Comparison of Curvelet and Wavelet Texture ... - Semantic Scholar
2012 IEEE International Conference on Multimedia and Expo
Comparison of Curvelet and Wavelet Texture Features for Content Based Image Retrieval
Ishrat Jahan Sumana, Guojun Lu and Dengsheng Zhang Gippsland School of Information Technology, Monash University Churchill, Victoria-3842, Australia {ishrat.sumana, Guojun.Lu, Dengsheng.Zhang}@monash.edu generation curvelet transform. This curvelet transform uses the complex ridgelet transform and found to be less efficient. To overcome this problem, Candès et al. proposed two curvelet transforms, namely, unequally-spaced fast Fourier transform (USFFT) and wrapping based fast curvelet transform in [11], which are known as the second generation curvelet transforms. Wrapping based curvelet transform is more effective and efficient than USFFT and ridgelet based curvelet transform [12]. Recently, wrapping based curvelet transform has been shown to have promising performance in capturing image edge information [11] which is important in texture representation. Sumana et al. employed wrapping based discrete curvelet transform to extract texture features and retrieve texture images in [2, 3]. From the experimental results, Sumana found curvelet texture feature is more effective than wavelet and Gabor filters features and it is robust to scale distortion [3]. M. M. Islam et al. made an effort to improve wrapping based curvelet retrieval by making curvelet feature rotation invariant [20] and have shown it to perform better than curvelet texture feature described in [2]. But this rotation invariant curvelet feature performs better only when the database contains rotated versions of the original images. Therefore, we choose wrapping based curvelet transform to compute our GGD texture feature. For convenience, we use the term ‘curvelet transform/feature’ to refer to ‘wrapping based curvelet transform/feature’ in this paper. In subband based texture feature extraction method, feature vector is created with the mean and standard deviation computed from each subband obtained by applying spectral transform to a given image. Several texture retrieval methods are developed based on this straight forward spectral approach. On the other hand, statistical framework treats texture analysis as a probability inference problem. Generally, as a pre-processing step, subband coefficients are generated in the spectral domain and these coefficients are then further analyzed under the statistical framework. Generalized Gaussian density is used to model wavelet coefficients in earlier research works [1, 13, 14]. To model the filter responses of an image more accurately, GGD is applied to the distribution of the wavelet subband coefficients [1]. It is an extension to the subband energy based texture characterization method. An initial attempt to model USFFT based curvelet coefficients with GGD
Abstract—Texture feature plays a vital role in content based Image retrieval (CBIR). Wavelet texture feature modeled by generalized Gaussian density (GGD) [1] performs better than discrete wavelet texture feature. Curvelet texture feature was proposed in [2]. In this paper, we compute a new texture feature by applying the generalized Gaussian density to the distribution of curvelet coefficients which we call curvelet GGD texture feature. The purpose of this paper is to investigate curvelet GGD texture feature and compare its retrieval performance with that of curvelet, wavelet and wavelet GGD texture features. Experimental results show that both curvelet and curvelet GGD features perform significantly better than wavelet and wavelet GGD texture features. Among the two types of curvelet based features, curvelet feature shows better performance in CBIR than curvelet GGD texture feature. The findings are discussed in the paper. Keywords-curvelet transform; wavelet transform; curvelet GGD texture feature; ML estimator; content based image retrieval.
I.
INTRODUCTION
A large number of digital images are generated and stored in the internet on a regular basis. This creates a collection of many millions of images in the web. Therefore, searching relevant images from this large data collection according to the users’ preference has attracted much interest among the researchers in recent years. Much work has been done on CBIR using low level image features such as color, texture and shape. Among these features, texture is an important and prominent visual property of an image. Effective and efficient texture representation and retrieval is a challenging research issue. There are two types of texture feature extraction approaches, spatial domain analysis and spectral domain analysis [3]. Spectral approaches like wavelet transform, Gabor filters, cosine transform and curvelet transform are more robust to noise than the spatial approaches such as, mean, standard deviation, Tamura features, edge histogram, etc. Therefore, spectral approaches are widely used for texture feature extraction. Wavelet transform has been used in many CBIR approaches [4-9] due to its good texture representation capability. It has been used in many image classification problems as well. Curvelet transform is a new member in the spectral domain analysis. It was first proposed by Candès and Donoho [10] and is known as the first 978-0-7695-4711-4/12 $26.00 © 2012 IEEE DOI 10.1109/ICME.2012.90
290
moment is found in [21] for texture classification of a small database containing only 450 textures of 10 categories. However, feature dimension is not mentioned anywhere in this paper and there was no comparison with other techniques. Application of GGD is motivated by recent psychological research on human texture perception. Generally, two homogeneous textures are difficult to discriminate if they show similar densities of responses from a bank of filters [15]. The version of GGD which is used to model the distribution of wavelet subband coefficients in [1] is also known as the exponential power distribution or the generalized error distribution [16]. It is a useful way to parameterize symmetric heavy-tailed density distribution [16] which is often the case in wavelet and wavelet like subband coefficients. The probability distribution function of GGD is defined as β
p( x; α , β ) = β e− (| x− μ |/α ) / (2αΓ(1 / β )) where ∞
Ƚ(.)
is
the
Γ( z ) = ³ e − t t z −1dt , z > 0 ,
Gamma
function,
Leibler distance (KLD) in [1] gives better CBIR performance than the combination of wavelet moment feature and similarity measurement using Euclidean distance [13]. Sumana et al. proposed curvelet texture feature and have shown it to perform better than wavelet in CBIR [3]. In this paper, we propose to apply GGD on curvelet coefficients to obtain curvelet GGD features and investigate its performance. First, discrete curvelet coefficients are obtained from a given image by applying the discrete curvelet transform on that image. Second, the distribution of curvelet coefficients are modeled using generalized Gaussian density. The Gaussian parameters obtained from each curvelet subband coefficients are estimated using ML estimator, which is found to be the most effective in estimating statistical data [17]. Third, these GGD parameters are used to create curvelet GGD texture feature vector. Once the feature vector is calculated, KLD is used to measure the similarity between the query image and the database images. Finally, retrieval performance of the proposed curvelet GGD method is compared with that of the conventional curvelet, wavelet and wavelet GGD texture features. We test the curvelet GGD texture feature on a larger database of 1792 Brodatz texture images. The rest of the paper is organized as follows. Section 2 describes the curvelet GGD texture feature extraction mechanism, feature vector generation method and image similarity measurement using KLD. In Section 3, we present our CBIR experiments using the proposed curvelet GGD feature, CBIR performance evaluation and comparison with some of the most effective texture features, e.g., curvelet feature, wavelet feature and wavelet GGD feature. We provide the conclusion of this paper in Section 4.
(1) i.e.,
μ is the mean and ( α 2 / 2 ) is
0
the variance. β is known as the shape parameter and α is the scale parameter. α models the width of the probability distribution function’s peak and β is inversely proportional to the decreasing rate of the peak. Gaussian probability distribution function for different values of β is shown in Fig. 1. The probability distribution function of GGD contains the normal distribution and the Laplace distribution as two special cases, when β = 2 and β = 1 , respectively.
II. CURVELET COEFFICIENTS MODELING WITH GENERALIZED GAUSSIAN DENSITY AND SIMILARITY MEASUREMENT A. Curvelet GGD Feature Extraction The discrete curvelet transform of an image is taken on a 2-D Cartesian grid f [m, n], 0 ≤ m <M, 0≤ n
Comparison of Curvelet and Wavelet Texture Features for Content Based Image Retrieval
Ishrat Jahan Sumana, Guojun Lu and Dengsheng Zhang Gippsland School of Information Technology, Monash University Churchill, Victoria-3842, Australia {ishrat.sumana, Guojun.Lu, Dengsheng.Zhang}@monash.edu generation curvelet transform. This curvelet transform uses the complex ridgelet transform and found to be less efficient. To overcome this problem, Candès et al. proposed two curvelet transforms, namely, unequally-spaced fast Fourier transform (USFFT) and wrapping based fast curvelet transform in [11], which are known as the second generation curvelet transforms. Wrapping based curvelet transform is more effective and efficient than USFFT and ridgelet based curvelet transform [12]. Recently, wrapping based curvelet transform has been shown to have promising performance in capturing image edge information [11] which is important in texture representation. Sumana et al. employed wrapping based discrete curvelet transform to extract texture features and retrieve texture images in [2, 3]. From the experimental results, Sumana found curvelet texture feature is more effective than wavelet and Gabor filters features and it is robust to scale distortion [3]. M. M. Islam et al. made an effort to improve wrapping based curvelet retrieval by making curvelet feature rotation invariant [20] and have shown it to perform better than curvelet texture feature described in [2]. But this rotation invariant curvelet feature performs better only when the database contains rotated versions of the original images. Therefore, we choose wrapping based curvelet transform to compute our GGD texture feature. For convenience, we use the term ‘curvelet transform/feature’ to refer to ‘wrapping based curvelet transform/feature’ in this paper. In subband based texture feature extraction method, feature vector is created with the mean and standard deviation computed from each subband obtained by applying spectral transform to a given image. Several texture retrieval methods are developed based on this straight forward spectral approach. On the other hand, statistical framework treats texture analysis as a probability inference problem. Generally, as a pre-processing step, subband coefficients are generated in the spectral domain and these coefficients are then further analyzed under the statistical framework. Generalized Gaussian density is used to model wavelet coefficients in earlier research works [1, 13, 14]. To model the filter responses of an image more accurately, GGD is applied to the distribution of the wavelet subband coefficients [1]. It is an extension to the subband energy based texture characterization method. An initial attempt to model USFFT based curvelet coefficients with GGD
Abstract—Texture feature plays a vital role in content based Image retrieval (CBIR). Wavelet texture feature modeled by generalized Gaussian density (GGD) [1] performs better than discrete wavelet texture feature. Curvelet texture feature was proposed in [2]. In this paper, we compute a new texture feature by applying the generalized Gaussian density to the distribution of curvelet coefficients which we call curvelet GGD texture feature. The purpose of this paper is to investigate curvelet GGD texture feature and compare its retrieval performance with that of curvelet, wavelet and wavelet GGD texture features. Experimental results show that both curvelet and curvelet GGD features perform significantly better than wavelet and wavelet GGD texture features. Among the two types of curvelet based features, curvelet feature shows better performance in CBIR than curvelet GGD texture feature. The findings are discussed in the paper. Keywords-curvelet transform; wavelet transform; curvelet GGD texture feature; ML estimator; content based image retrieval.
I.
INTRODUCTION
A large number of digital images are generated and stored in the internet on a regular basis. This creates a collection of many millions of images in the web. Therefore, searching relevant images from this large data collection according to the users’ preference has attracted much interest among the researchers in recent years. Much work has been done on CBIR using low level image features such as color, texture and shape. Among these features, texture is an important and prominent visual property of an image. Effective and efficient texture representation and retrieval is a challenging research issue. There are two types of texture feature extraction approaches, spatial domain analysis and spectral domain analysis [3]. Spectral approaches like wavelet transform, Gabor filters, cosine transform and curvelet transform are more robust to noise than the spatial approaches such as, mean, standard deviation, Tamura features, edge histogram, etc. Therefore, spectral approaches are widely used for texture feature extraction. Wavelet transform has been used in many CBIR approaches [4-9] due to its good texture representation capability. It has been used in many image classification problems as well. Curvelet transform is a new member in the spectral domain analysis. It was first proposed by Candès and Donoho [10] and is known as the first 978-0-7695-4711-4/12 $26.00 © 2012 IEEE DOI 10.1109/ICME.2012.90
290
moment is found in [21] for texture classification of a small database containing only 450 textures of 10 categories. However, feature dimension is not mentioned anywhere in this paper and there was no comparison with other techniques. Application of GGD is motivated by recent psychological research on human texture perception. Generally, two homogeneous textures are difficult to discriminate if they show similar densities of responses from a bank of filters [15]. The version of GGD which is used to model the distribution of wavelet subband coefficients in [1] is also known as the exponential power distribution or the generalized error distribution [16]. It is a useful way to parameterize symmetric heavy-tailed density distribution [16] which is often the case in wavelet and wavelet like subband coefficients. The probability distribution function of GGD is defined as β
p( x; α , β ) = β e− (| x− μ |/α ) / (2αΓ(1 / β )) where ∞
Ƚ(.)
is
the
Γ( z ) = ³ e − t t z −1dt , z > 0 ,
Gamma
function,
Leibler distance (KLD) in [1] gives better CBIR performance than the combination of wavelet moment feature and similarity measurement using Euclidean distance [13]. Sumana et al. proposed curvelet texture feature and have shown it to perform better than wavelet in CBIR [3]. In this paper, we propose to apply GGD on curvelet coefficients to obtain curvelet GGD features and investigate its performance. First, discrete curvelet coefficients are obtained from a given image by applying the discrete curvelet transform on that image. Second, the distribution of curvelet coefficients are modeled using generalized Gaussian density. The Gaussian parameters obtained from each curvelet subband coefficients are estimated using ML estimator, which is found to be the most effective in estimating statistical data [17]. Third, these GGD parameters are used to create curvelet GGD texture feature vector. Once the feature vector is calculated, KLD is used to measure the similarity between the query image and the database images. Finally, retrieval performance of the proposed curvelet GGD method is compared with that of the conventional curvelet, wavelet and wavelet GGD texture features. We test the curvelet GGD texture feature on a larger database of 1792 Brodatz texture images. The rest of the paper is organized as follows. Section 2 describes the curvelet GGD texture feature extraction mechanism, feature vector generation method and image similarity measurement using KLD. In Section 3, we present our CBIR experiments using the proposed curvelet GGD feature, CBIR performance evaluation and comparison with some of the most effective texture features, e.g., curvelet feature, wavelet feature and wavelet GGD feature. We provide the conclusion of this paper in Section 4.
(1) i.e.,
μ is the mean and ( α 2 / 2 ) is
0
the variance. β is known as the shape parameter and α is the scale parameter. α models the width of the probability distribution function’s peak and β is inversely proportional to the decreasing rate of the peak. Gaussian probability distribution function for different values of β is shown in Fig. 1. The probability distribution function of GGD contains the normal distribution and the Laplace distribution as two special cases, when β = 2 and β = 1 , respectively.
II. CURVELET COEFFICIENTS MODELING WITH GENERALIZED GAUSSIAN DENSITY AND SIMILARITY MEASUREMENT A. Curvelet GGD Feature Extraction The discrete curvelet transform of an image is taken on a 2-D Cartesian grid f [m, n], 0 ≤ m <M, 0≤ n
