Research on Similarity Measurement for Texture Image Retrieval

A complete texture image retrieval system includes two techniques: texture feature extraction and similarity measurement. Specifically, similarity measurement is a key problem for texture image retrieval study. In this paper, we present an effective similarity measurement formula. The MIT vision texture database, the Brodatz texture database, and the Outex texture database were used to verify the retrieval performance of the proposed similarity measurement method. Dual-tree complex wavelet transform and nonsubsampled contourlet transform were used to extract texture features. Experimental results show that the proposed similarity measurement method achieves better retrieval performance than some existing similarity measurement methods.


Introduction
With the rapid expansion of digital image libraries and multimedia databases, content-based image retrieval (CBIR) has become a hot research topic in the computer science field. Content of images includes color characteristics, shape characteristics, texture characteristics, and semantics characteristics. Because texture is a type of inherent property for most physical surfaces, texture characteristics usually play an important role in CBIR.
A complete texture image retrieval system includes two techniques: texture features extraction and similarity measurement. Texture features used in CBIR are usually extracted by space-frequency domain approaches [1][2][3][4][5][6][7][8]. Shutao Li and John Shawe-Taylor used a wavelet transform and a contourlet transform to extract texture features for image classifying [9]. A Gabor filter has a nice effect on descripting texture features, but it still has two shortcomings: one is that redundant information is produced after different Gabor filters; the other is that feature extraction by Gabor filters usually has considerably high computational complexity. N. Kingsbury et al used a dual-tree complex wavelet transform (DT-CWT) to extract texture features [10][11][12]. DT-CWT can overcome two drawbacks of the Discrete Wavelet Transform (DWT); one is that invariance, the other is that DWT has only limited directivity. DT-CWT not only has good localization in time-frequency domains, but also has approximate translation invariance, more directivity and limited data redundancy. A nonsubsampled contourlet transform (NSCT) has anisotropy and translation invariance [13][14]. In this paper, DT-CWT and NSCT are respectively used to extract texture features of images.
Similarity measurement is a key technique for texture image retrieval. Kokare. M. et al in [15] compared nine distance similarity measurements, such as Weighted-Mean-Variance distance (WMVD), Euclidean distance (ED), Canberra distance (CD), Bray-Curtis distance (BCD), Manhattan distance, Mahalanobis distance, Chebyshev distance, Squared Chi-Squared distance, and Squared Chord distance for texture image retrieval. Experimental results show that WMVD, CD and BCD are the three best distance similarity measurements for image retrieval problems, but the retrieval rates are not ideal when using WMVD, CD and BCD. Therefore, exploring more effective similarity measurements is a problem worth studying.
In this paper, we present an effective similarity measurement. A dual-tree complex wavelet transform and a nonsubsampled contourlet transform were respectively used to extract texture features. The MIT vision texture database (640 images), the Brodatz texture database (1776 images), and the Outex texture database (5104 images) were used to verify the retrieval performance. Experimental results show that the retrieval performance can be improved by the proposed similarity measurement more than some existing similarity distance measurement methods.

Related Works
Because WMVD, CD and BCD are the best three similarity measurements for image retrieval [15], so here we focus on the WMVD similarity measurement, the CD similarity measurement and the BCD similarity measurement.
WMVD (Weighted-Mean-Variance distance) is widely used in image retrieval [1] [7]. Generally, two patterns x and y are considered, where x is a query image and y is a target image in the database. F x and F y are, respectively, the feature vectors of x and y. The WMV is defined as the following, Where Where m denotes the scale, and n is the number of subbands in each scale.m x mn and s x mn are the mean and the standard deviation of each subband for a query image. m y mn and s y mn are the mean and the standard deviation of each subband for a target image. s(m mn ) and s s mn ð Þ are the standard deviations of m mn and s mn respectively over the entire database, and they are used to normalize the individual feature components.
If x and y are two n-dimensional feature vectors of an image to retrieve and query the image: The ED is defined as the following, the CD is defined as the following, and the BCD is defined as the following, In this paper, we present an effective distance measurement that is more effective than the above three distance measurement methods.

Proposed Distance Similarity Measure
We present an effective Average Euclidean distance (AED). If X and Y are two n-dimensional feature vectors of an image from a database and the query image, we give the new similarity measurement as the following, The proposed distance similarity measurement not only contains some relations between objects, but also comprehensively considers all dimensional feature parameters. When the proposed similarity distance measurement is used for texture image retrieval, the experimental results show that the retrieval performances are better using the proposed similarity distance measurement than the existing similarity measurements.

Extraction of texture features based on
nonsubsampled contourlet transform. A nonsubsampled contourlet transform includes a nonsubsampled pyramid and nonsubsampled directional filter banks [13][14]. A nonsubsampled pyramid includes a set of two-channel nonsubsampled filter banks (NSFB). Nonsubsampled filtering does not implement a downsampling operation on an image but implements upsampling for filter banks, so NSCT has not only anisotropy but also the shift invariance.
Two-level NSCT decomposition is shown in Figure 1.
A nonsubsampled Laplace pyramid is a two-channel nonsubsampled transform. The condition of perfect reconstruction is shown as the following, Where, H 0 (z) and H 1 (z) denote low frequency and high frequency decomposition filters. G 0 (z) and G 1 (z) denote low frequency and high-frequency reconstruction filters. For practical image decomposition, a nonsubsampled àtrous wavelet transform is used to obtain a high frequency subband and a low frequency subband; a  certain number of directional filters are then used to get some directional subbands. In order to get multiresolution analysis, one can continue to decompose the à trous wavelet transform low frequency subband.
Each image is decomposed five levels using a nonsubsampled Laplace pyramid decomposition; all the obtained high frequency subbands then continue to be decomposed by the nonsubsampled directional filter banks. A ''pyr'' pyramidal filter and a ''vk'' directional filter are used to lower the time complexity in our       2) Brodatz image database. There are 1776 texture images from 111 different classes from the Brodatz texture database [17] in the image database. Each original Brodatz texture image is divided into sixteen nonoverlapping 128|128 subimages. The total number of images in this database is 1776 (111|16). The query image is any one of the 1776 subimages; the other 15 subimages from the same class are relevant candidate images. Different classes from the Brodatz texture database are shown as Figure 3.
3) Outex image database. There are 5104 texture images from 319 different classes from the Outex texture database [18] in the image database. Each original Outex texture image is divided into sixteen nonoverlapping 128|128 subimages. The total number of images in this database is 5104 (319|16). The query image is any one of the 5104 subimages; the other 15 subimages from the same class are relevant candidate images.  Different classes from the Outex texture database are shown as Figure 4.

The Existing and the Proposed Texture Image Retrieval Methods
In our experiments, each image is decomposed by DT-CWT and NSCT respectively. Ten kinds of texture image retrieval methods are given as follows: Method 1: use DT-CWT and ED.

Experimental Results
The average precision ratio is used to evaluate retrieval performance. The average precision ratio is calculated using the following formula, Where N is the total number of the images in the texture database. M i is the number of similar images that belong to the same class in the image database. m i is the number of images that are properly ferreted out from the texture database in practice. In this paper, there are sixteen 128|128 subimages in the same class. The number of top retrieved images is considered as 16. m i is the number of images of the top 16 retrieved images belonging to the same class. The proposed method improves retrieval performance on the database, compared with the other four similarity measurements. The experimental results are shown as Table 1, Table 2,  Table 3, Table 4, Table 5, and Table 6.  We evaluate the performance in terms of the average retrieval rate of relevant images as a function of the number of top retrieved images; the retrieval performance is shown as Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, and Figure 10. The experimental results show that the proposed similarity measurement can improve average precision on the image retrieval.

Discussion
The ED measurement lacks the interrelations between objects. When the ED measurement is used as a similarity measurement for texture image retrieval in a wavelet domain, retrieval accuracy is not always satisfied. The WMVD similarity measurement has been widely used for image retrieval, but it has a shortcoming: the similarity measurement between two images is sometimes affected by some uncorrelated images in the whole image database, because the standard deviation of all the images in the whole database needs to be calculated in order to normalize the Euclidean distance. CD and BCD similarity measurements use the difference and the normalization of the difference between two image features; they do not have scaling effects, but their drawback is that they both sum differences in a simple manner. The proposed similarity measurement first uses the denominator to normalize the difference between the two image features, so it can avoid scaling effects. Next, the differences in each dimension are squared, and they are summed before extracting the square root. The proposed similarity measurement can comprehensively use all features; it can avoid the limitations of CD and BCD similarity measurements.

Conclusion
We present an effective similarity distance measurement for image retrieval. Features of all the images were extracted using DT-CWT and NSCT respectively. Experimental results demonstrate that the proposed similarity distance measurement achieves higher retrieval accuracy than some existing similarity measures.