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## Classification algorithms

One strategy consists of using classification algorithms to label each pixel of the hyperspectral image. This technique requires to have a clear spectral definition of both the adulterant and the material. Vermeulen et al. [41] studied the adulteration of cereals by ergot bodies on a conveyer belt using a NIR HSI. The authors used Support vector Machine (SVM) and Partial Least Square Discriminant Analysis (PLSDA) to discriminate the spectra. As ergot bodies and cereals are larger than one pixel of the camera, each pixel likely contains either ergot or cereals but not both at the same time. Hence, there is no spectral mixing to consider in the pixel. In that case, Vermeulen et al. showed that the classification method is efficient for the detection.

**Spectral similarities**

Another method consists of using spectral similarity analysis to compare spectra from the hyperspectral image with a reference. Fu et al. used this method to detect melamine adulteration in milk powders down to a concentration of 0.02 % [10]. In this case, the particles of melamine and milk powders are smaller than the pixel meaning the spectral signal may be mixed in the pixels. For this reason, the authors used a threshold on the spectral similarity scores to identify pixels containing melamine. Huang et al. studied the same melamine and milk powder case [12]. They used the band ratio method that consists of analyzing the reflectance ratio of two wavelengths. As previously, the authors proposed a detection algorithm based on a threshold of the band ratio.

**Quantification methods**

A third method consists of the calibration of an algorithm that quantifies the adulterant proportion in each pixel. Lim et al. used a PLS regression to detect and quantify the melamine in milk powders [13]. As shown in the previous works, the melamine could be detected at 0.02 % global adulteration. The PLS regression coefficients show the same important wavelengths as the one selected by the band ratio method in [12]. Zhao et al. studied the adulteration of wheat flour by walnut and peanut flour using PLS model calibration [16]. The authors concluded that the model could detect adulteration over 1 % of global concentration. They noticed that the localization of peanut and walnut particles was impossible with this methodology because of two reasons: the particle size which is smaller than the pixel, and the similar trends of spectral curves among pure samples.

**The Multivariate Curve Resolution model**

For melamine detection in milk powders, the particle sizes are smaller than the standard pixel sizes in NIR HSI (0.2 ๏ด 0.2 mm) [2]. Huang et al. uses an unmixing approach to determine the concentration map of melamine and milk in mixed samples [11]. They compare the PCA, the Classical Least Squares (CLS) and the Multivariate Curve Resolution Alternative Least-Squares (MCR-ALS) approaches. The authors showed that the MCR-ALS approach provides the best quantitative results. This method is based on the following bilinear model: ๐= ๐๐๐+๐.

**The constraints of the Multivariate Curve Resolution model**

The non-negativity constraint imposes the concentration and/or spectral profiles only contain positive values. This constraint is relevant with NIR spectra because intensity, reflectance or, absorbance values should always be positive. The closure constraint imposes the sum of all contributions is equal to a constant (often 1), which implies interdependencies between the species contribution. This constraint can be seen as a type of normalization which affects the intensity ambiguity [46]. The knowledge of pure spectra or concentration profiles can be introduced as a constraint in the ALS procedure. It should be used when a profile is known.

Although many constraint methods were implemented in the MCR-ALS, it is still tricky to reduce the rotational ambiguity because it often requires a prior knowledge of the spectral profiles, which is not always possible. The consequence of a rotational ambiguity could be that the spectral signals are not well unmixed. It may lead to misleading conclusion, in particular for detection purposes. Many constraints have been developed and could be useful to reduce the rotational ambiguity. The correspondence of species can be applied in the case of a multiset analysis. In this situation, a column-wise augmented matrix is used to indicate which experiment contains or does not contain a specific component.

The matrix augmentation is not a constraint as such, but it enables to reduce the rotational ambiguity of the MCR solutions [47]. It enables to introduce several matrices that share one dimension. The augmented matrix strategy is a possible solution by stacking the unfolded matrices on top of each other: (๐ฟ๐๐ฟ๐๐ฟ๐)=(๐ช๐๐ช๐๐ช๐)๐บ๐ป+(๐ฌ๐๐ฌ๐๐ฌ๐)=๐ช๐๐๐๐บ๐ป+๐ฌ๐๐๐.

**Thickness target values**

The sample holder designed for the study is made such that the thickness of wheat flour varies. In the following, wheat flour thickness is referred as the ๐ target value. This thickness depends on the sample holder geometry. As a consequence, the ๐ target vector is constructed using the geometry of the central pit of the sample holder. Since it is designed as a slope between 0.05 cm and 0.35 cm, a linear interpolation vector was created and assigned to each of the 100-pixel lines across the sample holder. This procedure leads to a 2-dimensional mask that can be applied on the hyperspectral image (Figure 9). For spectral analysis, hyperspectral cubes are unfolded to obtain matrices of 24 600 lines and 256 columns. The 2-dimensional mask for ๐ values is unfolded in the same way so that each spectrum of the matrix is associated with the appropriate ๐ target.

### Partial Least-Squares Regression

The PLS regression is an algorithm used for predicting a target value ๐ using predictors ๐ with a linear relationship: ๐=๐๐ท+๐. PLS is a good alternative to classical Multiple Linear Regression (MLR) or Principal Component Regression (PCR) when predictors are NIR spectral data. For this kind of data, there are a great number of variables (several hundreds) that are mostly correlated to each other. As a consequence, the construction of orthogonal latent variables is required for applying multiple linear regression. PCA is one method used for constructing such variables that are orthogonal and ranked according to the amount of variance they represent in ๐. PCR is achieved by performing MLR on these new variables. However, PCR does not take into account the relationship with target values ๐ in the construction of the orthogonal latent variables. PLS solves this problem by constructing latent variables based on the covariance between ๐ and ๐ [20 – 21]. PLS has been widely used in chemometrics as it is particularly suitable for near infrared spectral data [61]. In this study, PLS is used in order to quantify the amount of PLA signal in the diffuse reflectance measurements. It is assumed that the signal of PLA is linked to the wheat flour thickness in the sample holder. As a consequence, the ๐ฒ thickness vector is used as target for the PLS calibration. The training was performed using cross-validation on the first sample replicate. 70% of the spectra from the cube were used for calibration and 30% for validation. This procedure was repeated 10 times to select the number of latent variables associated to the averaged minimum root mean square error of cross-validation (RMSECV).

#### Reflectance evolution for each wavelength

Figure 11 shows the reflectance spectral signatures of PLA and wheat flour. The spectrum of PLA exhibits high and resolute absorption peaks all along the near infrared range. The absorption peak at 1168 nm represents a high difference in reflectance between PLA and wheat flour. Figure 12 shows the reflectance profile at 1168 nm corresponding to this absorption peak. The experimental points exhibit a curve showing two behaviors. The first part of the curve corresponds to low thickness values and shows an increasing reflectance profile. The second part shows a stabilization of the reflectance level for high thickness values.

When the wheat flour thickness is low, the PLA plays an important role in the resulting diffuse reflectance signal. As it absorbs radiation around 1168 nm, the reflectance profile at this wavelength starts with low reflectance values. When the thickness increases, the role of wheat flour becomes more important than PLA in the resulting reflectance spectrum. Since wheat flour absorbs much less than PLA at 1168 nm, the reflectance level increases. This behavior can be interpreted using the theory of Kubelka-Munk presented in the next section.

**The Kubelka-Munk model**

The Kubelka-Munk model developed on a monochromatic case will be applied to the following one. It is assumed the results are applicable to every wavelength of the detector range between 1100 and 1350 nm. Let us consider a layer of wheat flour of thickness ๐ as shown in Figure 13. This case corresponds to a slice of the sample holder for a fixed thickness value. The surface of the sample holder is assumed to be wide enough so that the influence of borders can be neglected for the application of the Kubelka-Munk theory. The wheat flour is lying on a layer of PLA with a reflectance Rg. An infinitesimal layer of thickness dz is considered in the wheat flour at the height z. This layer is crossed by two fluxes: the descending flux i(z) and the ascending flux j(z). The wheat flour is assumed to be isotropic so that global absorption and scattering coefficients can be defined by K and S respectively. Taking into account the changes for both fluxes when crossing the layer of wheat flour leads to the following equations: โdi(z)= โKi(z)dzโSi(z)dz+Sj(z) dj(z)= โKi(z)dzโSi(z)dz+Si(z).

**Table of contents :**

**INTRODUCTION **

1. CONTEXT AND OBJECTIVES

2. STRUCTURE OF THE MANUSCRIPT

A. Main contributions

B. List of the published works

C. List of communications

3. THE INTEREST OF POWDER IN THE FOOD INDUSTRY

4. NEAR-INFRARED SPECTROSCOPY

5. NEAR-INFRARED HYPERSPECTRAL IMAGING

D. Physical contaminations

E. Defects

F. Microbiological contaminations

6. THE PENETRATION AND THE DETECTION DEPTH OF NIR RADIATIONS

A. The penetration depth

B. The detection depth

7. THE DETECTION OF SUBPIXEL FOOD PARTICLES

A. Classification algorithms

B. Spectral similarities

C. Quantification methods

D. Unmixing methods

E. Subspace detector

**I. THE DETECTION DEPTH OF A NEAR-INFRARED HYPERSPECTRAL IMAGING SYSTEM **

1. INTRODUCTION

2. MATERIAL AND METHODS

A. Samples

B. Hyperspectral imaging system

C. Data processing

D. Thickness target values

E. Reflectance profile extraction

F. Partial Least-Squares Regression

3. RESULTS AND DISCUSSIONS

A. Reflectance evolution for each wavelength

B. Physical interpretation

C. Determination of the penetration depth

D. Partial Least-Squares regression results

4. ADDITIONAL DISCUSSIONS

A. The detection depth versus the penetration depth

B. The effective detection depth

C. The consequences of the detection depth

D. The parameters influencing the detection depth

5. CONCLUSION AND PERSPECTIVES

**II. THE DETECTION OF PEANUT FLOUR USING THE MATCHED SUBSPACE DETECTOR **

1. INTRODUCTION

2. MATERIAL AND METHODS

A. Samples

B. Hyperspectral imaging system

C. Data processing

D. Spectral simulation using Principal Component Analysis

E. Detection using the Matched Subspace Detector

F. Software

3. RESULTS AND DISCUSSIONS

A. Evaluation of data simulation for the detector design

B. Evaluation of the Matched Subspace Detector Algorithm

4. CONCLUSIONS

**III. THE DETECTION OF PEANUT FLOUR IN CHOCOLATE POWDER USING MULTIVARIATE CURVE RESOLUTION **

1. INTRODUCTION

2. MATERIAL AND METHODS

A. Sample preparation

B. Hyperspectral imaging system

C. Data Processing

D. Hyperspectral cube unfolding

E. Multivariate Curve Resolution โ Alternating Least Squares

F. Detection algorithm

G. Software

3. RESULTS AND DISCUSSIONS

A. Principal Component Analysis

B. MCR-ALS

C. MCR-ALS-CSEL

D. The detection results

4. ADDITIONAL DISCUSSIONS

A. The pixel unmixing strategy

B. The detection sensitivity

C. The particle detection in hyperspectral images

5. CONCLUSION

**CONCLUSION AND FUTURE WORK **

1. CONCLUSION

2. FUTURE WORKS

APPENDICES

APPENDIX A: THE GAUSSIAN MIXTURE MODEL

APPENDIX B: THE MAHALANOBIS DISTANCE FOR OUTLIER DETECTION

**REFERENCESย **