Quaternion Markov Splicing Detection for Color Images Based on Quaternion Discrete Cosine Transform

Abstract

With the increasing amount of splicing images, many detection schemes of splicing images are proposed. In this paper, a splicing detection scheme for color image based on the quaternion discrete cosine transform (QDCT) is proposed. Firstly, the proposed quaternion Markov features are extracted in QDCT domain. Secondly, the proposed quaternion Markov features consist of global and local quaternion Markov, which utilize both magnitude and three phases to extract Markov features by using two different ways. In total, 2916-D features are extracted. Finally, the support vector machine (SVM) is used to detect the splicing images. In our experiments, the accuracy of the proposed scheme reaches 99.16% and 97.52% in CASIA TIDE v1.0 and CASIA TIDE v2.0, respectively, which exceeds that of the existing schemes.

1. Introduction

With the development of image processing technology, the cost of image forensics software is decreasing which destroys the trustworthiness of digital images[1]. Some image forensics issues have been proposed [2]-[7]. Besides, machine learning is used to solve forensics issues [8]-[10]. In forensics issues, splicing operation is a popular tampering method existed in our life, which may cause serious consequences in some cases, such as journalism, judicial investigation, and accident survey. It is very easy to manipulate images with image editing software such as Photoshop, while it is difficult for human being to distinguish the authentic images from splicing images. Therefore, to classify the authentic images, many detection methods of splicing images have been developed.

Image splicing is a common means in image tampering, which is a simple process of cutting and pasting parts of one image or different images to form a forged image. The process includes some post-processing such as Gaussian blur [11]. There are many existing splicing detection schemes, which mainly consist of two categories. One is to extract local features such as blur of the image, inconsistency between the spliced and the authentic regions. In [11]-[15], blur of the image is utilized to detect the splicing images. Documents [16]-[19] make use of neighbour graylevel between the spliced regions and the authentic images. This kind of schemes can not only distinguish splicing images from authentic images, also find the spliced regions. However, the classification accuracy of these schemes is not as high as the other category of schemes.

The other is to extract global features to classify the images. In [20] and [21], higher-order statistical characteristics of wavelet transform was used to reflect the inherent characteristics of natural images. It laid a foundation for many similar methods. In [22], a scheme based on the moments feature and Markov transition probability is proposed. In [23], gray level co-occurrence matrix is regarded as the classification features for splicing detection. In [24], a natural image model is presented based on Markovian rake transform on image luminance. In [25], a scheme based on Markov features in DCT (Discrete Cosine Transform) and DWT (Discrete Wavelet Transform) is proposed. These schemes cannot find the spliced regions, but they have higher classification accuracy than the first category. Our proposed scheme belongs to the second category.

In the last few years, many schemes are proposed [26]-[34]. Some of them have reached the high accuracy which is over 95%. In [26], Markov features based on spatial and DCT domain are combined for image splicing, the accuracy of which reaches 98.47% in the Columbia Image Splicing Detection Evaluation Dataset (CISDED) [28]. CISDED is not adopted in our experiments because the sample number of color images in this database is too small. Splicing detection based on Markov features in QDCT domain is proposed in [29]. The accuracy arrives at 96.44% in CASIA TIDE v1.0 [30]. In [31], local binary features based on SPT (Steerable Pyramid Transform) domain is extracted for classification. The accuracy reaches 97.33% in CASIA TIDE v2.0. In [32], features based on DCT and Contourlet transform domain are used for splicing detection. The accuracy arrives at 96.69% in an international competition organized by the IEEE IFS-TC. In [33], a new image forgery detection method based on deep learning technique is presented. The accuracy arrives at 98.04% in CASIA TIDE v1.0 and 97.83% in v2.0.

Most of the existing methods transform color images into grayscale images or utilize one part of RGB channels. Therefore, the inherent relationship among RGB channels is neglected. In this paper, we propose to extract features in QDCT domain and three imaginary parts of the quaternion is utilized to represent of RGB channels, respectively. Color image as a unit is processed. In contrast to [29], the proposed scheme makes full use of both the magnitude and three phases to extract Markov features. In experiments, the proposed scheme has better performance.

The rest of this paper is organized as follows. In Section 2, the quaternion and block QDCT are introduced. The proposed quaternion Markov is presented, and the quaternion Markov is composed of global quaternion Markov and local quaternion Markov. After presenting the proposed scheme, the experimental results and discussion are shown in Section 3. Section 4 draws a conclusion of this paper.

2. The Proposed Scheme

2.1. Introduction to QDCT

DCT has been widely used in image processing due to its superior capability in decorrelation and energy compaction. QDCT is extended from DCT. Therefore, compared with DCT, QDCT not only owns the similar function as DCT but obtains the channel correlation and color information of color images. As a result, features extracted in QDCT domain have more efficient information to promote the performance of the proposed scheme.

2.1.1. Quaternion

The quaternion is proposed by Hamilton in 1843 in [35]. A quaternion is composed of one real part and three imaginary parts. The quaternion is formed as.

𝑞 = 𝑎 + 𝑏𝒊 + 𝑐𝒋 + 𝑑k       (1)

, where a, b, c, d ∈ R.i, j, k obey the following constraints:

𝒊² = 𝒋² = 𝒌² = −1       (2)

𝒊𝒊j = −𝒋i = 𝒌,𝒋k = −𝒌j = 𝒊, 𝒌i = −𝒊k = 𝒌       (3)

From Eq. (3), we can observe that the commutative of the quaternion doesn’t meet the law of multiplication. The magnitude of a quaternion is defined as follows:

\(|q|=\sqrt{a^{2}+b^{2}+c^{2}+d^{2}}\)(4)

A polar form of the quaternion is composed of the magnitude and three angles (𝜑, 𝜃, 𝜓) called phase. The equation is written as follows:

𝑞 = |𝑞|𝑒^𝒊𝜑𝑒^𝒋𝜃𝑒^𝒌𝜓       (5)

\(\varphi=\frac{\operatorname{atan}\left(2(c d+a b),\left(a^{2}-b^{2}+c^{2}-d^{2}\right)\right)}{2}+k \pi\)       (6)

\(\theta=\frac{\operatorname{atan}\left(2(b d+a c),\left(a^{2}+b^{2}-c^{2}-d^{2}\right)\right)}{2}\)       (7)

\(\psi=\frac{\arcsin (2(a d-b c))}{2}\)       (8)

, where 𝜑 ∈ [−π, π], 𝜃 ∈ [−π/2, π/2], 𝜓 ∈ [−π/4, π/4], k ∈ Z. Referred to [36], the magnitude and three angles are used to represent QDCT coefficients in the proposed scheme. Usually, we consider a quaternion composed of a scalar and vector part as follows:

𝑞 = 𝑆(𝑞) + 𝑉(𝑞)       (9)

, where S(q) = a and V (q) = bi + cj + dk. If S(q) = 0, q is called a pure quaternion. If |q| = 1 , q is called a unit quaternion

2.1.2. Definition of QDCT

QDCT is derived from DCT. The definition of QDCT is referred to [37]. There are two forms of QDCT, L-QDCT, and R-QDCT. This subsection only introduce L-QDCT which are used in the proposed scheme. L-QDCT is as follows:

\(Q D C T_{q}^{L}(p, s)=a(p) a(s) \sum_{m=0}^{M-1} \sum_{n=0}^{N-1} u_{q} f_{q} T(p, s, m, n)\)       (10)

, where 𝑓𝑞(m, n) is a M × N quaternion matrix. 𝑢𝑢𝑞𝑞 is a unit and pure quaternion. \(Q D C T_{q}^{L}(p, s)\) is the transformed matrix. p and s are row and column of the obtained matrix, respectively. α(p), α(s) and T(p, s, m, n) are defined as follows:

\(a(p)=\left\{\begin{array}{l} \sqrt{1 / M} p=0 \\ \sqrt{1 / M} p \neq 0 \end{array} a(s)=\left\{\begin{array}{l} \sqrt{1 / N} s=0 \\ \sqrt{1 / N} s \neq 0 \end{array}\right.\right.\)       (11)

\(T(p, s, m, n)=\cos \left[\frac{\pi(2 m+1) p}{2 M}\right] \cos \left[\frac{\pi(2 n+1) s}{2 N}\right]\)       (12)

There are two ways to calculate QDCT. One of the ways is to calculate QDCT directly with its definition. The other way is to use two complex numbers to represent the quaternion and then compute QDCT with DCT. More details are given in [37].

2.2. The Proposed Scheme

QDCT owns the property of energy concentration. The magnitude of quaternion represents the signal strength and the phases of quaternion depict the structure of the signal. Therefore, features extracted from the magnitude and phases can be used in the proposed scheme.

This section will first illustrate the framework of the proposed scheme briefly and analyze the difference between global and local quaternion Markov. Next, we will describe three threshold processing methods after obtaining the difference arrays of quaternion Markov. Then, six types of transition probability matrix will be introduced. Finally, the calculation steps of global and local quaternion Markov will be presented in detail.

2.2.1. The Framework of the Proposed Scheme

The framework of the proposed scheme is shown in Fig. 1. The framework is organized as follows:

Fig. 1. The framework of the proposed scheme

1) Use the block QDCT to decompose the color image.

2) Process the QDCT coefficients using the proposed quaternion Markov. The process is presented in Fig. 2. The quaternion Markov comprises global quaternion Markov and local quaternion Markov. Framework of global quaternion Markov is presented as follows:

Fig. 2. The proposed Quaternion Markov

(i) Compute the magnitude and three phases of QDCT coefficients.

(ii) Calculate the difference of the magnitude array and phase arrays in four directions. Process difference arrays with a threshold.

(iii) Obtain the transition probability matrices.

The framework of local quaternion Markov is shown as follows:

(i) Compute the difference of QDCT coefficients in four directions. Process difference arrays with a threshold.

(ii) Get the magnitude and phases of the difference arrays.

(iii) Figure up the transition probability matrices.

3) Transform the transition probability matrices into features. SVMRFE (SVM Recursive Feature Elimination) is used to sort features according to the importance and choose the features for training and testing with SVM. SVMRFE can be referred to [15] for more details.

The steps of two classes of quaternion Markov are similar, but their functions are different.

In global quaternion Markov, the magnitude array and phase array of QDCT coefficients are firstly computed to obtain strength information and texture information of the whole image. Therefore, Markov features that contain the integral information of QDCT coefficients are called global quaternion Markov. In local quaternion Markov, the difference arrays are firstly calculated and then the magnitude and phases of difference arrays are computed to get difference information of QDCT coefficients. Markov features that contain the difference information are named local quaternion Markov. There is a common difference processing in both global quaternion Markov and local quaternion Markov. Difference processing in global quaternion Markov is used to reduce the effect caused by the diversity of images, while in local quaternion Markov, difference processing is utilized to reflect the texture of QDCT coefficients.

The procedure of the proposed scheme is briefly described above. The subsection in the following will give the detailed introduction of the proposed quaternion Markov.

2.2.2. Threshold Processing of Difference Arrays

A difference array is obtained by computing the difference of each pair of the neighbors in the array in one direction. By using Equations (13) to (16), difference arrays in four directions (horizontal, vertical, main diagonal and minor diagonal) are obtained

𝐹_𝑢(𝑢, 𝑣) = 𝐹(𝑢, 𝑣) − 𝐹(𝑢 + 1, 𝑣)       (13)

𝐹_ℎ(𝑢, 𝑣) = 𝐹(𝑢, 𝑣) − 𝐹(𝑢, 𝑣 + 1)       (14)

𝐹_𝑑(𝑢, 𝑣) = 𝐹(𝑢, 𝑣) − 𝐹(𝑢 + 1, 𝑣 + 1)       (15)

𝐹_𝑠(𝑢, 𝑣) = 𝐹(𝑢 + 1, 𝑣) − 𝐹(𝑢, 𝑣 + 1)       (16)

where F denotes the 2-D array, 𝐹_𝑢, 𝐹_ℎ, 𝐹_𝑑 and 𝐹_𝑠 are difference arrays in horizontal, vertical, main diagonal and secondary diagonal directions, respectively. u and v are position of the array F.

In order to decrease computational complexity, threshold processing is conducted on difference arrays. The value scopes of magnitude arrays and phase arrays are different in the proposed scheme, so there are three methods of threshold processing according to Fig. 2. Here, x denotes an element in a difference array, and T denotes a threshold.

Method A (MA) It is applied to the difference in global quaternion magnitude. After Computing magnitude of QDCT coefficients and then calculating the difference arrays of the magnitude, we use Eq. (17) to process the difference arrays.

\(x=\left\{\begin{array}{cc} T, & \text { if } x>T \\ x, \text { if } & -T \leq x \leq T \\ -T, & \text { if } x<-T \end{array}\right.\)       (17)

Method B (MB) According to Equation (4), the magnitude is greater than or equal to zero. It is set for magnitude of local quaternion Markov. After computing difference arrays of QDCT coeffi- cients and then calculating the magnitude of the difference arrays, Eq. (18) is used to obtain new difference arrays.

\(x=\left\{\begin{array}{lr} T, & \text { if } x>T \\ x, & \text { if } 0 \leq x \leq T \end{array}\right.\)       (18)

Method C (MC) Pointing to phase feature in global and local quaternion Markov, we utilize Eq. (19) to replace all the elements in a difference array.

\(x=T * \frac{K * x}{\pi}, \quad K=1,2,4\)       (19)

2.2.3. Transition Probability Matrix

In the proposed scheme, there are six Probability transition matrices, which are calculated by Eq. (20) to (25).

\(P_{h h}=\frac{\sum_{v=0}^{V-2} \sum_{u=0}^{U-2} \delta\left(F_{h}(u, v)=a, F_{h}(u+1, v)=b\right)}{\sum_{v=0}^{V-2} \sum_{u=0}^{U-2} \delta\left(F_{h}(u, v)=a\right)}\)       (20)

\(P_{h h}=\frac{\sum_{v=0}^{V-2} \sum_{u=0}^{U-2} \delta\left(F_{h}(u, v)=a, F_{h}(u, v+1)=b\right)}{\sum_{v=0}^{V-2} \sum_{u=0}^{U-2} \delta\left(F_{h}(u, v)=a\right)}\)       (21)

\(P_{h h}=\frac{\sum_{v=0}^{V-2} \sum_{u=0}^{U-2} \delta\left(F_{v}(u, v)=a, F_{v}(u+1, v)=b\right)}{\sum_{v=0}^{V-2} \sum_{u=0}^{U-2} \delta\left(F_{v}(u, v)=a\right)}\)       (22)

\(P_{h h}=\frac{\sum_{v=0}^{V-2} \sum_{u=0}^{U-2} \delta\left(F_{v}(u, v)=a, F_{v}(u, v+1)=b\right)}{\sum_{v=0}^{V-2} \sum_{u=0}^{U-2} \delta\left(F_{v}(u, v)=a\right)}\)       (23)

\(P_{h h}=\frac{\sum_{v=0}^{V-2} \sum_{u=0}^{U-2} \delta\left(F_{d}(u, v)=a, F_{d}(u+1, v+1)=b\right)}{\sum_{v=0}^{V-2} \sum_{u=0}^{U-2} \delta\left(F_{d}(u, v)=a\right)}\)       (24)

\(P_{h h}=\frac{\sum_{v=0}^{V-2} \sum_{u=0}^{U-2} \delta\left(F_{s}(u+1, v)=a, F_{s}(u, v+1)=b\right)}{\sum_{v=0}^{V-2} \sum_{u=0}^{U-2} \delta\left(F_{s}(u, v)=a\right)}\)       (25)

, where a, b ∈ {−T, −T + 1, · · ·, T − 1, T} or {0, 1, · · ·, T − 1, T}, U and V denote the row number and column number of the array F , respectively, and

\(\delta(A=a, B=b)=\left\{\begin{array}{c} 1, \text { if } A=a, B=b \\ 0, \text { otherwise } \end{array}\right.\)       (26)

Eq. (20) and (21) are used for horizontal difference arrays, Eq. (22) and (23) are used for vertical difference arrays and Eq. (24) and (25) are used for main diagonal and minor diagonal difference arrays, respectively.

2.2.4. The Proposed Quaternion Markov

Markov feature can reflect the statistical change after image splicing. Therefore, it is adopted in this paper. However, there are some changes in the pro posed quaternion Markov compared to the traditional Markov in [12]. Traditional Markov is only suitable for real field while the proposed quaternion Markov is extended to quaternion. Therefore, its amount of transition probability matrices are different from that of the traditional Markov. The proposed quaternion Markov is presented as follows.

a) Global quaternion Markov is represented in detail. As shown in Fig. 3, it is divided into the following steps:

b) A color image is transformed by using the 8×8 block QDCT to obtain QDCT coefficients.

c) Compute the magnitude and three phases of each element of the quaternion array using Eq. (4), (6), (7) and (8). One magnitude array and three phase arrays can be obtained.

d) The difference arrays of magnitude and phase are calculated by using Eq. (13) to (16).

e) Handle the magnitude differences array and the phase difference arrays with threshold processing methods MA and MC, respectively. Therefore, 16 difference arrays are obtained, composed of 4 magnitude arrays and 12 phase arrays.

f) Round these 16 arrays.

g) Figure up the transition probability matrices of these 16 obtained arrays using Eq. (20) to (25).

Note that Eq. (20) to (25) are applied to the magnitude difference arrays and Eq. (20), (22), (24) and (25) are applied to the phase arrays. Therefore, 18 transition probability matrices for 6 matrices of magnitude and for 4 matrices of 3 phases φ, θ and ψ are finally obtained.

Local quaternion Markov is similar to global quaternion Markov. The distinction between two ways is the order of the steps. Local quaternion Markov is shown as follows:

a) It is similar to a) of global quaternion Markov.

b) Calculate the difference arrays of the quaternion array with Eq. (13) to (16) which is different from b) of global quaternion Markov.

c) The magnitude and three phases of each element of four difference array are computed. 16 difference arrays are obtained, composed of 4 magnitude and 12 phase arrays by using Eq. (4), (6), (7) and (8).

d) Handle the magnitude differences array and the phase difference arrays with threshold processing methods MB and MC.

e) Round these 16 arrays.

f) The transition probability matrices of these 16 arrays are obtained by using Eq. (20) to (25).

The computation of transition probability matrices in Local quaternion Markov is similar to that in Global quaternion Markov.

In total,there are 36 transition probability matrices obtained in the proposed quaternion Markov.

3. Experiments

To evaluate the performance of the proposed scheme, we conduct a series of experiments referred to [38] and [39]. The experimental results show the high accuracy of the proposed scheme. In this section, we will first introduce the image database used in our experiments. Then, the components of the features and the experiment al results are presented. Next, the choice of T will be discussed. At last, the comparison between the proposed scheme and the existing schemes are shown.

3.1. Introduction to Database

Due to the splicing detection for color image in the proposed scheme, the database should consist of color image. However, the database in [28] is too small number of color image to be adopted in this experiment. CASIA TIDE v1.0 and CASIA TIDE v2.0 are finally selected. CASIA TIDE v1.0 consists of 800 authentic images and 921 splicing images. The size of the images in this database is 384×256 pixels in the format of JEPG. CASIA TIDE v2.0 is composed of 7491 authentic images and 5123 splicing images. The size of the images in this database is from 240×160 to 900×600 pixels in the format of JEPG, BMP and TIFF. In our experiments, the image database is randomly divided into two halves, one half for training and the other for testing. Some samples which chosen from CASIA TIDE v1.0 and v2.0 are shown in Fig. 3 and Fig. 4. In both figures, the first row shows authentic images and the second row shows splicing images.

Fig. 3. Samples of CASIA TIDE v1.0

Fig. 4. Samples of CASIA TIDE v2.0

3.2. Feature Generation and Performance Evaluation

In our experiments, features are divided into four sets and listed as follows:

a) Set1: Features from the magnitude array in global quaternion Markov. (2 × 𝑇₁ + 1)² × 6 − 𝐷 (−𝐷 denotes the dimensionality) features can be obtained from this set.

b) Set2: Features are derived from the phase arrays in global quaternion Markov. (2 × 𝑇₂ + 1)² × 12 − 𝐷 features can be gotten from this set.

c) Set3: Features root in the magnitude arrays in local quaternion Markov. (2 × 𝑇₃ + 1)² × 6 − 𝐷 features can be obtained from this set.

d) Set4: Features in this set result from the phase arrays in local quaternion Markov. (2 × 𝑇₄ + 1)² × 12 − 𝐷 features can be computed.

In our experiments, we set the thresholds of the four sets as 4, 4, 8 and 4, respectively. The reason will be discussed in the following subsection. Therefore, there are 2916-D features totally

The 2916-D features bring many redundant features, which are composed of four sets. As a result, before presenting the performance of features, SVMRFE is used to sort the features according to their importance. After sorting the obtained features, we select the first hundreds of features and leave the rest of features. Finally, SVM is used for training and testing the images and the average accuracy of 5 echoes is adopted. It takes average 2.4331 seconds for an image in CASIA TIDE v2.0 to be classified, including feature extraction time and classification time.

In Table 1 and Table 2, the experiments of features in four sets and their feature combination are shown. In our experiments, it is found that the accuracy of the proposed scheme is 99.16% in CASIA TIDE v1.0 and 97.52% in CASIA TIDE v2.0 when the dimensionality equals 200. The performance of 100-D, 200-D and 300-D features is shown in Table 1 and Table 2.

Table 1. The experiments of 4 sets with database CASIA TIDE v1.0

Table 2. The experiments of 4 sets with database CASIA TIDE v2.0

There are two issues to be discussed in Table 1 and Table 2. The first issue is on the performance difference of magnitude and phase features between Table 1 and Table 2. In Table 1, it is obvious that the performance of magnitude features is better than that of phases features, while in Table 2, the performance of magnitude features and phase features is almost the same. The second issue is that the classification performance in Table 1 is higher than that in Table 2. They result from the different formats of the images between two databases. CASIA TIDE v1.0 consists of color images with the single JPEG format while CASIA TIDE v2.0 consists of images with JPEG, BMP and TIFF , three different formats. JPEG uses DCT to compress images, which has the property of energy concentration. The magnitude of QDCT represents the information strength, which means energy distribution features. The phases of QDCT depict the structure information, which means texture features. Therefore, the classification performance of magnitude features is better than that of phase features in CASIA TIDE v1.0. Meanwhile, the proposed scheme is based on QDCT, so the different formats of the images between two databases result in the second issue.

The distribution of 200 selected features are shown in Table 3. There are two conclusions can be drawn from Table 3. They are shown as follows:

Table 3. The weight ratio of four sets in 200 selected features

a) The ratio of magnitude features (Set1+Set3) to phases features (Set2+Set4) in CASIA TIDE v1.0 is near to 1:1 while the ratio in CASIA TIDE v2.0 is over 1:1.5. The phenomenon indicates that magnitude features are more suitable for detecting JEPG images than phase features.

b) From CASIA TIDE v1.0 to CASIA TIDE v2.0, the ratio of Set1 to Set2 is from over 1.5:1 to less than 1 and the ratio of Set3 to Set4 is from about 1:1 to less than 1:2. It manifests that with the amount of the formats increasing, the importance of phase features improves.

3.3. Impact of Different Thresholds on Accuracy

An issue about the threshold will be discussed in this subsection. In our experiments, there is a positive correlation between the computational work and the value of threshold. Therefore, the value of the threshold is limited. After threshold processing A or C, the value is limited from −T to T. After threshold processing B, the value is limited from 0 to T. For convenience, we set \(T_{1}=T_{2}=\frac{T_{3}}{2}=T_{4}\). If T is bigger than 4, it takes significantly bigger time, but accuracy dose not increase much. Therefore, T is set smaller than 5. According to Table 1 and Table 2, the feature dimensionality is set 200- D. The contrastive experiments with different thresholds in CASIA TIDE v2.0 have been done and the results are shown in Table 4. In Table 4, it is found that the accuracy of the proposed scheme reaches the highest when T equals 4. Therefore, the thresholds of four sets are set as 4, 4, 8, and 4.

To further prove the validity of selected thresholds, a set of experiments are conducted. 𝑇₁, 𝑇₂, \(\frac{T_{3}}{2}\) and 𝑇₄ change from 1 to 4. In order to show the trend of the accuracy, we only show Fig. 4, in which 𝑇₁ and 𝑇₂ are set as 4 and 4, respectively. It is easily judged in Fig. 5 that the selected thresholds are right.

Fig. 4. Samples of CASIA TIDE v2.0

Fig. 5. Experimental results of the classification accuracy with different thresholds of Set3 and Set4​​​​​​​

3.4. Comparison Experiment

In this subsection, the comparison results between the proposed scheme and the existing schemes will be shown.

In Table 5, the accuracy of the proposed scheme is 99.16% in CASIA TIDE v1.0 and 97.52% in CASIA TIDE v2.0. It exceeds the results of other methods in CASIA TIDE v1.0, and is slightly worse than that of [33] and exceeds that of [25], [29] and [31] in CASIA TIDE v2.0. In [31], a scheme based on the steerable pyramid transform and local binary pattern is proposed, which extracts features on single chrominance channel. It ignores the inherent relationships among three channels and so it is in [25] and [40]. Although in [29] QDCT is used, it only selects the magnitude to extract the classification features. This scheme utilizes the inherent relationship among three channels but it neglects the function of phases. From Section 4.2, it can been seen that the performance of phase is near to that of magnitude. Combination features of magnitude and phases possess more integral information of the whole image, so compared with other methods, the proposed scheme has the best performance.

Table 5. The comparison of the proposed scheme with the existing schemes​​​​​​​

4. Conclusion

In this paper, the correlation among three channels is effectively used. A novel quaternion Markov is proposed to extract classification features in QDCT domain, which consists of global quaternion Markov and local quaternion Markov. Pointing to the magnitude part and the phase part of the proposed quaternion Markov, three different methods are used to process the different arrays and obtain classification features. Meanwhile, in order to wipe off the redundant features, SVMRFE is used to improve the classifcation efficiency of SVM. The final experimental results show that the performance of the proposed scheme is the best compared to the existing schemes. In QDCT domain, strength information is more than texture information. To further obtain intact information of a color image, color quaternion wavelet transform (CQWT) will be used in future. How to extract the combination features in both QDCT and CQWT will be studied.