Animal fiber recognition based on feature fusion of the maximum inter-class variance

In this study, cashmere and wool fibers from northern China are used as raw materials for the experiment, and the experimental images obtained from cashmere and wool fibers by scanning electron microscope are used as the data set of this article. The cashmere and wool fiber images are 400 images each in this study, and the magnification is set to 1,000 times in the SEM, and the horizontal and vertical resolutions are set to 96 dpi, respectively. In Figure 2(a) and (b), microscopic images of cashmere and wool fibers magnified by scanning electron microscopy are shown, respectively. Image processing and feature extraction are implemented in Python. The data set is divided into two groups, one is used for the training set, as the cross-validation of the system, and the other is used as the test set to evaluate the final recognition effect.

Figure 2

In order to reduce the interference information and obtain the detailed information of the target fiber, the texture of the fiber image is first enhanced by the adaptive texture enhancement algorithm, and then these images are binarized by the Otsu threshold method [17]. This part mainly distinguishes the image background from the original fiber area, and then it fills the area of interest and removes noise. Then it calculates the angle that needs to be rotated after obtaining the center axis of the fiber to facilitate subsequent cropping operations. Finally, the fiber-filled image is used as a template, and the original image is cropped to obtain the target area for subsequent fiber feature extraction. This process is shown in Figure 3.

Figure 3

Wavelet transform is called image microscope in image processing. Its ability of the multi-scale decomposition can decompose and separate the image information layer by layer through low-pass and high-pass filters [18]. The Discrete Wavelet Transform of image is to use a series of wavelets with different scales to decompose the original image signal into multiple detail images and approximate images. In this article, the Haar wavelet is used to decompose the cashmere and wool fiber images. The Haar scale function is expressed by the following equation [19]: (1) ϕ ( x ) = 1 , for 0 ≤ x < 1 , 0 , otherwise . ϕ i j ( x ) = ϕ ( 2 j x − i ) , i = 0 , … , 2 j − 1 \phi (x)=\left\{\phantom{\rule[-1.25em]{}{0ex}}\begin{array}{ll}1,\hspace{1em}\text{for}\hspace{.25em}0\le x\lt 1,& \\ 0,\hspace{1em}\text{otherwise}.& \end{array}\right.\hspace{1em}{\phi }_{i}^{j}(x)=\phi ({2}^{j}x-i),\text{}i=0,\mathrm{..}.\hspace{-0.25em},\hspace{0.25em}{2}^{j}-1 The Haar wavelet function is expressed by the following equation: (2) ψ i j ( x ) = 1 , for 0 ≤ x < 1 2 , − 1 , for 1 2 ≤ x < 1 , 0 , otherwise . ψ i j ( x ) = ψ ( 2 j x − i ) , i = 0 , … , 2 j {\psi }_{i}^{j}(x)=\left\{\begin{array}{c}1,\hspace{1em}\text{for}\hspace{.25em}0\le x\lt \frac{1}{2},\\ -1,\hspace{0.25em}\text{for}\hspace{0.25em}\frac{1}{2}\le x\lt 1,\\ 0,\hspace{1em}\text{otherwise}\text{.}\end{array}\right.\hspace{1em}{\psi }_{i}^{j}(x)=\psi ({2}^{j}x-i),\text{}i=0,\mathrm{..}.\hspace{-0.25em},\hspace{0.25em}{2}^{j} The approximate and detail sub-images of the original cashmere and wool fiber images obtained by the Haar wavelet decomposition are shown in Figure 4.

Figure 4

In order to make full use of the image information in low-frequency and high-frequency domain, the Tamura texture feature is extracted through the detailed and approximate sub-images which are obtained after the wavelet decomposition [20], which will better characterize the difference of fiber scales. Constructing the texture feature vectors of cashmere and wool with the largest divisibility is based on the feature fusion using the maximum inter-class variance. Assuming that after the original image is subsampled, the feature vector of the approximate image is F LL = [ f LL 1 , f LL 2 , f LL 3 ] {F}_{\text{LL}}={[}{f}_{\text{LL}1},\hspace{.25em}{f}_{\text{LL}2},\hspace{.25em}{f}_{\text{LL}3}] . Suppose the feature vector is obtained by the sub-image on the horizontal detail, its formula is F LH = [ f LH 1 , f LH 2 , f LH 3 ] {F}_{\text{LH}}={[}{f}_{\text{LH}1},\hspace{.25em}{f}_{\text{LH}2},\hspace{.25em}{f}_{\text{LH}3}] . The eigenvector is represented by F HL = [ f HL 1 , f HL 2 , f HL 3 ] {F}_{\text{HL}}={[}{f}_{\text{HL}1},\hspace{.25em}{f}_{\text{HL}2},\hspace{.25em}{f}_{\text{HL}3}] , if it is acquired from the sub-image on the vertical detail. Assume that the eigenvector obtained from the sub-image on the diagonal detail is F HH = [ f HH 1 , f HH 2 , f HH 3 ] {F}_{\text{HH}}={[}{f}_{\text{HH}1},\hspace{.25em}{f}_{\text{HH}2},\hspace{.25em}{f}_{\text{HH}3}] . Because the features extracted from the decomposed sub-images are the surface roughness of fiber scales and contrast and linearity, these are used as feature descriptors for the original fibers. Therefore, the feature vectors with the maximum inter-class variance are obtained by linear fusion. By linearly adding features extracted from the four sub-images after introducing appropriate weights, we obtain the F with three-dimensional feature vectors, which can be expressed by the following equation: (3) F = a ⋅ F LL + b ⋅ F LH + c ⋅ F HL + d ⋅ F HH , F=a\cdot {F}_{\text{LL}}+b\cdot {F}_{\text{LH}}+c\cdot {F}_{\text{HL}}+d\cdot {F}_{\text{HH}}, where a + b + c + d = 1 a+b+c+d=1 , the first feature represents roughness, the second one means contrast, and the third is linearity in each feature vector.

For obtaining the optimal feature fusion coefficient, the metric is introduced to measure the contrast of inter-class variance and intra-class variance. Its representation is shown in the following equation: (4) λ = δ ex 2 δ in 2 , \lambda =\frac{{\delta }_{\text{ex}}^{2}}{{\delta }_{\text{in}}^{2}}, where δ in 2 {\delta }_{\text{in}}^{2} represents the intra-class variance of cashmere and wool fiber images calculated from the data of the experimental training set, and δ ex 2 {\delta }_{\text{ex}}^{2} represents the inter-class variance. Their expression formulas are as follows: (5) δ in 2 = 1 N 1 ∑ i = 1 N 1 ( x i − μ 1 ) 2 + 1 N 2 ∑ j = 1 N 2 ( x j − μ 2 ) 2 , {\delta }_{\text{in}}^{2}=\sqrt{\frac{1}{{N}_{1}}\mathop{\sum }\limits_{i=1}^{{N}_{1}}{({x}_{i}-{\mu }_{1})}^{2}+\frac{1}{{N}_{2}}\mathop{\sum }\limits_{j=1}^{{N}_{2}}{({x}_{j}-{\mu }_{2})}^{2}}, (6) δ ex 2 = 1 N 1 + N 2 ∑ l = 1 N 1 + N 2 ( x l − μ ) 2 , {\delta }_{\text{ex}}^{2}=\frac{1}{{N}_{1}+{N}_{2}}\mathop{\sum }\limits_{l=1}^{{N}_{1}+{N}_{2}}{({x}_{l}-\mu )}^{2}, where μ 1 {\mu }_{1} and μ 2 {\mu }_{2} are, respectively, the mean value of cashmere features and wool features in the training set, while μ \mu is the mean value of the whole sample. In addition, N 1 {N}_{1} represents the number of cashmere in the training set and N 2 {N}_{2} means the number of wool. x i {x}_{i} and x j {x}_{j} are the eigenvalue of cashmere and wool, respectively. When λ \lambda takes the maximum value, the feature vector with the maximum inter-class variance can be obtained to distinguish cashmere and wool. The experimental results show that at this time a = 0.3 , b = 0.1 , c = 0.2 , d = 0.4 . a=0.3,\hspace{.25em}b=0.1,\hspace{.25em}c=0.2,\hspace{.25em}d=0.4.

In the last step of the whole cashmere and wool recognition system, different classifiers are used to verify the fused feature performance for ten-fold cross-validation. These classifiers are K-nearest neighbors (KNN), support vector machine (SVM), and linear discriminant analysis (LDA) classifiers, respectively. KNN classifies the query points according to the similarity between the query points and their nearest K search points [21], SVM classifies the features by searching the optimal hyperplane in the space [22], and LDA classifies the features by obtaining the best projected line [23].