## 3 Spectral Scattering Imaging
### Analysis of Scattering Images
#### 3.2.3 Feature Extraction  
Multispectral and hyperspectral images can be treated as a number of scattering profiles at different wavelengths or spectra at different spatial points. These scattering profiles or spectra can be directly used for model calibration for quality prediction. However, it is cumbersome and also prone to overfitting due to a large amount of spatial and spectral data involved for each sample, especially for hyperspectral scattering images. Effective extraction of the meaningful information is one of the major tasks in analysing scattering images to assess fruit quality attributes. Several methods have been proposed to perform feature extraction from scattering images. One of the methods is to extract features from a scattering profile to replace the whole scattering profile for subsequent data analysis. [PERSON] (2015) calculated two statistic features, mean and standard deviation (SD) of scattering profiles, thus reducing each scattering profile to two parameters. The method is fast and simple to use, but it may be inadequate for effectively characterizing scattering profiles. [PERSON] and [PERSON] and [PERSON] (2015) noted that the scattering profile could be represented by an appropriate mathematical function. Several distribution functions including exponential, Gaussian, Lorentzian and Gompertz, as summarized in Table 1, which are commonly used for describing light scattering in optics, can model scattering profiles [PERSON] and [PERSON] (2015); [PERSON] and [PERSON] (2015); [PERSON] (2015); [PERSON] and [PERSON] (2015). Parameters in these functions can be used as scattering features to characterize the scattering profiles and each scattering profile is thus reduced to two to four features, resulting in great reductions in the raw data volume. In addition to these distribution functions, a diffusion approximation model that describes the radiation transfer of light within biological tissues, can also be used to extract optical properties from a scattering profile, i.e., the absorption and scattering coefficients [PERSON] and [PERSON] (2015); [PERSON] (2015). Details about the diffusion model and optical properties are further discussed in Section 5. Another method is to apply image processing algorithms for feature extraction. [PERSON] et al. [PERSON] et al. (2015); [PERSON] and [PERSON] (2015) proposed a histogram representation technique which extracted the histogram of frequencies of pixels at different intensities from a scattering image for quality prediction. Estimation of the parameters for the mathematical functions or model-based methods requires non-linear iteration procedures, which are usually computationally intensive and also can result in large estimation errors if the initial guesses for the iteration parameters are not well chosen. [PERSON] et al. [PERSON] et al. (2015) proposed a simpler and faster non-iterative method for analysing hyperspectral images, based on extracting several shape features, including zero-order moment (ZOM) and first-order moment (FOM), from a scattering profile, and confirmed its effectiveness through multivariate calibration for firmness prediction of apples. For hyperspectral scattering images, in addition to extracting the features of scattering profiles, there is a need for further reduction of spectral information. Principal component analysis (PCA) and minimum noise fraction (MNF) are two commonly used methods to transform a high-dimension