Content-based Trademark Retrieval



Noise Insensitive Trademark Retrieval Based on Zernike Moment

MUHAMMAD SUZURI HITAM, WAN NURAL JAWAHIR HJ WAN YUSSOF

AND MUSTAFA MAT DERIS

Department of Computer Science,

University College of Science and Technology Malaysia,

21030 Kuala Terengganu, Terengganu Darul Iman,

MALAYSIA.

Abstract: - Registered trademarks are increasing day to day. The task of copyright protection is increasingly difficult. In order to retrieve a trademark from a large trademark database, we present a method for such a system based on the image content, using a shape feature. Zernike moments can be used as an effective descriptor of global shape of a trademark in a large size of trademark database. To retrieve similarly shaped trademark, we use a weight Euclidean distance measure that commonly use in moment based vector matching. Experimental results tested on database containing 1000 trademark images corrupted with noises showed that the proposed method is very efficient to retrieve similar trademarks.

Key-Words: - Zernike moments, content-based image retrieval, trademard and weight euclidean distance.

1. Introduction

Digital images play an important role in fields of medicine, journalism, advertising, design, education and entertainment [5,7,8,10,11]. Thus, over the last few years, interests in the potential of digital images has been upsurge and with the increasing demands of managing digital images have led to the rise of techniques for efficient Content-based Image Retrieval (CBIR). In general, CBIR is a technique for automatic retrieving of images from image database based on derived set of features such as color, texture and shape [8]. CBIR systems are beginning to find a foothold in the marketplace; prime application areas include crime prevention (face recognition and fingerprint), intellectual property (trademark registration), journalism and advertising. Image retrieval based on image content is a key area for building and managing large multimedia databases. By principle, CBIR retrieves stored images from image database by comparing some predetermined features automatically extracted from the query image and the index image in image database.

It has been long recognized that trademark registration is prime application area for CBIR [12]. To ensure that there is no risk of confusion in identifying companies by their trademarks, products and services, a new candidate mark will be compared with existing marks. Trademarks are considered valueable intelectual properties-key component of goodwill of business [7,12]. Registered trademark is protected trough legal proceedings from misuse or imitation in the granted territories [7]. Copyright owners are able to seek out and take a legal action for an unauthorised use of trademarks.

Since shape is a fundamental property of trademark object, an effective shape descriptor must be used in order to retrieve a similar look trademark from a large trademark database. It should have enough discriminating power and immunity to noise. In most cases, the use of regular moments results in redundant information being retrieved. In addition, the use of high-order moments results in high sensitivity to noise. Therefore, a method which is insensitive to noise for trandemark retrieval is being searching for.

In this paper, we proposed an approach for trademark content-based trademark retrieval, which could is possible to retrieve similar look and its original queried image under various degree of noisy intensities. Experimental results showed that the use of Zerrnike moments is an effective method for global shape descriptor of a trademark images. To verify the efficiency of proposed method to possibly retrieve the similarly trademarks, several trademarks were submitted as query trademarks to a trademark database. We selected 50 trademarks randomly from database that consists of 1000 trademarks. Each of them was added with various type of noise such as Salt & Pepper, Gaussian, Poisson and speckle with various factors.

This paper is organized as follows. In section 2 is an overview Zernike moments as a feature set. In section 3, describes the problem solutions. Experimental results are discussed in Section 4, and Section 5 summarizes the paper.

2. Zernike Moment

Moment functions are used to capture the global feature of applications in image analysis [11,12]. A set of moments computed from a digital image, generally represents global characteristics of the image shape, and provides a lot of information about different types of geometrical features of the image. The Zernike functions, were first proposed in 1934 by Frits Zernike, the mathematician and physician [13]. His moment formulation appears to be one of the most popular, outperforming the alternatives in terms of noise resilience, information redundancy and reconstruction capability. Zernike moments are complex orthogonal moments whose magnitude has rotational invariant property [1,2,3,5,11,12]. They form a complete orthogonal basis set defined on the unit disc [pic].

1. Zernike Polynomial

Zernike polynomial is a set of orthogonal functions with simple rotation properties which forms a complete orthogonal set over the interior of the unit circle [11]. The form of these polynomials is

[pic] (1)

where [pic]and:

[pic]: positive integer or zero; i.e. [pic]

[pic]: positive integer subject to constraint [pic]

[pic] length of vector from origin to [pic] pixel, i.e. [pic]

[pic] angle between the vector [pic] and the [pic]axis in the counterclockwise direction.

The Radial polynomial is defined as

[pic] (2)

2. Zernike Moments

The complex Zernike moments of order [pic] with repetition [pic] for an image function [pic], in polar coordinate is defined as:

[pic] (3)

If [pic] is the number of pixels along each axis of the image, then Eq. (3) can be written in the discrete form

[pic], (4)

where

[pic] (5)

3. Square-To-Circular Trademark Transform

Since Zernike moments are defined in terms of polar coordinates [pic], the Zernike polynomials will have to evaluate at each pixel position, and the computations involved are significantly large compared to other moments. The polar form of Zernike moments suggests a square-to-circular image transformation [12], so that the Zernike polynomials need be computed only once for all pixels mapped to the same circle. The Zernike moments thus computed, though differ from the true moments of the rectangular image, can be used as feature descriptors for image identification and reconstruction applications. The procedure for the transformation of the pixels space from a square region to a circular region is schematically shown in Fig. 1.

As shown in Fig. 1, the image pixels can be thought of as arranged along concentric squares and can be mapped to concentric circles by the following transformation. If the image coordinate system [pic] is defined with the origin at the center of the square pixel grid, then the pixel coordinates of the transformed circular image can be represented by the two numbers [pic] where [pic] denotes the radius of the circle and [pic] the position index of the pixel on the circle.

[pic]

Fig. 1: Schematic of square-to-circular trademark transformation

The integral values of [pic] can be obtained as follows:

[pic] (6)

if [pic]

if [pic]

The above transformation, assumed that the image intensity values are preserved under the transformation, so that [pic]. If [pic] denotes the image size in pixels, then the ranges of values of the coordinate indices are given by

[pic] [pic] [pic]

(7)

The normalized polar coordinates [pic] of the pixel [pic] are given by

[pic] [pic] (8)

4. Computational of Zernike Moments of Gray-Level Trademarks

Using the square-to-circular image transform given the previous section, then it need an algorithm to compute the Zernike moments of a gray-level trademark. The real-valued Zernike moment components in Eq.(4) can be written in the discrete form using the coordinates of the transformed circular image with help of Eqs. (7), (8) as

[pic] (9)

2. Problem Solution

The block diagram of the proposed approach is shown in Fig. 2. It can be separated into two modules. In the query module, user can submit a query by a trademark example to get a list of database trademarks ranked by their similarity scores to the query trademark. The details of the proposed approach are presented in the following section.

[pic]

Fig. 2. The block diagram of trademarks retrieval.

1. Trademark Data Collection

Six hundred logos were collected from the internet. All trademark images were gray-scaled and normalized to the resolution of 100 X 100 pixels. Samples of these trademarks are shown in Fig. 3.

1 Feature Extraction

To enable retrieval of similar image from the image database, a set of features based on Zernike moment was chosen for both the query and index images. These features are constructed using a set of complex polynomials and are defined inside the unit circle and the radial polynomial vector [14]. 25 Zernike moments of order 0 to 8 in p and q are extracted. These computed features are shown in Table 1.

[pic][pic][pic]

[pic][pic][pic]

[pic][pic][pic][pic][pic][pic]

Fig. 3: Trademark samples

Table 1: List of Zernike moment up to order 8.

|n |ZMM |No. of ZMM |

|0 |Z00 |1 |

|1 |Z11 |1 |

|2 |Z20,Z22 |2 |

|3 |Z31,Z33 |2 |

|4 |Z40,Z42,Z44 |3 |

|5 |Z51,Z53,Z55 |3 |

|6 |Z60,Z62,Z64,Z66 |4 |

|7 |Z71,Z73,Z75,Z77 |4 |

|8 |Z80,Z82,Z84, Z86,Z88 |5 |

3 Feature Matching

Retrieving of the similar trademarks is done by matching the feature vector computed from the input trademark with a class of feature vectors stored in the database. Table 2 shows a table containing a set of reference feature vectors.

Table 2 : Example of a set of reference feature vectors

|Image |Feature vector |

|(k) |1 2 3 |

| |..... n |

|1 | |

|2 | |

|3 | |

|. | |

|. | |

|. |[pic] [pic] [pic] |

|k |..... [pic] |

We denote a feature vector corresponding to a trademark [pic] by

[pic] (10)

where each component [pic] is typically an invariant moment function of the trademark. The set of all [pic]’s constitute the reference library of feature vectors. The trademarks for which the reference vectors are computed and stored as above are either a set of patterns or different views of a three dimensional object.

2. Similarity Measure

To match a feature vector of V’ of the image of an unknown pattern or object view direction, weighted Euclidean distance measure algorithm is used in moment based feature vector matching.

[pic] (11)

The weighted Euclidean distance measure is defined as follows:

[pic], (12)

where [pic] denotes the weight added to the component [pic] to balance the variations in the dynamic range. The value of [pic] for which the function [pic] is minimum, is selected as the matched image index. The inverse of the variance of the column [pic] is frequently used as the weight [pic], i.e.,

[pic], (13)

where

[pic] (14)

4. Experimental Results

To verify the performance of the proposed trademark retrieval scheme, original trademark images were added with different degree of noises as follows:

i. Salt & Pepper - 50 randomly selected trademarks were added with salt & pepper noise by the following factors: 20%, 40%, 60%, 80% and 100%.

ii. Gaussian - 50 randomly selected trademarks were added by Gaussian noise by the following variance factors: 0.2, 0.4, 0.6, 0.8 and 1.0.

iii. Poisson - 50 randomly selected trademarks were added by Poisson noise without any factors.

iv. Speckle - 50 randomly selected trademarks were added with speckle noise by the following variance factors: 0.2, 0.4, 0.6, 0.8 and 1.

Examples of trademark corrupted with various type of noises are shown in Table 3. To illustrate the capability of the proposed method, randomly selected trademark is chosen as a query image. Table 4 shows the results obtained under different query images and its respective retrieved images from the image database in ranking order. These results confirmed that the Zernike moments is not sensitive to image corrupted by noise and thus could be efficiently used for trademark retrieval purposes.

5. Conclusion

In this paper, new content-based trademark retrieval method is presented using Zernike moments. Even though Zernike moment is more complicated computationally as compared to the other moments based methods, it had been proven to be superior and efficient for trademark retrieval under different degree of noise added to the original trademark image.

Table 3: Original trademark and its various looks after corrupted by different type of noises.

|[pic] |

|Original Trademark |

|[pic] [pic] [pic] [pic] [pic] |

|Speckle Noise with increasing order of factors. |

|[pic] [pic] [pic] [pic] [pic] |

|Salt & Pepper Noise with increasing order of factors. |

|[pic] [pic] [pic] [pic] [pic] |

|Gaussian Noise with increasing order of factors. |

|[pic] |

|Poisson Noise |

References:

[1] Chong, C.W., Raveendran, P. and Mukundan, R. 2003. A comparative analysis of algorithms for fast computation of Zernike moments. Journal of Pattern Recognition 36:731-742.

[2] Eakins, J.P., Boardman, J.M. and Graham, M.E. 1998. Similarity retrieval of trademark images, IEEE Multimedia 5(2):53-63.

[3] Gu, J., Shu, H.Z., Toumoulin, C. and Luo L.M. 2002. A novel algorithm for fast computation of Zernike Moments. Pattern Recognition 35:2905-2911.

[4] Jain, A.K. and Vailaya, A. 1996. Image retrieval using color and shape. Journal of Pattern Recognition 29(8):1233-1244.

[5] Jain, A. K. and Vailaya, A. 1998. Shape-based retrieval: a case study with trademark image databases. Journal of Pattern Recognition 31(9):1369-1390.

[6] Kankanhali, M.S., Mehtre, B.M. and Huang, H.Y. 1999. Color and spatial feature for content-based image retrieval. Journal of Pattern Recognition Lett.20:109-118.

Table 4: Samples of the top-10 trademark retrieved results.

|original |Retrieval results |

| |1 2 3 4 5 6 7 8 9 10|

|[pic] |[pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] |

| | |

|[pic] |[pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] |

| | |

|[pic] |[pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] |

| | |

|[pic] |[pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] |

| | |

|[pic] |[pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] |

| | |

|[pic] |[pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] |

[7] Kato, T. And Fujimura, K. 1990. TRADEMARK: multimedia image database system with intelligent human interface. Systems and Computers in Japan 21, 33-46.

[8] Kim, Y.S. and Kim, W.Y. 1998. Content-based trademark retrieval system using a visually salient feature. Image and Vision Computing 16:931-939.

[9] King, I. and Jin, Z. 2003. Integrated probability function and its application to content-based image retrieval by relevance feedback. Journal of Pattern Recognition 36:2117-2186.

[10] Liao, S.X. and Pawlak, M. 1998. On the accuracy of Zernike Moments for image analysis. IEEE transactions on pattern Analysis and Machin Intelligence. 20(12).

[11] Mehtre, B.M., Kankanhalli, M.S. and Lee, W.F. 1998. Content-based image retrieval using a composite color-shape approach. Journal of Information Processing and Management 34(1):109-120.

[12] Shih, J.L. and Chen, L.H. 2001. A new system for trademark segmentation and retrieval. Journal of Image and Vision Computing 19:1011-1018.

[13]Yin, P.Y. and Yeh, C.C. 2002. Content-based retrieval from trademark database. Journal of Pattern Recognition Lett. 23:113-126.

[14]Mukundan, R. and Ramakrishnan, K.R. Moment functions in image analysis-theory and applications. In Zernike Moments, pp 57-69. Singapore: World Scientific.

[15]Wee, C.Y., Raveendran, P. and Takeda, F. 2003. New computational methods for full and subset Zernike moments. Information Sciences.

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