feature vector and the auxiliary information of a query image is first calculated. Then a small number M of closest clusters are determined by computing the distances between the query image and all the K cluster centers. Second, the most N similar images are found among the small number M of closest clusters. A set of inequalities based on the new distance measure is derived to speed up both the image indexing 共clustering兲 and searching phases. A popular distance measure is the square sum error distance, in which different features have identical weighting coefficients.1 In practice, different features may have different dynamic ranges and different importances, i.e., different features may have different weighting coefficients. Here, the new distance measure called the weighted square sum error distance is employed. On the other hand, the first type of features, such as color, texture, shape, or sketch, is extracted from uncompressed images,11,19–22 whereas the second type of features is extracted from compressed images directly.23,24 In this study, two types of image features extracted from both uncompressed and compressed images are employed to represent images. The paper is organized as follows. Section 2 presents a brief overview of existing fast algorithms for vector quantization 共VQ兲. Section 3 addresses the proposed indexing and searching strategies for image database systems. Simulation results are included in Sec. 4, followed by concluding remarks. 2 Existing Fast Algorithms for VQ VQ is25–30 a generalization of scalar quantization to the quantization of a vector. Within VQ, a vector x ⫽(x 1 ,x 2 ,...,x k ) is compared with all the vectors 共code words兲 in the codebook to find the closest vector 共code word兲 yi ⫽(y i1 ,y i2 ,...,y ik ) using the square sum error distance function. The basic idea employed in most existing Journal of Electronic Imaging

Within the mean difference method 共MDM兲 proposed by Lee and Chen,25 let x⫽(x 1 ,x 2 ,...,x k ) be an input k-dimensional vector and y⫽(y 1 ,y 2 ,...,y k ) be a k-dimensional vector 共code word兲 in the codebook. Define the mean values of x and y as 1 m x⫽ k m y⫽

1 k

k

兺

j⫽1

xj ,

共1兲

yj .

共2兲

k

兺

j⫽1

For the square sum error distance function between x and y, i.e., d 2 (x,y)⫽ 兺 kj⫽1 (x j ⫺y j ) 2 , we have d 2 共 x,y兲 ⭓k 共 m x ⫺m y 兲 2 .

共3兲

That is, for a vector 共code word兲 y in the codebook, if k(m x ⫺m y ) 2 is larger than the current minimum distortion 2 d min , y will not be the closest vector 共code word兲 to the input vector x and thus can be rejected. 2.2 Equal-Average Equal-Variance NearestNeighbor Search Algorithm For the equal-average equal-variance nearest-neighbor search 共EENNS兲 algorithm proposed by Lee and Chen,26 the variance V 2x of x is defined as k

V 2x ⫽

兺 共 x j ⫺m x 兲 2 .

j⫽1

共4兲

It can be proved that d 共 x,y兲 ⭓ 兩 V x ⫺V y 兩 .

共5兲

Within the EENNS algorithm, the vectors 共code words兲 whose means are similar to m x , but whose variances are very different from V 2x will be rejected accordingly. 2.3 Baek et al.’s Method Within the algorithm proposed by Baek et al.,27 we have d 2 (x,y)⫽ 兺 kj⫽1 (x j ⫺y j ) 2 , then d 2 共 x,y兲 ⭓k 共 m x ⫺m y 兲 2 ⫹ 共 V x ⫺V y 兲 2 .

共6兲

2.4 Integral Projection Mean-Sorted Partial Search Algorithm For the integral projection mean-sorted partial search 共IPMPS兲 algorithm proposed by Lin and Tai,28 for an input k-dimensional vector x(i, j) arranged by two indices (i, j) with k⫽n⫻n, where i, j⫽1,2,...,n, the three kinds of integral projections are defined as follows:

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Fast indexing and searching strategies . . . n

1. vertical projection: v p x 共 j 兲 ⫽

兺 x共 i, j 兲 ,

i⫽1

1⭐ j⭐n, 共7兲

n

2. horizontal projection: hp x 共 i 兲 ⫽

兺 x共 i, j 兲 , j⫽1

1⭐i⭐n, 共8兲

and n

3. massive projection: m p x ⫽

n

兺兺

i⫽1 j⫽1

x共 i, j 兲 .

共9兲

For the three simple distortion measures given by 2 dm 共 x,y兲 ⫽ 共 mp x ⫺mp y 兲 2 ,

共10兲

Fig. 2 Computation of cooccurrence matrices for a 4⫻4 block: (a) a 4⫻4 image block with gray-values 0 to 3, (b) the general form of a cooccurrence matrix, (c) neighboring gray-value pairs for computing S0 deg(1), and (d) the contents of S0 deg(1).

n

d 2v 共 x,y兲 ⫽

兺 关v p x共 l 兲 ⫺ v p y 共 l 兲兴 2 ,

l⫽1

共11兲

n

d 2h 共 x,y兲 ⫽

兺 关 hp x共 l 兲 ⫺hp y 共 l 兲兴 2 ,

l⫽1

共12兲

we have 2 dm 共 x,y兲 ⭐n 2 d 2 共 x,y兲 ,

共13兲

d 2v 共 x,y兲 ⭐nd 2 共 x,y兲 ,

共14兲

and d 2h 共 x,y兲 ⭐nd 2 共 x,y兲 .

共15兲

2.5 Chang and Hu’s Method In the generalized integral projection 共GIP兲 model developed by Chang and Hu,29 a k-dimensional vector can be partitioned into any p segments and each segment has q components 共pixels兲, where p and q are two positive integers with k⫽ p⫻q. For each of the p segments of a codevector x, the q components 共pixel values兲 can be summed to obtain a projection P x (l), for l⫽1,2,...,p. If the distortion measure between two codevectors is given by p

d 共2p,q 兲 共 x,y兲 ⫽

兺 关 P x共 l 兲 ⫺ P y 共 l 兲兴 2 ,

l⫽1

共16兲

where P x (l) and P y (l), l⫽1,2,...,p, are projections of the codevectors x and y, respectively, we have d 共2p,q 兲 共 x,y兲 ⭐q⫻d 2 共 x,y兲 . 3

共17兲

Proposed Fast Indexing and Searching Strategies for Image Database Systems

Features Extracted from Uncompressed and Compressed Images In this study, the first type of features extracted from uncompressed images is the color coherence vector31 共CCV兲,

which is a type of histogram-based features incorporating the spatial information. Within the CCV, each pixel in a given color bucket is classified into either ‘‘coherent’’ or ‘‘incoherent.’’ A pixel is coherent if the size of its connected component exceeds a predefined threshold ␶; otherwise, it is incoherent. A CCV stores the number of coherent and incoherent pixels for each color bucket. The CCV can take spatial information into account and outperform the traditional color histogram method.31 In the CCV method,31 the number n of color buckets is set to 64 and the threshold ␶ is set to be 1% of the size of an image, which are followed in this study. That is, n⫽64 and the threshold ␶ is set to be 655 共the size of an image is 65,536兲. Hence the CCV for an image can be represented as a 128-dimensional vector 关 ( ␣ 1 , ␤ 1 ),( ␣ 2 , ␤ 2 ),...,( ␣ 64 , ␤ 64) 兴 . In this study, the second type of features extracted from uncompressed images is the five 共among 14兲 statistical texture measures derived by Haralick et al.,32 which can be computed based on the gray-scale cooccurrence matrices. Haralick et al. derived the 14 measures, but only five of them are found to be truly useful.33 The gray-scale cooccurrence matrices, which describe spatial dependence of pixels in a gray-scale image, are often used in statistical analysis of textures. Figure 2共a兲 shows a 4⫻4 image block with gray values 0 to 3, and Fig. 2共b兲 shows the corresponding general form of a cooccurrence matrix, where each element (i, j) denotes the occurrence frequency of two neighboring pixels with gray-values i and j. If S␪ (d) denotes a cooccurrence matrix with distance d and direction ␪, Fig. 2共c兲 shows the neighboring gray-value pairs for computing S0 deg(1) and Fig. 2共d兲 shows the contents of S0 deg(1), where ‘‘⇔’’ denotes a neighboring gray-value pair. The other cooccurrence matrices can be similarly calculated. If N denotes the number of gray values and S␪ (i, j 兩 d) denotes the (i, j)’th element in S␪ (d), the five texture measures are given by32

3.1

Journal of Electronic Imaging

N⫺1 N⫺1

1. energy:

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f 1⫽

兺 兺

i⫽0 j⫽0

关 S␪ 共 i, j 兩 d 兲兴 2 ,

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Kang and Leou N⫺1 N⫺1

f 2 ⫽⫺

2. entropy:

兺 兺

i⫽0 j⫽0

N⫺1 N⫺1

C 共 u, v 兲 ⫽ ␣ 共 u 兲 ␣ 共 v 兲

S␪ 共 i, j 兩 d 兲 log S␪ 共 i, j 兩 d 兲 ,

冋

共19兲

⫻cos 1 f 3⫽ ␴ x␴ y

3. correlation:

N⫺1 N⫺1

兺 兺

i⫽0 j⫽0

共 i⫺u x 兲共 j⫺u y 兲

⫻S␪ 共 i, j 兩 d 兲 ,

f 4⫽

兺 兺

i⫽0 j⫽0

S␪ 共 i, j 兩 d 兲

共20兲

1⫹ 共 i⫺ j 兲

f 共 x,y 兲 ⫽

5. inertia:

f 5⫽

兺 兺

i⫽0 j⫽0

冋

共22兲

In Eq. 共20兲, u x , u y , ␴ x , and ␴ y are the means and standard deviations of S␪ (i, j 兩 d) along the horizontal and vertical directions, respectively, which are given by N⫺1 i⫽0

N⫺1

u y⫽

Sx 共 i, j 兩 d 兲 ,

Sy 共 i, j 兩 d 兲 ,

N⫺1

␴ 2x ⫽

兺

i⫽0

共23兲

N⫺1

兺 j j⫽0 兺

i⫽0

共27兲

␣ 共 u 兲 ␣ 共 v 兲 C 共 u, v 兲

册 冋

共 2x⫹1 兲 u ␲ 共 2y⫹1 兲v ␲ cos 2N 2N

册 共28兲

␣共 u 兲⫽

再

冉冊 冉冊 1 N

1/2

2 N

1/2

for u⫽0, 共29兲 for u⫽1,2,...,N⫺1.

In this study, a set of nine features ( f 1 , f 2 ,..., f 9 ) is determined as follows:

N⫺1

兺 i j⫽0 兺

u x⫽

册

for x,y⫽0,1,2,...,N⫺1, where

共 i⫺ j 兲 S␪ 共 i, j 兩 d 兲 .

兺 兺

u⫽0 v ⫽0

⫻cos

N⫺1 N⫺1 2

册 冋

共 2x⫹1 兲 u ␲ 共 2y⫹1 兲v ␲ cos 2N 2N

N⫺1 N⫺1

共21兲

, 2

f 共 x,y 兲

for u, v ⫽0,1,2,...,N⫺1,

4. inverse different moment 共IDM): N⫺1 N⫺1

兺 兺

x⫽0 y⫽0

共24兲

f 1 ⫽C 共 0,0兲 共 the dc coefficient兲 ,

共30兲

f 2 ⫽C 共 0,1兲 ⫹C 共 0,2兲 ⫹C 共 1,0兲 ⫹C 共 1,1兲 ⫹C 共 2,0兲 ,

共31兲

f 3 ⫽C 共 0,3兲 ⫹C 共 0,4兲 ⫹C 共 1,2兲 ⫹C 共 1,3兲 ⫹C 共 2,1兲 ⫹C 共 2,2兲 ⫹C 共 3,0兲 ⫹C 共 3,1兲 ⫹C 共 4,0兲 ,

N⫺1

共 i⫺u x 兲 2

兺

j⫽0

Sx 共 i, j 兩 d 兲 ,

共25兲

共32兲

f 4 ⫽C 共 0,5兲 ⫹C 共 0,6兲 ⫹C 共 1,4兲 ⫹C 共 1,5兲 ⫹C 共 2,3兲 ⫹C 共 2,4兲 ⫹C 共 3,2兲 ⫹C 共 3,3兲 ⫹C 共 4,1兲 ⫹C 共 4,2兲 ⫹C 共 5,0兲

N⫺1

␴ 2y ⫽

⫹C 共 5,1兲 ⫹C 共 6,0兲 ,

N⫺1

兺 共 j⫺u y 兲 2 i⫽0 兺 j⫽0

Sy 共 i, j 兩 d 兲 .

共26兲

f 5 ⫽C 共 0,0兲 ⫹C 共 1,0兲 ⫹C 共 2,0兲 ⫹C 共 3,0兲 ⫹C 共 4,0兲 ⫹C 共 5,0兲

To reduce the time complexity for computing these five texture measures, the gray levels of an image are requantized to contain only 16 gray levels by using a simple uniform quantization scheme32 and only d⫽1, ␪⫽0, 45, 90, and 135 deg are used.33 For each of the five texture measures, the means and the variances of the four corresponding values for ␪⫽0, 45, 90, and 135 deg are computed. Then the means and the variances of the five texture measures form a 10-D feature vector for representing an image. The seven invariant moments developed by Hu34 are used as shape features in this study, which are invariant to translation, rotation, and scaling.34,35 The 128 color features, 7 shape features, and 10 texture features form a 145-D feature vector for an uncompressed image. On the other hand, the image features extracted from compressed images are the discrete cosine transform 共DCT兲-based coefficients extracted from block-based DCTcompressed images.24 The two-dimensional 共2-D兲 DCT and inverse DCT 共IDCT兲 are given by Journal of Electronic Imaging

共33兲

⫹C 共 6,0兲 ⫹C 共 7,0兲 ,

共34兲

f 6 ⫽C 共 1,1兲 ⫹C 共 2,1兲 ⫹C 共 3,1兲 ⫹C 共 4,1兲 ⫹C 共 5,1兲 ⫹C 共 6,1兲 ⫹C 共 7,1兲 ,

共35兲

f 7 ⫽C 共 0,1兲 ⫹C 共 0,2兲 ⫹C 共 0,3兲 ⫹C 共 0,4兲 ⫹C 共 0,5兲 ⫹C 共 0,6兲 ⫹C 共 0,7兲 ,

共36兲

f 8 ⫽C 共 1,2兲 ⫹C 共 1,3兲 ⫹C 共 1,4兲 ⫹C 共 1,5兲 ⫹C 共 1,6兲 ⫹C 共 1,7兲 , 共37兲 f 9 ⫽C 共 2,2兲 ⫹C 共 2,3兲 ⫹C 共 3,2兲 ⫹C 共 3,3兲 ⫹C 共 3,4兲 ⫹C 共 4,3兲 ⫹C 共 4,4兲 ⫹C 共 4,5兲 ⫹C 共 5,4兲 ⫹C 共 5,5兲 .

共38兲

Extracting features from DCT-compressed images directly is efficient for indexing an image database system. The DCT coefficients represent some gray-level variations

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Fast indexing and searching strategies . . .

and dominant directions in the original image. Here f 1 is the dc coefficient representing the average energy of the corresponding image block; f 2 , f 3 , and f 4 represent frequency band characteristics; and f 5 , f 6 , f 7 , f 8 , and f 9 represent spatial characteristics.24 Each 8⫻8 block produces a 9-D feature vector ( f 1 , f 2 ,..., f 9 ) and the means and the variances of all the vectors within an image are calculated. Then the corresponding nine means and nine variances form an 18-D feature vector, which is the feature vector representing a compressed image.

Assume that x⫽(x 1 ,x 2 ,...,x k ) and y⫽(y 1 ,y 2 ,...,y k ) are two k-dimensional feature vectors representing two images, x and y, respectively, and w 1 , w 2 ,...,w k are the weighting coefficients for feature vectors with w j ⭓0, j⫽1,2,...,k and 兺 kj⫽1 w j ⫽1. The weighted square sum error distance d 2 (x,y) between two images or feature vectors x and y is given by k

兺

j⫽1

w j 共 x j ⫺y j 兲 2 .

共39兲

If the weighted sum m x and variance V 2x of x ⫽(x 1 ,x 2 ,...,x k ) are defined, respectively, as k

m x⫽

兺

j⫽1

w jx j ,

共40兲

w j 共 x j ⫺m x 兲 2 ,

共41兲

k

V 2x ⫽

兺

j⫽1

Lemma 1. If x⫽(x 1 ,x 2 ,...,x k ) and y⫽(y 1 ,y 2 ,...,y k ) are two k-dimensional feature vectors, Mx ⫽(m x ,m x ,...,m x ) and My ⫽(m y ,m y ,...,m y ), then 共42兲

Based on Eqs. 共39兲 to 共42兲, the second lemma can be derived as follows.

Lemma 2. If x⫽(x 1 ,x 2 ,...,x k ) and y⫽(y 1 ,y 2 ,...,y k ) are two k-dimensional feature vectors, then d 2 共 x,y兲 ⭓ 共 m x ⫺m y 兲 2 ,

共43兲

d 2 共 x,y兲 ⭓ 共 V x ⫺V y 兲 2 ,

共44兲

d 2 共 x,y兲 ⭓ 共 m x ⫺m y 兲 2 ⫹ 共 V x ⫺V y 兲 2 .

共45兲

Similar to the IPMPS algorithm28,29 for VQ, if x is a k-dimensional feature vector with k⫽n⫻n, i.e., x ⫽(x 11 ,x 12 ,...,x nn ). Using two indices, i and j, two weighted projections can be defined as Journal of Electronic Imaging

兺 wi jxi j

1

i⫽1

⭐ j⭐n,

共46兲 n

2. weighted horizontal projection: h p x 共 i 兲 ⫽ ⭐i⭐n.

兺

j⫽1

wi jxi j 1 共47兲

n

1. d 2v 共 x,y兲 ⫽

兺 关v p x共 i 兲 ⫺ v p y 共 i 兲兴 2 ,

i⫽1

共48兲

n

2. d 2h 共 x,y兲 ⫽

兺 关 h p x共 i 兲 ⫺h p y 共 i 兲兴 2 .

i⫽1

共49兲

Lemma 3. If x and y denote two k-dimensional feature vectors using two indices with k⫽n⫻n, then 1. d 2 共 x,y兲 ⭓d 2v 共 x,y兲 ,

共50兲

2. d 2 共 x,y兲 ⭓d 2h 共 x,y兲 .

共51兲

Similar to the GIP model29 for VQ, a k-dimensional feature vector can be segmented into any projection pair (p,q) with k⫽p⫻q, where p and q are two positive integers. For each of the p segments of a feature vector x, the weighted sum of q component values can be viewed as a weighted projection P x (l), for l⫽1,2,...,p. A distance measure between two feature vectors is defined as p

a lemma can be given as follows.

d 2 共 x,Mx 兲 ⭐d 2 共 x,My 兲 .

1. weighted vertical projection: v p x 共 j 兲 ⫽

If x⫽(x 11 ,x 12 ,...,x nn ) and y⫽(y 11 ,y 12 ,...,y nn ) are two k-dimensional feature vectors with k⫽n⫻n, two simple distance measures can be defined, respectively, as

3.2 Proposed Inequalities for the Weighted Square Sum Error Distance

d 2 共 x,y兲 ⫽

n

d 共2p,q 兲 共 x,y兲 ⫽

兺 关 P x共 l 兲 ⫺ P y 共 l 兲兴 2 ,

l⫽1

共52兲

where P x (l) and P y (l) are the weighted projections of feature vectors x and y, respectively, for l⫽1,2,...,p.

Lemma 4. If x and y are two k-dimensional feature vectors using two indices with k⫽ p⫻q, where p and q are two positive integers, then d 2 共 x,y兲 ⭓d 共2p,q 兲 共 x,y兲 .

共53兲

The set of inequalities 共lemmas 2 to 4兲 based on the weighted square sum error distance is used to speed up the indexing 共clustering兲 and searching phases of the proposed approach. 3.3 Proposed Fast Indexing and Searching Strategies The proposed approach consists of two phases, namely, the indexing 共clustering兲 phase and the searching phase. In the indexing phase, the feature vectors for all images are calculated and stored in the database system. And the images 共feature vectors兲 in the database system are classified into a

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prespecified number K of clusters with K cluster centers by the proposed fast modified K-means clustering techniques. In the searching phase, a small number M of closest clusters 共based on the cluster centers兲 for the query image is first determined and then the N most similar images 共ranks 1,2,...,N) for the query image will be searched among the M closest clusters. Within the indexing phase of the proposed approach, the feature vectors and some auxiliary information, such as weighted sums, variances, and weighted projections, and weighted generalized projections of feature vectors, for all images are calculated, sorted by variances, and stored in the database system. Within the proposed fast modified K-means clustering algorithm using the weighted square sum error distance, a set of derived inequalities 关Eqs. 共43兲 to 共45兲, 共50兲, 共51兲, and 共53兲兴 is used to speed up the modified clustering algorithm. On the other hand, the set of derived inequalities is also used to speed up the searching phase. The proposed searching approach is described as follows, where the input is a query image, an image database system containing K clusters, and a set of weighting coefficients, and the output is the N most similar images within the image database system of the query image. 1. Step 1. Extract the feature vector x from the query image and calculate the auxiliary information. 2. Step 2. Find the M closest clusters, C 1 , C 2 ,...,C M , among the K clusters of x. 3. Step 3. For each C i , i⫽1,2,...,M , of the M closest clusters, find the N closest feature vectors 共images兲 among C i of x. 4. Step 4. Determine the N closest feature vectors 共images兲 of x among the M N feature vectors 共images兲 obtained in step 3. The searching phase can be summarized in Fig. 3. Note that the six inequalities developed in this study can be ‘‘indi-

Fig. 3 Proposed searching process.

vidually’’ or ‘‘together’’ 共i.e., different sets of inequalities兲 used to speed up both the proposed indexing 共clustering兲 and searching phase. 4 Simulation Results Within the proposed fast indexing and searching strategies, an image database system containing 10,000 256⫻256 uncompressed images and 10,000 256⫻256 compressed images, respectively, is used to evaluate the performance of the proposed approaches. The 10,000 uncompressed images consist of 1000 texture images with 256 gray levels, 70 color texture images, 600 binary shape images, 30 color shape images, and 8300 natural color images, whereas the 10,000 compressed images are the corresponding JPEGcompressed version of the 10,000 uncompressed images.

Table 1 The processing times (in seconds) for clustering the 10,000 uncompressed images into 10, 50, and 100 clusters by the ES and the proposed approaches applying different sets of inequalities: (a) weighting coefficient set 1 and (b) weighting coefficient set 2. (a) Proposed (Different Sets of Inequalities) No. of Clusters 10 50 100

ES

Eq. (43)

Eq. (44)

Eq. (45)

Hor

Ver

HybridI

HybridII

HybridIII

156.10 144.29 70.03 72.18 150.50 174.05 70.75 173.62 80.41 725.24 675.09 224.87 235.69 715.02 836.07 225.28 839.59 278.86 8377.35 7363.20 2024.44 2138.03 7886.21 9332.66 2037.24 9236.11 2583.42 (b) Proposed (Different Sets of Inequalities)

No. of Clusters

ES

Eq. (43)

Eq. (44)

Eq. (45)

Hor

Ver

HybridI

HybridII

HybridIII

10

151.82

116.99

65.97

64.70

123.59

132.70

63.77

122.59

74.37

50 100

1937.00 1178.65 515.86 467.14 1276.80 1328.60 442.97 1051.77 580.46 7486.68 3937.28 1603.83 1375.77 4161.65 4191.36 1251.70 2887.98 1702.80

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Fast indexing and searching strategies . . . Table 2 The processing times (in seconds) for clustering the 10,000 DCT-compressed images into 10, 50, and 100 clusters by the ES and the proposed approaches applying different sets of inequalities: (a) weighting coefficient set 1 and (b) weighting coefficient set 2. (a) Proposed (Different Sets of Inequalities) No. of Clusters

ES

Eq. (43)

Eq. (44)

Eq. (45)

Hor

Ver

HybridI

HybridII

HybridIII

10 50

61.40 253.09

32.30 87.06

22.52 51.47

27.19 71.34

43.33 122.21

58.99 189.33

21.75 43.72

37.29 90.30

26.09 60.70

100

1528.96

416.71

237.44

355.48 591.38 988.27 224.75 380.09 (b) Proposed (Different Sets of Inequalities)

269.03

No. of Clusters

ES

Eq. (43)

Eq. (44)

Eq. (45)

Hor

Ver

HybridI

HybridII

HybridIII

10 50

64.37 539.26

31.42 163.85

22.30 100.41

27.19 143.63

42.02 232.23

55.09 340.76

21.43 83.10

36.85 164.28

26.20 111.55

100

906.27

224.26

136.98

212.01

330.76

507.56

107.93

205.97

145.82

The processing time 共in seconds兲 for indexing and searching of the image database system is employed as the performance measure. The proposed fast indexing 共clustering兲 approach is compared with the exhaustive search approach, denoted by ES. The proposed fast searching approach is compared with four existing searching approaches: 共1兲 ES; 共2兲 clustering all the images in the database system first, and exhaustive searching among a small number of clusters 共denoted by CES兲; 共3兲 fast searching for all the images in the database system without clustering 共denoted by FSWC兲, which is the degenerated version of the proposed fast searching approach without clustering; and 共4兲 the hybrid tree 共denoted by HT兲. The HT is a very good tree-based multidimensional indexing and searching structure, which significantly outperforms both purely DP-based and SP-based index mechanisms at all

dimensionalities for large database.7 The source code of the hybrid tree7 is available on http://www.ics.uci.edu/ ⬃kaushik/research/htree.html. In this paper, the dimensionality of the uncompressed image feature vector is 145, including 128 color features, 7 shape features, and 10 texture features, whereas the dimensionality of the compressed image feature vector is 18. The six proposed inequalities are tested individually and together. For the uncompressed images, the (p,q) in Eq. 共53兲 is set to be 共5,29兲 and 共29,5兲, denoted by Hor and Ver, respectively. For the DCT-compressed images, the (p,q) in Eq. 共53兲 is set to be 共3,6兲 and 共6,3兲, also denoted by Hor and Ver, respectively. The hybrid inequality includes three variations: 共1兲 applying Eqs. 共44兲 and 共45兲 共denoted by Hybrid-I兲; 共2兲 applying Eq. 共43兲, Hor, and Ver 共denoted by

Table 3 The average processing times (in seconds) for searching the 10 most similar images from the 10,000 uncompressed images by the proposed approaches applying different sets of inequalities: (a) weighting coefficient set 1 and (b) weighting coefficient set 2. (a) Proposed (Different Sets of Inequalities) No. of Clusters

Eq. (43)

Eq. (44)

Eq. (45)

10 50 100

0.3109 0.1351 0.1466

0.2032 0.1219 0.1373

0.2060 0.1236 0.1401

Hor

Ver

HybridI

HybridII

HybridIII

0.3312 0.1434 0.1549 (b)

0.4119 0.1769 0.1889

0.2037 0.1230 0.1395

0.4334 0.1862 0.1972

0.2796 0.1659 0.1845

Proposed (Different Sets of Inequalities) No. of Clusters

Eq. (43)

Eq. (44)

Eq. (45)

Hor

Ver

HybridI

HybridII

HybridIII

10

0.2400

0.1675

0.1395

0.2565

0.3246

0.1373

0.2867

0.2043

50 100

0.1461 0.1483

0.1269 0.1356

0.1198 0.1340

0.1565 0.1570

0.1950 0.1895

0.1197 0.1335

0.1972 0.1960

0.1714 0.1823

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Eq. (43)

Eq. (44)

Eq. (45)

Hor

Ver

HybridI

HybridII

HybridIII

10 50

0.0368 0.0280

0.0248 0.0220

0.0230 0.0214

0.0500 0.0368

0.0670 0.0418

0.0192 0.0208

0.0461 0.0407

0.0302 0.0302

100

0.0313

0.0269

0.0259

0.0390 0.0433 0.0253 (b) Proposed (Different Sets of Inequalities)

0.0450

0.0379

No. of Clusters

Eq. (43)

Eq. (44)

Eq. (45)

Hor

Ver

HybridI

HybridII

HybridIII

10 50

0.0346 0.0280

0.0236 0.0226

0.0220 0.0203

0.0434 0.0362

0.0594 0.0428

0.0182 0.0197

0.0396 0.0395

0.0264 0.0307

100

0.0313

0.0259

0.0253

0.0384

0.0433

0.0247

0.0445

0.0368

Hybrid-II兲; and 共3兲 applying Eq. 共44兲, Hor, and Ver 共denoted by Hybrid-III兲. The processing times 共in seconds兲 for indexing 共clustering兲 the 10,000 uncompressed images and the 10,000 compressed images, respectively, with 10, 50, and 100 clusters by the ES and the proposed approaches applying different sets of inequalities 共two different weighting coefficient sets兲 are listed in Tables 1 and 2. The average processing times 共in seconds兲 for searching the 10 most similar images from the 10,000 uncompressed images and the 10,000 compressed images, respectively, for 250 query images randomly selected from the same image database by the proposed approaches applying different sets of inequalities 共two different weighting coefficient sets兲 are listed in Tables 3 and 4. Here when the image database system is clustered into 10, 50, and 100 clusters 共i.e., K⫽10, 50, 100兲, the corresponding searching processes are performed in the closest 2, 5, and 10 clusters 共i.e., M ⫽2, 5, 10兲, respectively. The processing time 共in seconds兲 of an iteration for designing a codebook containing 256 codevectors for vector quantization 共equal weighting coefficients兲 by the existing approach 共ES兲 and the proposed approaches applying different sets of inequalities is listed in Table 5, where the dimension of a codevector 共image block兲 is 16, and the training set consists of 16,384 codevectors. The sets of inequalities selected for comparison in Table 5 are according to the existing sets of inequalities developed25–29 for VQ.

The average processing times 共in seconds兲 for searching the 10 most similar images from the 10,000 uncompressed images and the 10,000 DCT-compressed images, respectively, for 250 query images randomly selected from the same image database by the four existing approaches for comparison, namely, ES, CES, FSWC, and HT, and the proposed approach 共Hybrid-I兲 共two different weighting coefficient sets兲 are listed in Tables 6 and 7 and illustrated in Figs. 4 and 5. Here when the sizes of an image database are 2000, 5000, and 10,000, the image database is clustered into 10, 20, and 50 clusters 共i.e., K⫽10, 20, 50兲, respectively, and the corresponding searching processes are performed in the closest 2, 2, and 5 clusters 共i.e., M ⫽2, 2, 5兲, respectively. The two different weighting coefficient sets are 共1兲 identical weighting coefficients for all the dimensions of a feature vector 共denoted by weighting coefficient set 1兲, in this case, the weighted square sum error distance is equivalent to the square sum error distance employed in VQ; and 共2兲 1/25, 1/640, and 2/35 for each dimension of the texture, color, and shape features, respectively, for uncompressed images and a set of weighting coefficients, 兵3/28,2/28,2/ 28,2/28,1/28,1/28,1/28,1/28,1/28,3/28,2/28,2/28,2/28,1/28, 1/28,1/28,1/28,1/28其, for compressed images 共denoted by weighting coefficient set 2兲. For the weighting coefficient set 2 of the feature vectors for uncompressed images, the weighting coefficients for the texture and shape features are

Table 5 The processing times (in seconds) of each iteration for designing a codebook containing 256 ( K ⫽256) codevectors for VQ (equal weighting coefficients) by the existing approach (ES) and the proposed approaches applying different sets of inequalities. Proposed (Different Sets of Inequalities)

Time

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ES

Eq. (43)

Eqs. (43) and (44)

Eqs. (43) and (45)

Hor

Ver

Eq. (43) ⫹ Hor⫹Ver

4227.40

362.62

264.85

273.80

1614.92

1605.09

412.05

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Fast indexing and searching strategies . . . Table 6 The average processing times (in seconds) for searching the 10 most similar images from the 10,000 uncompressed images by the four existing approaches ES, CES, FSWC, HT, and the proposed approach with K ⫽50 and M ⫽5 (weighting coefficient sets 1 and 2 are denoted by Set 1 and Set 2, respectively).

ES

CES

FSWC

HT

Percentage of Improvement with Respect Proposed to HT

Set 1 0.5019 0.0635 0.2673 0.4192

0.0539

87.14%

Set 2 0.5074 0.0674 0.0474 0.4436

0.0496

88.82%

Fig. 4 Average processing times (in seconds) for searching the 10 most similar images from the 10,000 uncompressed images by the four existing approaches, namely, ES, CES, FSWC, and HT, and the proposed approach (weighting coefficient set 1).

upgraded and that for the color features are degraded. The color features consist of 128 dimensions among the 145 dimensions, which may dominate the whole feature vector if the importances of all the 145 dimensions are identical. We select that the percentages for texture and shape features are 40%, respectively, and 20% for color features. For the weighting coefficient set 2 of the feature vectors for DCT-compressed images, the first and tenth dimensions correspond to the dc information, which represent the average energy 共the most important features兲 of the image. Therefore, the weighting coefficients of these two dimensions are highlighted and the others are degraded. Some query results for several uncompressed and compressed images using two different weighting coefficient sets are shown in Figs. 6 –11. The query results for an uncompressed image retrieved from only 1, 2, and 50 共ES兲 (M ⫽1,2,5) closest clusters within the 50 (K⫽50) clusters of the 10,000 uncompressed images are, respectively, shown in Figs. 12–14. 5

Concluding Remarks

Based on the simulation results obtained in this study, several observations can be found. First, based on the simulation results shown in Tables 1 and 2, the processing times for clustering the stored images in the database system of the proposed approaches are better than that of the existing approach 共ES兲 for comparison. Second, based on the simulation results shown in Tables 1 to 4, within both the indexing 共clustering兲 and searching phases, Eq. 共44兲 and Hybrid-I 关Eqs. 共44兲 and 共45兲兴 are the two most effective sets of inequalities for the proposed approaches applying different sets of inequalities. Because in

most cases, applying Hybrid-I is better than applying Eq. 共44兲, it is recommended that the proposed approach apply Hybrid-I. Third, based on the simulation results shown in Tables 1 to 4, the performances of the proposed approaches depend on the characteristics of feature-based image data. For the uncompressed image data, the proposed inequality using variance 关Eq. 共44兲兴 is a good inequality to reject many unlikely feature vectors 共images兲 so that a great deal of computation time can be saved, whereas the other inequalities are not so good for such a type of feature-based image data. For the compressed image data, the proposed inequality using variance 关Eq. 共44兲兴 is a good inequality to reject unlikely feature vectors 共images兲, whereas the proposed Hybrid-I is a better set of inequalities to reject many unlikely feature vectors 共images兲. Fourth, based on the simulation results shown in Tables 6 and 7 and Figs. 4 and 5, the average processing times for searching the 10 most similar images from the 10,000 images of the proposed approaches are better than that of the existing approaches for comparison, namely, ES, CES, FSWC, and HT. Although the HT is suitable for low- and medium-dimensional vectors 共e.g., k⫽18) and outperforms other tree-based approaches,7 the performance of the HT is degraded, as compared to the proposed approach, when the dimensionality of the feature vector is a large number 共e.g., k⫽145). The performance characteristics of the other existing approaches, CES and FSWC, are similar to that of the HT. That is, the proposed approach is more insensitive

Table 7 The average processing times (in seconds) for searching the 10 most similar images from the 10,000 DCT-compressed images by the four existing approaches ES, CES, FSWC, HT, and the proposed approach with K ⫽50 and M ⫽5 (weighting coefficient sets 1 and 2 are denoted by Set 1 and Set 2, respectively).

ES

CES

FSWC

HT

Set 1 0.0932 0.0106 0.0050 0.0060 Set 2 0.0998 0.0114 0.0062 0.0124

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Percentage of Improvement with Respect Proposed to HT 0.0044 0.0048

26.67% 61.29%

Fig. 5 Average processing times (in seconds) for searching the 10 most similar images from the 10,000 DCT-compressed images by the four existing approaches, namely, ES, CES, FSWC, and HT, and the proposed approach (weighting coefficient set 1).

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Fig. 6 Query results for an uncompressed image using weighting coefficient set 1: (a) the query image and the first retrieved image and (b) to (j) the retrieved images from ranks 2 to 10.

Fig. 7 Query results for an uncompressed image using weighting coefficient set 2: (a) the query image and the first retrieved image and (b) to (j) the retrieved images from ranks 2 to 10.

Fig. 8 Query results for an uncompressed image using weighting coefficient set 1: (a) the query image and the first retrieved image and (b) to (j) the retrieved images from ranks 2 to 10.

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Fig. 9 Query results for an uncompressed image using weighting coefficient set 1: (a) the query image and the first retrieved image and (b) to (j) the retrieved images from ranks 2 to 10.

to feature dimension variation than the existing approaches for comparison. The reason is that within the proposed approaches, a high-dimensional feature vector is projected into the low-dimensional ‘‘working’’ vector space, including the weighted sum, the weighted variance, the weighted vertical projection, and the weighted horizontal projection, etc., so that the dimensionality of the ‘‘working’’ vector space is greatly reduced. Because the processing time or the computational complexity of the distance calculations between two feature vectors of the ‘‘working’’ vector space will be greatly reduced, the proposed approaches will be more efficient in high-dimensional feature vector space than the existing approaches for comparison. Fifth, based on the simulation results shown in Tables 1 to 5, the weighting coefficients of feature vectors will influence the performances of the proposed approaches. Different sets of inequalities are usually suitable for the same feature vectors using different weighting coefficients. For example, if all the weighting coefficients are identical, the weighted square sum error distance employed in this paper will be equivalently reduced to the square sum error distance employed in VQ. Based on the simulation results shown in Table 5, the processing time for designing a codebook for vector quantization by using the proposed approaches using equal weighting coefficients is only about 6% of the processing time required by the ES approach. In VQ, a feature vector 共codevector兲 is formed by the pixels within an image block, which are highly concentrated about the feature 共pixel兲 mean. That is, two image blocks having

similar pixel means may be very similar. Therefore, the inequalities developed for VQ are very effective for clustering codevectors. However, because the dynamic ranges of different feature components are greatly different in this paper, if the weighting coefficients are not properly adjusted, the proposed inequalities in this paper will be less effective than that for VQ. For example, the sum of the 128 color features is equal to the size of an image. If all the weighting coefficients are identical, the weighted sums will be the same for all equal-sized images. Additionally, if the dimensionality of the color features is relatively high and the weighted sums of all feature vectors are very similar, the proposed inequalities using the weighted sums 关Eqs. 共43兲, 共50兲, 共51兲, and 共53兲兴 will not be effective. Therefore, all the stored images in an image database system are sorted according to their variances, instead of their weighted sums. Sixth, based on the simulation results shown in Tables 1 to 4, if the number K of clusters is increased, some sets of inequalities become more effective, whereas some sets of inequalities become less effective. Seventh, based on the simulation results shown in Figs. 6 to 11, the retrieved images 共ranks 1 to 10兲 may be different for different weighting coefficient sets. That is so because the values of the weighted square sum error distance are different for different weighting coefficient sets. Eighth, Jain and Vailaya addressed an image retrieval method for large image databases.6 They used CLUSTER, a squared-error clustering algorithm, to reduce the search space. The query image is compared only with the cluster centers to determine its cluster membership. Once the cluster membership of the query image is established, it must be matched only with images in that cluster 共the closest cluster兲. Based on the simulation results shown in Figs. 12 to 14, the query results retrieved from only one closest cluster may not be the same as that of the ES. That is, the retrieved results may be incorrect if only one closest cluster is considered. In this study, for example, the query image will be compared with the five closest clusters within the 50 clusters, and the query results are the same as that of the exhaustive search approach.

Fig. 10 Query results for a DCT-compressed image using weighting coefficient set 1: (a) the query image and the first retrieved image and (b) to (j) the retrieved images from ranks 2 to 10.

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Fig. 11 Query results for a DCT-compressed image using weighting coefficient set 2: (a) the query image and the first retrieved image and (b) to (j) the retrieved images from ranks 2 to 10.

Fig. 12 Query results for an uncompressed image retrieved from only one closest cluster within the 50 clusters of the 10,000 uncompressed images: (a) the query image and the first retrieved image and (b) to (j) the retrieved images from ranks 2 to 10.

Fig. 13 Query results for an uncompressed image retrieved from two closest clusters within the 50 clusters of the 10,000 uncompressed images: (a) the query image and the first retrieved image and (b) to (j) the retrieved images from ranks 2 to 10.

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Fig. 14 Query results for an uncompressed image retrieved by the exhaustive search from the 10,000 uncompressed images: (a) the query image and the first retrieved image and (b) to (j) the retrieved images from ranks 2 to 10.

Finally, referring to Eq. 共8兲, different query 共searching兲 approaches may return slightly different results with different processing times. A ‘‘good’’ query 共searching兲 approach will return the same result as that returned by the exhaustive search approach. Based on the ‘‘goodness’’ 共precision兲 criterion, the query 共searching兲 approach proposed by Jain and Vailaya6 is one of the fast searching approaches, whereas their query approach is not a ‘‘good’’ query approach 共Figs. 12 to 14兲. Based on the performance measure 共the processing time兲 and the ‘‘goodness’’ 共precision兲 criterion, the proposed query 共searching兲 approaches are ‘‘fast’’ and ‘‘good’’ query 共searching兲 approaches. The four existing approaches for comparison are all ‘‘good’’ query approaches based on the ‘‘goodness’’ 共precision兲 criterion, but the proposed approaches outperform 共are faster than兲 the four existing approaches for comparison, based on the performance measure 共the processing time兲. In this paper, fast indexing and searching strategies for image database systems were proposed. A set of proposed inequalities based on the weighted square sum error distance is used to speed up both the image indexing 共clustering兲 and searching processes for feature-based image database systems. Based on the simulation results obtained in this paper, in terms of performance measure, namely, the processing time for indexing and searching in feature-based image database systems, the proposed approaches are superior to several existing approaches for comparison. In particular, based on the test image databases in this study, the percentage of improvement of the proposed approach with respect to the HT approach7 can achieve about 87.14 and 88.82 and 26.67 and 61.29% for 145-D uncompressed feature vectors and 18-D compressed feature vectors using two weighting coefficients sets, respectively. Due to the fast that the performance of the proposed approach depends on the employed image features and the selected weighting coefficients, different weighting coefficients will lead to different clustering and searching results. Because the selection of the weighting coefficients is usually application-dependent, only some sets of coefficients were tested here. If the image features extracted are good Journal of Electronic Imaging

enough and the weighting coefficients are adjusted properly, the proposed approaches will find the expected results efficiently. In addition, the proposed approach is not only effective for indexing and searching in feature-based image database systems, but is also suitable for any other multidimensional data indexing and searching based on the weighted square sum error distance or the square sum error distance, such as closest code word search and codebook design in VQ.

Acknowledgments This work was supported in part by National Science Council, Republic of China under Grants NSC 89-2213-E-194026 and NSC 90-2213-E-194-039.

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Kang and Leou 14. B. G. Kim, J. H. Lee, S. H. Noh, and H. C. Lim, ‘‘A filtering method for k-nearest neighbor query processing in multimedia data retrieval applications,’’ in Proc. IEEE Region 10 Conf. on TENCON’99, pp. 337–340 共1999兲. 15. J. K. Wu, ‘‘Content-based indexing of multimedia databases,’’ IEEE Trans. Knowl. Data Eng. 9共6兲, 978 –989 共1997兲. 16. Y. Gong, C. H. Chuan, and G. Xiaoyi, ‘‘Image indexing and retrieval based on color histograms,’’ Multimed. Tools Appl. 2, 133–156 共1996兲. 17. M. Vazirgiannis, Y. Theodoridis, and T. Sellis, ‘‘Spatio-temporal composition and indexing for large multimedia applications,’’ Multimedia Syst. 6, 284 –298 共1998兲. 18. A. K. Jain and A. Vailaya, ‘‘Shape-based retrieval: a case study with trademark image databases,’’ Pattern Recogn. 31共9兲, 1369–1390 共1998兲. 19. M. J. Swain and D. H. Ballard, ‘‘Color indexing,’’ Int. J. Comput. Vis. 7共1兲, 11–32 共1991兲. 20. B. S. Manjunath and W. Y. Ma, ‘‘Texture features for browsing and retrieval of image data,’’ IEEE Trans. Pattern Anal. Mach. Intell. 18共8兲, 837– 842 共1996兲. 21. G. L. Gimel’Farb and A. K. Jain, ‘‘On retrieving textured images from an image database,’’ Pattern Recogn. 29共9兲, 1461–1483 共1996兲. 22. B. Gunsel and A. M. Tekalp, ‘‘Shape similarity matching for queryby-example,’’ Pattern Recogn. 31共7兲, 931–944 共1998兲. 23. M. Shneier and M. Abdel-Mottaleb, ‘‘Exploiting the JPEG compression scheme for image retrieval,’’ IEEE Trans. Pattern Anal. Mach. Intell. 18共8兲, 849– 853 共1996兲. 24. H. J. Bae and S. H. Jung, ‘‘Image retrieval using texture based on DCT,’’ in Proc. 1st IEEE Int. Conf. on Information Communications and Signal Processing, Vol. 2, pp. 1065–1068 共1997兲. 25. C. H. Lee and L. H. Chen, ‘‘High-speed closest codeword search algorithms for vector quantization,’’ Signal Process. 43, 323–331 共1995兲. 26. C. H. Lee and L. H. Chen, ‘‘Fast closest codeword search algorithm for vector quantisation,’’ IEE Proc. Vision Image Signal Process. 141共3兲, 143–148 共1994兲. 27. S. J. Baek, B. K. Jeon, and K. M. Sung, ‘‘A fast encoding algorithm for vector quantization,’’ IEEE Signal Process. Lett. 4共12兲, 325–327 共1997兲. 28. Y. C. Lin and S. C. Tai, ‘‘A fast Linde-Buzo-Gray algorithm in image vector quantization,’’ IEEE Trans. Circuits Syst., II: Analog Digital Signal Process. 45共3兲, 432– 435 共1998兲. 29. C. C. Chang and Y. C. Hu, ‘‘A fast LBG codebook training algorithm for vector quantization,’’ IEEE Trans. Consum. Electron. 44共4兲, 1201–1208 共1998兲. 30. J. S. Pan and K. C. Huang, ‘‘A new vector quantization image coding algorithm based on the extension of the bound for Minkowski metric,’’ Pattern Recogn. 31共11兲, 1757–1760 共1998兲.

Journal of Electronic Imaging

31. G. Pass, R. Zabih, and J. Miller, ‘‘Comparing images using color coherence vectors,’’ in Proc. 4th ACM Multimedia, pp. 65–78 共1996兲. 32. R. M. Haralick, K. Shanmugam, and I. Dinstein, ‘‘Textural features for image classification,’’ IEEE Trans. Syst. Man Cybern. 3共6兲, 610– 621 共1973兲. 33. M. Nadler and E. P. Smith, Pattern Recognition Engineering, Wiley, New York 共1993兲. 34. M. K. Hu, ‘‘Visual pattern recognition by moment invariants,’’ IRE Trans. Inf. Theory 8, 179–187 共1962兲. 35. B. M. Mehtre, M. S. Kankanhalli, and W. F. Lee, ‘‘Shape measures for content based image retrieval: a comparison,’’ Inf. Process. Manage. 33共3兲, 319–337 共1997兲. Li-Wei Kang received his BS and MS degrees in computer science and information engineering in 1997 and 1999, respectively, both from National Chung Cheng University, Chiayi, Taiwan, where since September 1999, he has been working toward his PhD degree in computer science and information engineering. His current research interests include image/video processing, image/video communication, and pattern recognition. Jin-Jang Leou received his BS degree in communication engineering in 1979, his MS degree in communication engineering in 1981, and his PhD degree in electronics in 1989, all from National Chiao Tung University, Hsinchu, Taiwan. From 1981 to 1983, he was a communication officer with the Chinese Army. From 1983 to 1984, he was a lecturer with the National Chiao Tung University. Since August 1989, he has been on the faculty of the Department of Computer Science and Information Engineering at National Chung Cheng University, Chiayi, Taiwan. His current research interests include image/video processing, image/video communication, pattern recognition, and computer vision.

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