SPCD - SPATIAL COLOR DISTRIBUTION DESCRIPTOR

A Fuzzy Rule based Compact Composite Descriptor Appropriate for Hand Drawn

Color Sketches Retrieval

Savvas A. Chatzichristoﬁs

, Yiannis S. Boutalis

a,b

and Mathias Lux

Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi 67100, Greece

Department of Electrical, Electronic and Communication Engineering, Chair of Automatic Control

Friedrich-Alexander University of Erlangen-Nuremberg, 91058 Erlangen, Germany

Institute of Information Technology, Klagenfurt University, Austria

Keywords:

Image retrieval, Compact composite descriptors, Spatial distribution, Hand-drawn sketches.

Abstract:

In this paper, a new low level feature suitable for Hand Drawn Color Sketches retrieval is presented. The

proposed feature structure combines color and spatial color distribution information. The combination of

these two features in one vector classiﬁes the proposed descriptor to the family of Composite Descriptors. In

order to extract the color information, a fuzzy system is being used, which is mapping the number of colors

that are included in the image into a custom palette of 8 colors. The way by which the vector of the proposed

descriptor is being formed, describes the color spatial information contained in images. To be applicable in

the design of large image databases, the proposed descriptor is compact, requiring only 48 bytes per image.

Experiments demonstrate the effectiveness of the proposed technique.

1 INTRODUCTION

As content based image retrieval (CBIR) is deﬁned

any technology, that in principle helps to organize

digital image archives by their visual content. By this

deﬁnition, anything ranging from an image similarity

function to a robust image annotation engine falls un-

der the purview of CBIR (Datta et al., 2008).

In CBIR systems, the visual content of the images is

mapped into a new space named the feature space.

The features that are chosen have to be discrimina-

tive and sufﬁcient for the description of the objects.

The key to attaining a successful retrieval system is

to choose the right features that represent the images

as “strong” as possible (Chatzichristoﬁs and Boutalis,

2007). A feature is a set of characteristics of the im-

age, such as color, texture, and shape. In addition,

a feature can be enriched with information about the

spatial distribution of the characteristic, that it de-

scribes.

Regarding CBIR schemes which rely on single fea-

tures like color and/or color spatial information sev-

eral schemes have been proposed. The algorithm pro-

posed in (Jacobs et al., 1995) makes use of multires-

olution wavelet decompositions of the images. In

(Pass et al., 1997), each pixel as coherent or nonco-

herent based on whether the pixel and its neighbors

have similar color. In (Rao et al., 1999)(Cinque et al.,

2001)(Lim and Lu, 2003) are presented the Spatial

Color Histograms in which, in addition to the statis-

tics in the dimensions of a color space, the distribu-

tion state of each single color in the spatial dimen-

sion is also taken into account. In (Sun et al., 2006) a

color distribution entropy (CDE) method is proposed,

which takes account of the correlation of the color

spatial distribution in an image. In (Huang, 1997) a

color correlograms method is proposed, which col-

lects statistics of the co-occurrence of two colors. A

simpliﬁcation of this feature is the autocorrelogram,

which only captures the spatial correlation between

identical colors. The MPEG-7 standard (Manjunath

et al., 2001) includes the Color Layout Descriptor

(Kasutani and Yamada, 2001), which represents the

spatial distribution of color of visual signals in a very

compact form.

The schemes which include more than one features

in a compact vector can be regarded that they be-

long to the family of Compact Composite Descriptors

(CCD). In (Chatzichristoﬁs and Boutalis, 2008a) and

(Chatzichristoﬁs and Boutalis, 2008b) 2 descriptors

are presented, that contain color and texture informa-

tion at the same time in a very compact representation.

A. Chatzichristoﬁs S., S. Boutalis Y. and Lux M. (2010).

SPCD - SPATIAL COLOR DISTRIBUTION DESCRIPTOR - A Fuzzy Rule based Compact Composite Descriptor Appropriate for Hand Drawn Color

Sketches Retrieval.

In Proceedings of the 2nd International Conference on Agents and Artiﬁcial Intelligence - Artiﬁcial Intelligence, pages 58-63

DOI: 10.5220/0002725800580063

 SciTePress

In (Chatzichristoﬁs and Boutalis, 2009) a descriptor

is proposed, that includes brightness and texture in-

formation in a vector with size of 48 bytes.

In this paper a new CCD is proposed, which combines

color and spatial color distribution information. The

descriptors of this type can be used for image retrieval

by using hand-drawn sketch queries, since this de-

scriptor captures the layout information of color fea-

ture. In addition, the descriptors of this structure are

considered to be suitable for colored graphics, since

such images contain relatively small number of color

and less texture regions than the natural color images.

The rest of the paper is organized as follows: Sec-

tion 2 describes how to extract the color information,

which is embedded in the proposed descriptor, while

Section 3 describes in details the descriptor’s forma-

tion. Section 4 contains the experimental results of

an image retrieval system that uses either the pro-

posed desciptor or the MPEG-7 CLD descriptor on

two benchmarking databases. Finally, the conclusions

are given in Section 5.

2 COLOR INFORMATION

An easy way to extract color features from an image

is by linking the color space channels. Linking is de-

ﬁned as the combination of more than one histogram

to a single one. An example of color linking methods

is the Scalable Color Descriptor (Manjunath et al.,

2001), which is included in the MPEG-7 standard.

In the literature several methods are mentioned, that

perform the linking process by using Fuzzy systems.

In (Konstantinidis et al., 2005) the extraction of a

fuzzy-linking histogram is presented based on the

color space CIE-L*a*b*. Their 3-input fuzzy system

uses the L*, a* and b* values from each pixel in

an image to classify that pixel into one of 10 preset

colors, transforming the image into a palette of the

10 preset colors. In this method, the defuzzyﬁcation

algorithm classiﬁes the input pixel into one and

only one output bin (color) of the system (crisp

classiﬁcation). Additionally, the required conversion

of an image from the RGB color space to CIEXYZ and

ﬁnally to CIE-L*a*b* color space makes the method

noticeably time-consuming. In (Chatzichristoﬁs

and Boutalis, 2007), the technique is improved by

replacing the color space and the defuzzyﬁcation

algorithm. In (Chatzichristoﬁs and Boutalis, 2008a),

a second fuzzy system is added, in order to replace

the 10 colors palette with a new 24 color palette.

In this paper a new fuzzy linking system is proposed,

that maps the colors of the image in a custom 8 colors

palette. The system uses the three channels of HSV

as inputs, and forms an 8-bin histogram as output.

Each bin represents a present color as follows: (0)

Black, (1) Red, (2) Orange/Yellow, (3) Green, (4)

Cyan, (5) Blue, (6) Magenta and (7) White.

The system’s operating principle is described as

follows: Each pixel of the image is transformed to

the HSV color space. The H, S and V values interacts

with the fuzzy system. Depending on the activation

value of the membership functions of the 3 system

inputs, the pixel is classiﬁed by a participation value

in one or more of the preset colors, that the system

uses.

Figure 1: Membership Functions of (a) Hue, (b) Saturation

and (c) Value.

For the defuzziﬁcation process, a set of 28 TSK-like

(Zimmermann, 1987) rules is used, with fuzzy an-

tecedents and crisp consequents.

The Membership Value Limits and the Fuzzy Rules

are given in the Appendix.

3 DESCRIPTOR FORMATION

In order to incorporate the spatial distribution infor-

mation of the color to the proposed descriptor, from

each image, 8 Tiles with size of 4x4 pixels are cre-

ated. Each Tile corresponds to one of the 8 preset col-

ors described in Section 2. The Tiles are described

SPCD - SPATIAL COLOR DISTRIBUTION DESCRIPTOR - A Fuzzy Rule based Compact Composite Descriptor

Appropriate for Hand Drawn Color Sketches Retrieval

as T (c),c ∈ [0, 7], while the Tiles’ pixel values are

described as T (c)

M,N

, M, N ∈ [0, 3]. The Tiles’ cre-

ation process is described as follows: A given image

J is ﬁrst sub-divided into 16 sub-images according

to ﬁgure 2(a). Each sub image is denoted as

M,N

Each pixel that belongs to

M,N

is denoted as P(i)

M,N

i ∈ [0, I], I Number of pixels in

M,N

. Each

M,N

con-

tributes to the formation of the T (c)

M,N

for each c.

Each P(i)

M,N

is transformed to the HSV color space

and the values of H, S and V constitute inputs to

the Fuzzy-Linking system, which gives a participa-

tion value in space [0, 1] for each one of the 8 preset

colors. The participation value of each color is de-

ﬁned as MF(c), c ∈ [0, 7].

∑

c=0

MF(c) = 1 (1)

Each T (c)

M,N

increases by MF(c). The process is

repeated for all P(i)

M,N

until i = I. Subsequently, the

value of each T (c)

M,N

for each c is replaced according

to the following formula:

T (c)

M,N

T (c)

M,N

(2)

In this way, a normalization on the number I of the

pixels, that participate in any

M,N

is achieved. On the

completion of the process, the value of each T (c)

M,N

is quantized using a linear quantization table to an in-

teger value within the interval [0, 7].

Figure 2: (a) The image is divided into 16 sub images, (b)

Result of the 8 Tiles production from the image (a).

The described process is repeated for each (M, N).

On completion of the process 8 images of 3 bits

are produced, where each one of them describes the

distribution (quantitative and spatial) of each color.

Figure 2(b) shows the resulting Tiles of Figure 2(a).

Scanning row-by-row each tile T (c), a 16-

dimensional vector can be formed, with each

vector element requiring 3-bits for its representation.

In this vector the element’s index determines position

(M, N) in the tile T (c)

M,N

. The element’s value

determines the color quantity at the position (M, N)

quantized in space [0, 7]. By repeating the process for

all the Tiles, 8 such vectors can be produced, which

if combined, by placing them successively, a 48 bytes

descriptor is formed.

16(Elements) × 8(Tiles)×

(bytes) = 48bytes

This size compared with the size of other compact

composite descriptors is considered satisfactory. The

problem occurs in the length of the ﬁnal vector which

is set in 128 elements. During data retrieval from

databases, the length of the retrieved information is

of great signiﬁcance. In order to compress the length

of the proposed descriptor the following information

lossless procedure is applied. The 8 Tiles of 3 bits are

combined in order to form a new 24-bit Tile (“color”

Tile) of the same size. This Tile is deﬁned as φ,

while the values of the pixels are described as φ

M,N

M, N ∈ [0, 3]. In order to deﬁne each φ

M,N

, 3 val-

ues are needed. R(φ

M,N

) describes the amount of red,

G(φ

M,N

) describes the amount of green and B(φ

M,N

)

describes the amount of blue.

The value of each T (c)

M,N

is expressed in binary

form. Given that the value of each T (c)

M,N

is de-

scribed by 3 bits, 3 binary digits are needed for its

description.

The binary form of T (c)

M,N

value is deﬁned as a 3

places matrix, T (c)

M,N

[B], B ∈ [0, 2].

M,N

pixel is shaped using the following rules:

R(φ

M,N

) =

∑

c=0

× T (c)

M,N

[0] (3)

G(φ

M,N

) =

∑

c=0

× T (c)

M,N

[1] (4)

B(φ

M,N

) =

∑

c=0

× T (c)

M,N

[2] (5)

The process is repeated for each (M, N).

In order to make clear the production process of φ,

the following example is given. The T(c)

M,N

val-

ues of the 8 Tiles for a given image J are presented

in Table 1. Next to the 3-bit representation of each

value, the binary form of the value appears. The ﬁrst

bit represents T (c)

M,N

[0], the second one represents

T (c)

M,N

[1] and the third bit represents T (c)

M,N

[2].

The value of each φ

M,N

channel depends on the com-

bination, using Eq. 3, Eq. 4 or Eq. 5, of all the

T (c)

M,N

[B], c ∈ [0, 7]. For example, The Blue chan-

nel of φ

M,N

depends on the combination of all the

T (c)

M,N

[2] (last column of the table). At the given ex-

ample, the B(φ

M,N

) value is equal to 0× 2

+1 × 2

0 × 2

+ 1 × 2

+ 0 × 2

+ 1 × 2

153.

ICAART 2010 - 2nd International Conference on Agents and Artificial Intelligence

Table 1: Combining the 8 T (c)

M,N

values to create the φ

M,N

value.

c 3-Bit Value T (c)

M,N

[0] T (c)

M,N

[1] T (c)

M,N

[2]

0 1 0 0 1

1 0 0 0 0

2 0 0 0 0

3 3 0 1 1

4 1 0 0 1

5 0 0 0 0

6 0 0 0 0

7 1 0 0 1

R(φ

M,N

) G(φ

M,N

) B(φ

M,N

)

0 8 153

After applying the procedure to each (M, N) the φ

combined “color” tile is formed.

Scanning row-by-row the φ, a 48-dimensional vector

is formed.

16(Elements) × 3(Channels) = 48Elements

where the values of each element are quantized in the

interval [0, 255] requiring 1 byte each. Therefore, the

storage requirements of the descriptor remained the

same (48 bytes), but its length was losslessly com-

pressed by 62.5%. This feature allows the faster re-

trieval from the databases, which it is stored.

4 EXPERIMENTAL RESULTS

The extraction process of the proposed descriptor is

applied to all images of the database and an XML ﬁle

with the entries is created. Given that, the proposed

descriptor is an MPEG-7 like descriptor, the schema

of the SpCD as an MPEG-7 extension is described as

follows.

<?xml version ="1.0" encoding="UTF-8"?>

<schema xmlns="http://www.w3.org/2001/XMLSchema"

xmlns:mpeg7="urn:mpeg:mpeg7:schema :2004"

xmlns:SpCDNS="SpCDNS" targetNamespace="SpCDNS">

<import namespace="urn:mpeg:mpeg7:schema:2004"

schemaLocation="Mpeg7-2004.xsd"/>

<listitemType="mpeg7:unsigned3"/>

</simpleType>

</restriction>

</simpleType>

</element>

</sequence>

</extension>

</complexContent>

</complexType>

</schema>

During the retrieval process, the user enters a query

image in the form of Hand Drawn Color Sketch.

From this image the 8 Tiles are exported and the

128-dimensional vector is formed. Next, each de-

scriptor from the XML ﬁle is transformed from

the 48-dimensional vector to the corresponding 128-

dimensional vector, following the exact opposite pro-

cedure to that described in Section 3.

For the similarity matching we propose, in accor-

dance to the other Compact Composite Descriptors,

the Tanimoto coefﬁcient. The distance T of the vec-

tors X

and X

is deﬁned as T

i j

and is calculated as

follows:

i j

= t(X

, X

) =

× X

+ X

× X

− X

× X

(6)

Where X

is the transpose vector of X. In the ab-

solute congruence of the vectors the Tanimoto coefﬁ-

cient takes the value 1, while in the maximum devia-

tion the coefﬁcient tends to zero.

Figure 3: Image Retrieval Procedure.

After repeating the process in all the images contained

in the XML ﬁle, the images appear to the user sorted

according to the distance with the query image. The

process is described in Figure 3.

In order to evaluate the performance of the proposed

descriptor, experiments were carried out on 2 bench-

marking image databases. The ﬁrst database contains

1030 images, which they depict ﬂags from around

the world. The database consists of state ﬂags, ﬂags

of unrecognized states, ﬂags of formerly independent

states, municipality ﬂags, dependent territory ﬂags

and ﬂags of ﬁrst-level country subdivisions. All the

images are taken from Wikipedia. We used 20 Hand

Drawn Color Sketches as query images and as ground

truth (list of similar images of each query) we consid-

ered only the ﬂag that was attempted to be drawn with

the Hand Drawn Color Sketch.

The “Paintings” database was also used. This

database is incorporated in (Zagoris et al., 2009) and

includes 1771 images of paintings by internationally

well known artists. Also in this case, as query im-

ages were used 20 Hand Drawn Color Sketches and as

SPCD - SPATIAL COLOR DISTRIBUTION DESCRIPTOR - A Fuzzy Rule based Compact Composite Descriptor

Appropriate for Hand Drawn Color Sketches Retrieval

ground truth was considered only the painting, which

was attempted to be drawn with the Hand Drawn

Color Sketch. Figure 4 shows a query sample from

each database as well as the retrieval results.

The objective Averaged Normalized Modiﬁed Re-

trieval Rank (ANMRR)(Manjunath et al., 2001) is

employed to evaluate the performance of the proposed

descriptor.

The average rank AVR(q) for a given query q is:

AVR(q) =

NG(q

∑

k=1)

Rank(k)

NG(q)

(7)

Where

• NG(q) is the number of ground truth images for

the query q. In our case NG(q) = 1

• K is the top ranked retrievals examined where:

– K = min(X × NG(q), 2GMT ), GMT =

max(NG(q)), in our case K = 2

– NG(q) > 50 then X = 2 else X = 4

• Rank(k) is the retrieval rank of the ground truth

image. Considering a query assume that as a re-

sult of the retrieval, the k

ground truth image for

this query q is found at a position R. If this image

is in the ﬁrst K retrievals then Rank(k) = R else

Rank(k) = K + 1

The modiﬁed retrieval rank is:

MRR(q) = AV R(q) − 0.5 − 0.5 × N(q) (8)

The normalized modiﬁed retrieval rank is com-

puted as follows:

NMRR(q) =

MRR(q)

K + 0.5 − 0.5 × N(q)

(9)

The average of NMRR over all queries deﬁned as:

ANMRR(q) =

∑

q=1

NMRR(q) (10)

Table 2 illustrates the ANMRR results in both

databases. The results are compared with the cor-

responding results of the Color Layout Descriptor

(CLD). The implementation of the CLD matches the

implementation in (Lux and Chatzichristoﬁs, 2008).

The reason for this comparison is that only the CLD,

from the descriptors that were referred in the intro-

duction, is compact.

Considering the results, it is evident that the pro-

posed descriptor is able to achieve satisfactory re-

trieval results by using Hand Drawn Color Sketches

as queries. The proposed descriptor is imple-

mented in the image retrieval system img(Rummager)

Figure 4: Hand Drawn Color Sketch queries (i) for the Flags

database and (ii) for the Paintings database. In each one of

the queries (a) shows the ﬁrst 3 results of the CLD, while

(b) shows the ﬁrst 3 results of the proposed descriptor.

Table 2: ANMRR results.

Database SpCD ANMRR CLD ANMRR

Flags 0.225 0.425

Paintings 0.275 0.45

(Chatzichristoﬁs et al., 2009) and is available online

along with the image databases and the queries.

5 CONCLUSIONS

In this paper, a new compact composite descriptor

is presented which combines color and spatial color

distribution information.Characteristics of the pro-

posed descriptor are its small storage requirements

(48 bytes/ per image) and its small length (48 el-

ements). Experiments that were performed at 2

databases with artiﬁcial images showed that the pro-

posed descriptor can achieve better retrieval results

than the MPEG-7 CLD.

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APPENDIX

Table 3: Fuzzy Interface Rules.

If HUE is And SATURATION is And VALUE is Then OUT is

RED 1 GRAY WHITE WHITE

RED 1 GRAY BLACK BLACK

RED 1 COLOR WHITE RED

RED 1 COLOR BLACK RED

YELLOW GRAY WHITE WHITE

YELLOW GRAY BLACK BLACK

YELLOW COLOR WHITE YELLOW

YELLOW COLOR BLACK YELLOW

GREEN GRAY WHITE WHITE

GREEN GRAY BLACK BLACK

GREEN COLOR WHITE GREEN

GREEN COLOR BLACK GREEN

CYAN GRAY WHITE WHITE

CYAN GRAY BLACK BLACK

CYAN COLOR WHITE CYAN

CYAN COLOR BLACK CYAN

BLUE GRAY WHITE WHITE

BLUE GRAY BLACK BLACK

BLUE COLOR WHITE BLUE

BLUE COLOR BLACK BLUE

MAGENTA GRAY WHITE WHITE

MAGENTA GRAY BLACK BLACK

MAGENTA COLOR WHITE MAGENTA

MAGENTA COLOR BLACK MAGENTA

RED 2 GRAY WHITE WHITE

RED 2 GRAY BLACK BLACK

RED 2 COLOR WHITE RED

RED 2 COLOR BLACK RED

Table 4: Fuzzy 8-bin Color System.

Membership Function Activation Value

0 1 1 0

HUE

RED 1 0 0 5 55

YELLOW 5 55 60 115

GREEN 60 115 120 175

CYAN 120 175 180 235

BLUE 180 235 240 295

MAGENTA 240 295 300 355

RED 2 300 355 360 360

SATURATION

GRAY 0 0 25 55

COLOR 25 55 255 255

VALUE

WHITE 0 0 100 156

BLACK 100 156 255 255

SPCD - SPATIAL COLOR DISTRIBUTION DESCRIPTOR - A Fuzzy Rule based Compact Composite Descriptor

Appropriate for Hand Drawn Color Sketches Retrieval