Due to the environment factors (such as temperature, and humidity), the measured spectra may contain noise, baseline drift, wavelength drift and other measurement errors. To remove the useless information, the spectra are pretreated with multivariate scatter corrected (MSC) as follows

Step 1: Calculate the average spectra of the sample x̅(1× m) as

x̅=∑i=1nxin(1)

where n is the number of the samples and m is the number of the wavelengths.

Step 2: Do linear regression between each sample spectra x_i and average spectra x̅as

xi=ai+x̅bi(2)

where a_i, b_i are linear regression coefficients.

Step 3: Do multiple scattering correction for each sample spectra as

xi, MSC=xi-Iaibi(3)

where I∈ R^{n× 1} is unit vector.

The infrared spectra can reflect the vibration of the molecule. When different frequencies of infrared lights are projected to the molecule in proper order, the different absorption can be obtained. Let Z_i denotes the absorbance matrix of spectra as

Zi=[A1A2…Ai-1Ai]T(4)

where [A₁A₂ … A_i-1A_i] are the infrared light absorbance vector. The one-dimensional infrared spectra are obtained by plotting the absorbance T% versus frequency λ . To transform the one-dimensional spectrum into 2D spectral contour map, the absorbance matrix is multiplied by its transpose as

Zii=ZiZiT=A12A2A1…AiA1A1A2A22…AiA2……⋱…A1AiA2Ai…Ai2(5)

The different correlation coefficient values are represented with different color.

Image recognition is a technology to identify a variety of different patterns in the field of computer application, which uses computer to process and analyze the image. Generally, the system of image recognition mainly includes the information acquisition of image, preprocessing of image, feature extraction and classification ^[12]. In this work, the local extrema of image are extracted as classification features and the BP neural network is applied as the classifier. The procedure of molecular spectra analysis based on image recognition is illustrated in Fig.1.

Fig.1

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	Fig.1 The procedure of molecular spectra analysis based on image recognition

Feature extraction is a very important step in the procedure of image recognition. The extracted features need to be stable and can represent the typical characteristics to ensure the accuracy of the classification. The features for image recognition include color feature, edge feature, shape feature and local extrema feature. The local extrema feature is usually not affected by the disturbance of external environment. In this work, the local extrema feature is chosen as the classification feature for edible oils.

The local extrema are extracted by the image dilation with the two dimensional data. The image dilation is an image processing method based on the dilation element operator in mathematical morphology. In the image dilation, target image X and structural elements S are looked as two sets of pixels, move structure element S from the origin to S_xy, if S_xy hit or is included in X, then form the coordinates of the dilation set as

X⊕S={(x, y)|Sxy↑X}(6)

where x, y are the horizontal and vertical coordinate respectively of the structural elements moved to.

Comparing the original data and image dilation, only a relatively large value can overlap with the result after the dilation. According to this principle, the local extremacan be extracted. In this work, the classifier of back propagation (BP) neural network is designed based on the supervised learning.

72 edible oil samples are provided by the National Institute of Metrology (NIM) of China. They belong to nine types of edible oil of sesame, corn, canola, blend, sunflower, peanut and olive. 54 samples are chosen as calibration set and the remaining 18 samples are chosen as the validation set. The number of calibration set and validation set for eachtypes of samples is shown in Table 1.

Table 1

Table 1

Table 1 Statistics of samples Name No. Total sample number Samples in calibration set Samples in validation set Sesame oil 1 15 12 3 Corn oil 2 4 3 1 Canola oil 3 8 5 3 Blend oil 4 10 8 2 Sunflower oil 5 7 5 2 Peanut oil 6 12 9 3 Olive oil 7 16 12 4 Total 7 72 54 18

Table 1 Statistics of samples

In this work, the infrared spectra of the samples are scanned by Attenuated Totalinternal Reflectance Fourier Transform Infrared (ATR-FTIR) spectrometer. The samples of edible oil and spectrometer are shown in Fig.2. The spectra are collected from 650 to 4 000 cm^-1 with a resolution 4 cm^-1 and with 10 scans. Each sample is scanned three times and the average is used for analysis. The spectra of all samples measured on ATR instrument are shown in Fig.3.

Fig.2

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	Fig.2 ATR spectrometer and edible oil samples

Fig.3

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	Fig.3 The spectra of all samples measured on ATR spectrometer

2D spectra contour map is used to generate the spectra image based on autocorrelation analysis. The spectra of two samples belong to sesame oil and blend oil respectively are shown in Fig.4. The shapes of spectra of edible oils are almost the same in Fig.4. The spectra from 558 to 598 cm^-1 are processed into a spectral image by the visualization method. The spectral images of two kind edible oil are shown in Fig.5. Obviously, the spectral difference after visualization becomes apparent and it is easier to classify the visualized spectra of edible oils.

Fig.4

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	Fig.4 The IR spectra of sesame and blend oil

Fig.5

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	Fig.5 The IR spectral images of sesame (a) and blend oil (b)

The characteristic absorption band in IR is caused by vibration of molecular groups and appears as the local extrema, which can be extracted by the image dilation in the visualized spectra image. Choose the local extrema of the spectra image and then observe the distribution of the extrema. The distribution of the first extreme is more representative, as shown in Fig.6.

Fig.6

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	Fig.6 The distribution of the first extreme (four kinds of edible oil)

In this work, BP neural network with supervised learning is applied to classify the local extrema in the spectra image of edible oil, and the minimum training rate of the BP neural network is 0.1, and the error is 0.01, and the number of iterations is 800, and the training process is shown in Fig.7, and the BP classification model is established.

Fig.7

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	Fig.7 The trainingstate of BP neural network

18 validation samples are predicted by the established BP classification model, and the results are shown in Fig.8 and the accuracy are shown in Table 2.

Fig.8

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	Fig.8 The prediction results of with the trained BP classification model

Table 2

Table 2

Table 2 Classification results based on molecular spectra image recognition Method Sample number Correct classification Error classification Accuracy /% Spectra image recognition 18 17 1 94.4

Table 2 Classification results based on molecular spectra image recognition

PCA is applied to analyze the calibration set of edible oil. The principle component number is chosen as 3 and the first three principal components score graphic of IR spectra is shown in Fig.9. From Fig.9, it can be seen that the projections of the IR spectra overlap on the principal component subspaces, therefore it is difficult to classify them directly.

Fig.9

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	Fig.9 Spatial distribution of IR spectra PCA for different edible oils

Let the IR spectra data compressed by PCA and KL decomposition as the input of the neural networks to establish the classifiers of PCA-BP and KL-BP. The classification results are shown in Table 3. Since IR spectra projections of edible oils overlap on the principal component subspaces, and the nonlinear classifiers such as the neural networks are needed to classify them.

Table 3

Table 3

Table 3 Classification results of PCA, PCA-BP and KL-BP Methods Sample number Correct classification Error classification Accuracy /% PCA 18 11 8 61.1 PCA-BP 18 12 6 66.7 KL-BP 18 15 3 83.3

Table 3 Classification results of PCA, PCA-BP and KL-BP